TSTP Solution File: RNG108+4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG108+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n026.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  : 600s
% DateTime : Mon Jul 18 20:34:28 EDT 2022

% Result   : Theorem 1.44s 1.66s
% Output   : CNFRefutation 6.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :   79
% Syntax   : Number of formulae    : 3249 (1501 unt;  45 typ;   0 def)
%            Number of atoms       : 35758 (12370 equ;   0 cnn)
%            Maximal formula atoms :   23 (  11 avg)
%            Number of connectives : 82060 (22460   ~;16906   |; 488   &;42120   @)
%                                         (   6 <=>;  80  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   58 (  58   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  45 usr;  10 con; 0-4 aty)
%            Number of variables   : 8253 (   0   ^8209   !;  44   ?;8253   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_aDivisorOf0,type,
    aDivisorOf0: $i > $i > $o ).

thf(tp_aElement0,type,
    aElement0: $i > $o ).

thf(tp_aElementOf0,type,
    aElementOf0: $i > $i > $o ).

thf(tp_aGcdOfAnd0,type,
    aGcdOfAnd0: $i > $i > $i > $o ).

thf(tp_aIdeal0,type,
    aIdeal0: $i > $o ).

thf(tp_aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

thf(tp_aSet0,type,
    aSet0: $i > $o ).

thf(tp_doDivides0,type,
    doDivides0: $i > $i > $o ).

thf(tp_iLess0,type,
    iLess0: $i > $i > $o ).

thf(tp_misRelativelyPrime0,type,
    misRelativelyPrime0: $i > $i > $o ).

thf(tp_sK10_SY73,type,
    sK10_SY73: $i > $i ).

thf(tp_sK11_W0,type,
    sK11_W0: $i ).

thf(tp_sK12_W0,type,
    sK12_W0: $i ).

thf(tp_sK13_W1,type,
    sK13_W1: $i > $i ).

thf(tp_sK14_W1,type,
    sK14_W1: $i > $i ).

thf(tp_sK15_W1,type,
    sK15_W1: $i > $i ).

thf(tp_sK16_W1,type,
    sK16_W1: $i > $i ).

thf(tp_sK17_W1,type,
    sK17_W1: $i > $i ).

thf(tp_sK18_W1,type,
    sK18_W1: $i > $i ).

thf(tp_sK19_W1,type,
    sK19_W1: $i > $i ).

thf(tp_sK1_W2,type,
    sK1_W2: $i > $i > $i ).

thf(tp_sK20_W1,type,
    sK20_W1: $i > $i ).

thf(tp_sK21_W1,type,
    sK21_W1: $i > $i ).

thf(tp_sK2_SY72,type,
    sK2_SY72: $i > $i > $i ).

thf(tp_sK3_W4,type,
    sK3_W4: $i > $i > $i > $i > $i ).

thf(tp_sK4_W2,type,
    sK4_W2: $i > $i > $i ).

thf(tp_sK5_W2,type,
    sK5_W2: $i > $i > $i ).

thf(tp_sK6_W2,type,
    sK6_W2: $i > $i > $i ).

thf(tp_sK7_W1,type,
    sK7_W1: $i > $i ).

thf(tp_sK8_W1,type,
    sK8_W1: $i > $i ).

thf(tp_sK9_W1,type,
    sK9_W1: $i > $i ).

thf(tp_sbrdtbr0,type,
    sbrdtbr0: $i > $i ).

thf(tp_sdtasasdt0,type,
    sdtasasdt0: $i > $i > $i ).

thf(tp_sdtasdt0,type,
    sdtasdt0: $i > $i > $i ).

thf(tp_sdteqdtlpzmzozddtrp0,type,
    sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).

thf(tp_sdtpldt0,type,
    sdtpldt0: $i > $i > $i ).

thf(tp_sdtpldt1,type,
    sdtpldt1: $i > $i > $i ).

thf(tp_slsdtgt0,type,
    slsdtgt0: $i > $i ).

thf(tp_smndt0,type,
    smndt0: $i > $i ).

thf(tp_sz00,type,
    sz00: $i ).

thf(tp_sz10,type,
    sz10: $i ).

thf(tp_xI,type,
    xI: $i ).

thf(tp_xa,type,
    xa: $i ).

thf(tp_xb,type,
    xb: $i ).

thf(tp_xc,type,
    xc: $i ).

thf(1,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrIdeal) ).

thf(2,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( W1 != sz00 ) )
     => ? [W2: $i,W3: $i] :
          ( ( aElement0 @ W2 )
          & ( aElement0 @ W3 )
          & ( W0
            = ( sdtpldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W3 ) )
          & ( ( W3 != sz00 )
           => ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).

thf(3,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( iLess0 @ W0 @ W1 )
       => $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatLess) ).

thf(4,axiom,
    ! [W0: $i] :
      ( ( ( aElement0 @ W0 )
        & ( W0 != sz00 ) )
     => ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEucSort) ).

thf(5,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).

thf(6,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aIdeal0 @ W0 )
        & ( aIdeal0 @ W1 ) )
     => ( ! [W2: $i] :
            ( ( aElement0 @ W2 )
           => ( aElementOf0 @ W2 @ ( sdtpldt1 @ W0 @ W1 ) ) )
       => ! [W2: $i,W3: $i] :
            ( ( ( aElement0 @ W2 )
              & ( aElement0 @ W3 ) )
           => ? [W4: $i] :
                ( ( aElement0 @ W4 )
                & ( sdteqdtlpzmzozddtrp0 @ W4 @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ W4 @ W3 @ W1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mChineseRemainder) ).

thf(7,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aIdeal0 @ W0 )
        & ( aIdeal0 @ W1 ) )
     => ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeInt) ).

thf(8,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aIdeal0 @ W0 )
        & ( aIdeal0 @ W1 ) )
     => ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIdeSum) ).

thf(9,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aSet0 @ W0 )
        & ( aSet0 @ W1 ) )
     => ( ( ! [W2: $i] :
              ( ( aElementOf0 @ W2 @ W0 )
             => ( aElementOf0 @ W2 @ W1 ) )
          & ! [W2: $i] :
              ( ( aElementOf0 @ W2 @ W1 )
             => ( aElementOf0 @ W2 @ W0 ) ) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).

thf(10,axiom,
    ! [W0: $i] :
      ( ( aSet0 @ W0 )
     => ! [W1: $i] :
          ( ( aElementOf0 @ W1 @ W0 )
         => ( aElement0 @ W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

thf(11,axiom,
    ! [W0: $i] :
      ( ( aSet0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).

thf(12,axiom,
    sz10 != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).

thf(13,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( ( ( sdtasdt0 @ W0 @ W1 )
          = sz00 )
       => ( ( W0 = sz00 )
          | ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).

thf(14,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtasdt0 @ W0 @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ W0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

thf(15,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
          = ( smndt0 @ W0 ) )
        & ( ( smndt0 @ W0 )
          = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).

thf(16,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
          = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).

thf(17,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtasdt0 @ W0 @ sz10 )
          = W0 )
        & ( W0
          = ( sdtasdt0 @ sz10 @ W0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).

thf(18,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
        = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

thf(19,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( ( sdtasdt0 @ W0 @ W1 )
        = ( sdtasdt0 @ W1 @ W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

thf(20,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
          = sz00 )
        & ( sz00
          = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

thf(21,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ sz00 )
          = W0 )
        & ( W0
          = ( sdtpldt0 @ sz00 @ W0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

thf(22,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 )
        & ( aElement0 @ W2 ) )
     => ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
        = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

thf(23,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( ( sdtpldt0 @ W0 @ W1 )
        = ( sdtpldt0 @ W1 @ W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

thf(24,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

thf(25,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aElement0 @ W0 )
        & ( aElement0 @ W1 ) )
     => ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

thf(26,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => ( aElement0 @ ( smndt0 @ W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).

thf(27,axiom,
    aElement0 @ sz10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

thf(28,axiom,
    aElement0 @ sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

thf(29,axiom,
    ! [W0: $i] :
      ( ( aElement0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).

thf(30,axiom,
    ( ( aSet0 @ xI )
    & ! [W0: $i] :
        ( ( aElementOf0 @ W0 @ xI )
       => ( ! [W1: $i] :
              ( ( aElementOf0 @ W1 @ xI )
             => ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
          & ! [W1: $i] :
              ( ( aElement0 @ W1 )
             => ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
    & ( aIdeal0 @ xI )
    & ! [W0: $i] :
        ( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
      <=> ? [W1: $i] :
            ( ( aElement0 @ W1 )
            & ( ( sdtasdt0 @ xa @ W1 )
              = W0 ) ) )
    & ! [W0: $i] :
        ( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
      <=> ? [W1: $i] :
            ( ( aElement0 @ W1 )
            & ( ( sdtasdt0 @ xb @ W1 )
              = W0 ) ) )
    & ! [W0: $i] :
        ( ( aElementOf0 @ W0 @ xI )
      <=> ? [W1: $i,W2: $i] :
            ( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ W1 @ W2 )
              = W0 ) ) )
    & ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

thf(31,axiom,
    ( ( aElement0 @ xc )
    & ? [W0: $i] :
        ( ( aElement0 @ W0 )
        & ( ( sdtasdt0 @ xc @ W0 )
          = xa ) )
    & ( doDivides0 @ xc @ xa )
    & ( aDivisorOf0 @ xc @ xa )
    & ( aElement0 @ xc )
    & ? [W0: $i] :
        ( ( aElement0 @ W0 )
        & ( ( sdtasdt0 @ xc @ W0 )
          = xb ) )
    & ( doDivides0 @ xc @ xb )
    & ( aDivisorOf0 @ xc @ xb )
    & ! [W0: $i] :
        ( ( ( ( ( aElement0 @ W0 )
              & ( ? [W1: $i] :
                    ( ( aElement0 @ W1 )
                    & ( ( sdtasdt0 @ W0 @ W1 )
                      = xa ) )
                | ( doDivides0 @ W0 @ xa ) ) )
            | ( aDivisorOf0 @ W0 @ xa ) )
          & ( ? [W1: $i] :
                ( ( aElement0 @ W1 )
                & ( ( sdtasdt0 @ W0 @ W1 )
                  = xb ) )
            | ( doDivides0 @ W0 @ xb )
            | ( aDivisorOf0 @ W0 @ xb ) ) )
       => ( ? [W1: $i] :
              ( ( aElement0 @ W1 )
              & ( ( sdtasdt0 @ W0 @ W1 )
                = xc ) )
          & ( doDivides0 @ W0 @ xc ) ) )
    & ( aGcdOfAnd0 @ xc @ xa @ xb ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2129) ).

thf(32,axiom,
    ( ( xa != sz00 )
    | ( xb != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).

thf(33,axiom,
    ( ( aElement0 @ xa )
    & ( aElement0 @ xb ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

thf(34,conjecture,
    ( ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xa @ W0 )
            = sz00 ) )
      | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    & ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xa @ W0 )
            = xa ) )
      | ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    & ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xb @ W0 )
            = sz00 ) )
      | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    & ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xb @ W0 )
            = xb ) )
      | ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(35,negated_conjecture,
    ( ( ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xa @ W0 )
              = sz00 ) )
        | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xa @ W0 )
              = xa ) )
        | ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xb @ W0 )
              = sz00 ) )
        | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xb @ W0 )
              = xb ) )
        | ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[34]) ).

thf(36,plain,
    ( ( ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xa @ W0 )
              = sz00 ) )
        | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xa @ W0 )
              = xa ) )
        | ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xb @ W0 )
              = sz00 ) )
        | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
      & ( ? [W0: $i] :
            ( ( aElement0 @ W0 )
            & ( ( sdtasdt0 @ xb @ W0 )
              = xb ) )
        | ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(37,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(38,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 )
            & ( W1 != sz00 ) )
         => ? [W2: $i,W3: $i] :
              ( ( aElement0 @ W2 )
              & ( aElement0 @ W3 )
              & ( W0
                = ( sdtpldt0 @ ( sdtasdt0 @ W2 @ W1 ) @ W3 ) )
              & ( ( W3 != sz00 )
               => ( iLess0 @ ( sbrdtbr0 @ W3 ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(39,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aNaturalNumber0 @ W0 )
            & ( aNaturalNumber0 @ W1 ) )
         => ( ( iLess0 @ W0 @ W1 )
           => $true ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(40,plain,
    ( ( ! [W0: $i] :
          ( ( ( aElement0 @ W0 )
            & ( W0 != sz00 ) )
         => ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(41,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(42,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aIdeal0 @ W0 )
            & ( aIdeal0 @ W1 ) )
         => ( ! [W2: $i] :
                ( ( aElement0 @ W2 )
               => ( aElementOf0 @ W2 @ ( sdtpldt1 @ W0 @ W1 ) ) )
           => ! [W2: $i,W3: $i] :
                ( ( ( aElement0 @ W2 )
                  & ( aElement0 @ W3 ) )
               => ? [W4: $i] :
                    ( ( aElement0 @ W4 )
                    & ( sdteqdtlpzmzozddtrp0 @ W4 @ W2 @ W0 )
                    & ( sdteqdtlpzmzozddtrp0 @ W4 @ W3 @ W1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(43,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aIdeal0 @ W0 )
            & ( aIdeal0 @ W1 ) )
         => ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(44,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aIdeal0 @ W0 )
            & ( aIdeal0 @ W1 ) )
         => ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(45,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aSet0 @ W0 )
            & ( aSet0 @ W1 ) )
         => ( ( ! [W2: $i] :
                  ( ( aElementOf0 @ W2 @ W0 )
                 => ( aElementOf0 @ W2 @ W1 ) )
              & ! [W2: $i] :
                  ( ( aElementOf0 @ W2 @ W1 )
                 => ( aElementOf0 @ W2 @ W0 ) ) )
           => ( W0 = W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(46,plain,
    ( ( ! [W0: $i] :
          ( ( aSet0 @ W0 )
         => ! [W1: $i] :
              ( ( aElementOf0 @ W1 @ W0 )
             => ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(47,plain,
    ( ( ! [W0: $i] :
          ( ( aSet0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(48,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(49,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 ) )
         => ( ( ( sdtasdt0 @ W0 @ W1 )
              = sz00 )
           => ( ( W0 = sz00 )
              | ( W1 = sz00 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(50,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( ( ( sdtasdt0 @ W0 @ sz00 )
              = sz00 )
            & ( sz00
              = ( sdtasdt0 @ sz00 @ W0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(51,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
              = ( smndt0 @ W0 ) )
            & ( ( smndt0 @ W0 )
              = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(52,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 )
            & ( aElement0 @ W2 ) )
         => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
            & ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
              = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(53,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( ( ( sdtasdt0 @ W0 @ sz10 )
              = W0 )
            & ( W0
              = ( sdtasdt0 @ sz10 @ W0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(54,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 )
            & ( aElement0 @ W2 ) )
         => ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(55,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 ) )
         => ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(56,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
              = sz00 )
            & ( sz00
              = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(57,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( ( ( sdtpldt0 @ W0 @ sz00 )
              = W0 )
            & ( W0
              = ( sdtpldt0 @ sz00 @ W0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(58,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 )
            & ( aElement0 @ W2 ) )
         => ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(59,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 ) )
         => ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(60,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 ) )
         => ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(61,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aElement0 @ W0 )
            & ( aElement0 @ W1 ) )
         => ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(62,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(63,plain,
    ( ( aElement0 @ sz10 )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(64,plain,
    ( ( aElement0 @ sz00 )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(65,plain,
    ( ( ! [W0: $i] :
          ( ( aElement0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(66,plain,
    ( ( ( aSet0 @ xI )
      & ! [W0: $i] :
          ( ( aElementOf0 @ W0 @ xI )
         => ( ! [W1: $i] :
                ( ( aElementOf0 @ W1 @ xI )
               => ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) )
            & ! [W1: $i] :
                ( ( aElement0 @ W1 )
               => ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) ) )
      & ( aIdeal0 @ xI )
      & ! [W0: $i] :
          ( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
        <=> ? [W1: $i] :
              ( ( aElement0 @ W1 )
              & ( ( sdtasdt0 @ xa @ W1 )
                = W0 ) ) )
      & ! [W0: $i] :
          ( ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
        <=> ? [W1: $i] :
              ( ( aElement0 @ W1 )
              & ( ( sdtasdt0 @ xb @ W1 )
                = W0 ) ) )
      & ! [W0: $i] :
          ( ( aElementOf0 @ W0 @ xI )
        <=> ? [W1: $i,W2: $i] :
              ( ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              & ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              & ( ( sdtpldt0 @ W1 @ W2 )
                = W0 ) ) )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(67,plain,
    ( ( ( aElement0 @ xc )
      & ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xc @ W0 )
            = xa ) )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xc @ W0 )
            = xb ) )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ! [W0: $i] :
          ( ( ( ( ( aElement0 @ W0 )
                & ( ? [W1: $i] :
                      ( ( aElement0 @ W1 )
                      & ( ( sdtasdt0 @ W0 @ W1 )
                        = xa ) )
                  | ( doDivides0 @ W0 @ xa ) ) )
              | ( aDivisorOf0 @ W0 @ xa ) )
            & ( ? [W1: $i] :
                  ( ( aElement0 @ W1 )
                  & ( ( sdtasdt0 @ W0 @ W1 )
                    = xb ) )
              | ( doDivides0 @ W0 @ xb )
              | ( aDivisorOf0 @ W0 @ xb ) ) )
         => ( ? [W1: $i] :
                ( ( aElement0 @ W1 )
                & ( ( sdtasdt0 @ W0 @ W1 )
                  = xc ) )
            & ( doDivides0 @ W0 @ xc ) ) )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(68,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(69,plain,
    ( ( ( aElement0 @ xa )
      & ( aElement0 @ xb ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(70,plain,
    ( ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xa @ W0 )
            = sz00 ) )
      | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[36]) ).

thf(71,plain,
    ( ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xa @ W0 )
            = xa ) )
      | ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[36]) ).

thf(72,plain,
    ( ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xb @ W0 )
            = sz00 ) )
      | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[36]) ).

thf(73,plain,
    ( ( ? [W0: $i] :
          ( ( aElement0 @ W0 )
          & ( ( sdtasdt0 @ xb @ W0 )
            = xb ) )
      | ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[36]) ).

thf(74,plain,
    ( ( ~ ( ? [W0: $i] :
              ( ( aElement0 @ W0 )
              & ( ( sdtasdt0 @ xa @ W0 )
                = sz00 ) )
          | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[70]) ).

thf(75,plain,
    ( ( ~ ( ? [W0: $i] :
              ( ( aElement0 @ W0 )
              & ( ( sdtasdt0 @ xa @ W0 )
                = xa ) )
          | ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[71]) ).

thf(76,plain,
    ( ( ~ ( ? [W0: $i] :
              ( ( aElement0 @ W0 )
              & ( ( sdtasdt0 @ xb @ W0 )
                = sz00 ) )
          | ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[72]) ).

thf(77,plain,
    ( ( ~ ( ? [W0: $i] :
              ( ( aElement0 @ W0 )
              & ( ( sdtasdt0 @ xb @ W0 )
                = xb ) )
          | ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[73]) ).

thf(78,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xa @ W0 )
           != sz00 )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[74]) ).

thf(79,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xa @ W0 )
           != xa )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[75]) ).

thf(80,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xb @ W0 )
           != sz00 )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[76]) ).

thf(81,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xb @ W0 )
           != xb )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[77]) ).

thf(82,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(83,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( W1 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( aElement0 @ ( sK1_W2 @ W1 @ W0 ) )
            & ( aElement0 @ ( sK2_SY72 @ W1 @ W0 ) )
            & ( W0
              = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 ) @ ( sK2_SY72 @ W1 @ W0 ) ) )
            & ( ( ( sK2_SY72 @ W1 @ W0 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ W1 @ W0 ) ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(84,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[39]) ).

thf(85,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(86,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(87,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( ( aElement0 @ ( sK4_W2 @ W1 @ W0 ) )
            & ~ ( aElementOf0 @ ( sK4_W2 @ W1 @ W0 ) @ ( sdtpldt1 @ W0 @ W1 ) ) )
          | ! [W2: $i,W3: $i] :
              ( ~ ( aElement0 @ W2 )
              | ~ ( aElement0 @ W3 )
              | ( ( aElement0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W3 @ W1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(88,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(89,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[44]) ).

thf(90,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aSet0 @ W0 )
          | ~ ( aSet0 @ W1 )
          | ( ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W0 )
            & ~ ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W1 ) )
          | ( ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W1 )
            & ~ ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W0 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[45]) ).

thf(91,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aSet0 @ W0 )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ W0 )
              | ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(92,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(93,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(94,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
           != sz00 )
          | ( W0 = sz00 )
          | ( W1 = sz00 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[49]) ).

thf(95,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz00 )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(96,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
            = ( smndt0 @ W0 ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( smndt0 @ W0 )
            = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[51]) ).

thf(97,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(98,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz10 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtasdt0 @ sz10 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[53]) ).

thf(99,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[54]) ).

thf(100,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[55]) ).

thf(101,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[56]) ).

thf(102,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtpldt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[57]) ).

thf(103,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[58]) ).

thf(104,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[59]) ).

thf(105,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[60]) ).

thf(106,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[61]) ).

thf(107,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[62]) ).

thf(108,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[65]) ).

thf(109,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ W1 @ W2 )
               != W0 ) )
          | ( aElementOf0 @ W0 @ xI ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ( ( aElementOf0 @ ( sK9_W1 @ W0 ) @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ ( sK10_SY73 @ W0 ) @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ ( sK9_W1 @ W0 ) @ ( sK10_SY73 @ W0 ) )
              = W0 ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xb @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
          | ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK8_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xa @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
          | ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK7_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElement0 @ W1 )
              | ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
      & ( aSet0 @ xI )
      & ( aIdeal0 @ xI )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[66]) ).

thf(110,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK21_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK21_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK20_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK20_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK19_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK19_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK18_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK18_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK17_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK17_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK16_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK16_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK15_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK15_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK14_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK14_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK13_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK13_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ( ( sdtasdt0 @ xc @ sK12_W0 )
        = xa )
      & ( aElement0 @ sK12_W0 )
      & ( aElement0 @ xc )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ( ( sdtasdt0 @ xc @ sK11_W0 )
        = xb )
      & ( aElement0 @ sK11_W0 )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[67]) ).

thf(111,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[68]) ).

thf(112,plain,
    ( ( ( aElement0 @ xa )
      & ( aElement0 @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(113,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(114,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK21_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK21_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK20_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK20_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK19_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK19_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK18_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK18_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK17_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK17_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK16_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK16_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK15_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK15_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK14_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK14_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK13_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK13_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ( ( sdtasdt0 @ xc @ sK12_W0 )
        = xa )
      & ( aElement0 @ sK12_W0 )
      & ( aElement0 @ xc )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ( ( sdtasdt0 @ xc @ sK11_W0 )
        = xb )
      & ( aElement0 @ sK11_W0 )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(115,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ W1 @ W2 )
               != W0 ) )
          | ( aElementOf0 @ W0 @ xI ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ( ( aElementOf0 @ ( sK9_W1 @ W0 ) @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ ( sK10_SY73 @ W0 ) @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ ( sK9_W1 @ W0 ) @ ( sK10_SY73 @ W0 ) )
              = W0 ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xb @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
          | ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK8_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xa @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
          | ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK7_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElement0 @ W1 )
              | ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
      & ( aSet0 @ xI )
      & ( aIdeal0 @ xI )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(116,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(117,plain,
    ( ( aElement0 @ sz00 )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(118,plain,
    ( ( aElement0 @ sz10 )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(119,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(120,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(121,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(122,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(123,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(124,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtpldt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(125,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(126,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(127,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(128,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz10 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtasdt0 @ sz10 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(129,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(130,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
            = ( smndt0 @ W0 ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( smndt0 @ W0 )
            = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(131,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz00 )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(132,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
           != sz00 )
          | ( W0 = sz00 )
          | ( W1 = sz00 ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(133,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(134,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(135,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aSet0 @ W0 )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ W0 )
              | ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(136,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aSet0 @ W0 )
          | ~ ( aSet0 @ W1 )
          | ( ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W0 )
            & ~ ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W1 ) )
          | ( ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W1 )
            & ~ ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W0 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(137,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(138,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(139,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( ( aElement0 @ ( sK4_W2 @ W1 @ W0 ) )
            & ~ ( aElementOf0 @ ( sK4_W2 @ W1 @ W0 ) @ ( sdtpldt1 @ W0 @ W1 ) ) )
          | ! [W2: $i,W3: $i] :
              ( ~ ( aElement0 @ W2 )
              | ~ ( aElement0 @ W3 )
              | ( ( aElement0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W3 @ W1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(140,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(141,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(142,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(143,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( W1 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( aElement0 @ ( sK1_W2 @ W1 @ W0 ) )
            & ( aElement0 @ ( sK2_SY72 @ W1 @ W0 ) )
            & ( W0
              = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 ) @ ( sK2_SY72 @ W1 @ W0 ) ) )
            & ( ( ( sK2_SY72 @ W1 @ W0 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ W1 @ W0 ) ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(144,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(145,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xa @ W0 )
           != sz00 )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(146,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i,SX2: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                                | ( ( sdtpldt0 @ SX1 @ SX2 )
                                 != SX0 ) )
                            | ( aElementOf0 @ SX0 @ xI ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                                 != SX0 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xb @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ xa @ SX1 )
                                             != SX0 )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                             != SX0 )
                                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElement0 @ SX1 )
                                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                        | ~ ( aSet0 @ xI ) )
                                  | ~ ( aIdeal0 @ xI ) ) ) ) )
          | ( xI
           != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[115]) ).

thf(147,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                                 != xa )
                                                                | ~ ( aElement0 @ sK12_W0 ) )
                                                          | ~ ( aElement0 @ xc ) )
                                                    | ~ ( doDivides0 @ xc @ xa ) )
                                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                         != xb )
                                        | ~ ( aElement0 @ sK11_W0 ) ) )
                            | ~ ( doDivides0 @ xc @ xb ) )
                      | ~ ( aDivisorOf0 @ xc @ xb ) ) )
          | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[114]) ).

thf(148,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aIdeal0 @ SX0 )
          | ~ ( aIdeal0 @ SX1 )
          | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SX1 @ SX0 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SX1 @ SX0 ) @ ( sdtpldt1 @ SX0 @ SX1 ) ) )
          | ! [SX2: $i,SX3: $i] :
              ( ~ ( aElement0 @ SX2 )
              | ~ ( aElement0 @ SX3 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[139]) ).

thf(149,plain,
    ( ( ~ ( ~ ( aElement0 @ xa )
          | ~ ( aElement0 @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[112]) ).

thf(150,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz10 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[128]) ).

thf(151,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
                  = ( smndt0 @ SX0 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( smndt0 @ SX0 )
                  = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[130]) ).

thf(152,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[129]) ).

thf(153,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aSet0 @ SX0 )
          | ~ ( aSet0 @ SX1 )
          | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[136]) ).

thf(154,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 = sz00 )
          | ~ ( aElement0 @ SX0 )
          | ~ ( aElement0 @ SX1 )
          | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SX1 @ SX0 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) )
                    | ( SX0
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 ) @ ( sK2_SY72 @ SX1 @ SX0 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SX1 @ SX0 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[143]) ).

thf(155,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[125]) ).

thf(156,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz00 )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[131]) ).

thf(157,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ sz00 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[124]) ).

thf(158,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( sdtasdt0 @ xa @ SX0 )
                 != sz00 )
                | ~ ( aElement0 @ SX0 ) )
          | ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[145]) ).

thf(159,plain,
    ( ( ( ( xa != sz00 ) )
      = $true )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(160,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(161,plain,
    ! [SV2: $i] :
      ( ( ~ ( aElement0 @ SV2 )
        | ( aElement0 @ ( smndt0 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(162,plain,
    ! [SV3: $i] :
      ( ( ! [SY74: $i] :
            ( ~ ( aElement0 @ SV3 )
            | ~ ( aElement0 @ SY74 )
            | ( aElement0 @ ( sdtpldt0 @ SV3 @ SY74 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(163,plain,
    ! [SV4: $i] :
      ( ( ! [SY75: $i] :
            ( ~ ( aElement0 @ SV4 )
            | ~ ( aElement0 @ SY75 )
            | ( aElement0 @ ( sdtasdt0 @ SV4 @ SY75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(164,plain,
    ! [SV5: $i] :
      ( ( ! [SY76: $i] :
            ( ~ ( aElement0 @ SV5 )
            | ~ ( aElement0 @ SY76 )
            | ( ( sdtpldt0 @ SV5 @ SY76 )
              = ( sdtpldt0 @ SY76 @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(165,plain,
    ! [SV6: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( aElement0 @ SV6 )
            | ~ ( aElement0 @ SY77 )
            | ~ ( aElement0 @ SY78 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SY77 ) @ SY78 )
              = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SY77 @ SY78 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(166,plain,
    ! [SV7: $i] :
      ( ( ! [SY79: $i] :
            ( ~ ( aElement0 @ SV7 )
            | ~ ( aElement0 @ SY79 )
            | ( ( sdtasdt0 @ SV7 @ SY79 )
              = ( sdtasdt0 @ SY79 @ SV7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(167,plain,
    ! [SV8: $i] :
      ( ( ! [SY80: $i,SY81: $i] :
            ( ~ ( aElement0 @ SV8 )
            | ~ ( aElement0 @ SY80 )
            | ~ ( aElement0 @ SY81 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SY80 ) @ SY81 )
              = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SY80 @ SY81 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(168,plain,
    ! [SV9: $i] :
      ( ( ! [SY82: $i] :
            ( ~ ( aElement0 @ SV9 )
            | ~ ( aElement0 @ SY82 )
            | ( ( sdtasdt0 @ SV9 @ SY82 )
             != sz00 )
            | ( SV9 = sz00 )
            | ( SY82 = sz00 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(169,plain,
    ( ( sz10 = sz00 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[133]) ).

thf(170,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(171,plain,
    ! [SV11: $i] :
      ( ( ~ ( aSet0 @ SV11 )
        | ! [SY83: $i] :
            ( ~ ( aElementOf0 @ SY83 @ SV11 )
            | ( aElement0 @ SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(172,plain,
    ! [SV12: $i] :
      ( ( ! [SY84: $i] :
            ( ~ ( aIdeal0 @ SV12 )
            | ~ ( aIdeal0 @ SY84 )
            | ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SY84 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(173,plain,
    ! [SV13: $i] :
      ( ( ! [SY85: $i] :
            ( ~ ( aIdeal0 @ SV13 )
            | ~ ( aIdeal0 @ SY85 )
            | ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SY85 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(174,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(175,plain,
    ! [SV15: $i] :
      ( ( ( SV15 = sz00 )
        | ~ ( aElement0 @ SV15 )
        | ( aNaturalNumber0 @ ( sbrdtbr0 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(176,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 )
        | ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(177,plain,
    ! [SV16: $i] :
      ( ( ~ ( aElement0 @ SV16 )
        | ( aIdeal0 @ ( slsdtgt0 @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(178,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) )
      | ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(179,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) )
      | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(180,plain,
    ! [SV17: $i] :
      ( ( ! [SY86: $i] :
            ( ~ ( aIdeal0 @ SV17 )
            | ~ ( aIdeal0 @ SY86 )
            | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SY86 @ SV17 ) )
                | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SY86 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SY86 ) ) )
            | ! [SY87: $i,SY88: $i] :
                ( ~ ( aElement0 @ SY87 )
                | ~ ( aElement0 @ SY88 )
                | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY88 @ SY87 @ SY86 @ SV17 ) )
                          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY88 @ SY87 @ SY86 @ SV17 ) @ SY87 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY88 @ SY87 @ SY86 @ SV17 ) @ SY88 @ SY86 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[148]) ).

thf(181,plain,
    ( ( ~ ( aElement0 @ xa )
      | ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(182,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(183,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(184,plain,
    ! [SV18: $i] :
      ( ( ~ ( ~ ! [SY89: $i,SY90: $i] :
                  ( ~ ( aElement0 @ SV18 )
                  | ~ ( aElement0 @ SY89 )
                  | ~ ( aElement0 @ SY90 )
                  | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SY89 @ SY90 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SY89 ) @ ( sdtasdt0 @ SV18 @ SY90 ) ) ) )
            | ~ ! [SY91: $i,SY92: $i] :
                  ( ~ ( aElement0 @ SV18 )
                  | ~ ( aElement0 @ SY91 )
                  | ~ ( aElement0 @ SY92 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SY91 @ SY92 ) @ SV18 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SY91 @ SV18 ) @ ( sdtasdt0 @ SY92 @ SV18 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(185,plain,
    ! [SV19: $i] :
      ( ( ! [SY93: $i] :
            ( ~ ( aSet0 @ SV19 )
            | ~ ( aSet0 @ SY93 )
            | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SY93 @ SV19 ) @ SV19 )
                | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SY93 @ SV19 ) @ SY93 ) )
            | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SY93 @ SV19 ) @ SY93 )
                | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SY93 @ SV19 ) @ SV19 ) )
            | ( SV19 = SY93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(186,plain,
    ! [SV20: $i] :
      ( ( ! [SY94: $i] :
            ( ( SY94 = sz00 )
            | ~ ( aElement0 @ SV20 )
            | ~ ( aElement0 @ SY94 )
            | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SY94 @ SV20 ) )
                            | ~ ( aElement0 @ ( sK2_SY72 @ SY94 @ SV20 ) ) )
                      | ( SV20
                       != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SY94 @ SV20 ) @ SY94 ) @ ( sK2_SY72 @ SY94 @ SV20 ) ) ) )
                | ~ ( ( ( sK2_SY72 @ SY94 @ SV20 )
                      = sz00 )
                    | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SY94 @ SV20 ) ) @ ( sbrdtbr0 @ SY94 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(187,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(188,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(189,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(190,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xa @ SX0 )
             != sz00 )
            | ~ ( aElement0 @ SX0 ) )
      | ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(191,plain,
    ( ( ( xa = sz00 )
      = $false )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(192,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( aElement0 @ SV2 ) )
        = $true )
      | ( ( aElement0 @ ( smndt0 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(193,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ~ ( aElement0 @ SV3 )
        | ~ ( aElement0 @ SV21 )
        | ( aElement0 @ ( sdtpldt0 @ SV3 @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[162]) ).

thf(194,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ~ ( aElement0 @ SV4 )
        | ~ ( aElement0 @ SV22 )
        | ( aElement0 @ ( sdtasdt0 @ SV4 @ SV22 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[163]) ).

thf(195,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ~ ( aElement0 @ SV5 )
        | ~ ( aElement0 @ SV23 )
        | ( ( sdtpldt0 @ SV5 @ SV23 )
          = ( sdtpldt0 @ SV23 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(196,plain,
    ! [SV24: $i,SV6: $i] :
      ( ( ! [SY95: $i] :
            ( ~ ( aElement0 @ SV6 )
            | ~ ( aElement0 @ SV24 )
            | ~ ( aElement0 @ SY95 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SY95 )
              = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SY95 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(197,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ~ ( aElement0 @ SV7 )
        | ~ ( aElement0 @ SV25 )
        | ( ( sdtasdt0 @ SV7 @ SV25 )
          = ( sdtasdt0 @ SV25 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[166]) ).

thf(198,plain,
    ! [SV26: $i,SV8: $i] :
      ( ( ! [SY96: $i] :
            ( ~ ( aElement0 @ SV8 )
            | ~ ( aElement0 @ SV26 )
            | ~ ( aElement0 @ SY96 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SY96 )
              = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SY96 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(199,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ~ ( aElement0 @ SV9 )
        | ~ ( aElement0 @ SV27 )
        | ( ( sdtasdt0 @ SV9 @ SV27 )
         != sz00 )
        | ( SV9 = sz00 )
        | ( SV27 = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[168]) ).

thf(200,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( aSet0 @ SV11 ) )
        = $true )
      | ( ( ! [SY83: $i] :
              ( ~ ( aElementOf0 @ SY83 @ SV11 )
              | ( aElement0 @ SY83 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[171]) ).

thf(201,plain,
    ! [SV28: $i,SV12: $i] :
      ( ( ~ ( aIdeal0 @ SV12 )
        | ~ ( aIdeal0 @ SV28 )
        | ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(202,plain,
    ! [SV29: $i,SV13: $i] :
      ( ( ~ ( aIdeal0 @ SV13 )
        | ~ ( aIdeal0 @ SV29 )
        | ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(203,plain,
    ! [SV15: $i] :
      ( ( ( ( SV15 = sz00 )
          | ~ ( aElement0 @ SV15 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[175]) ).

thf(204,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(205,plain,
    ! [SV16: $i] :
      ( ( ( ~ ( aElement0 @ SV16 ) )
        = $true )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[177]) ).

thf(206,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[178]) ).

thf(207,plain,
    ( ( ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[178]) ).

thf(208,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[179]) ).

thf(209,plain,
    ( ( ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[179]) ).

thf(210,plain,
    ! [SV30: $i,SV17: $i] :
      ( ( ~ ( aIdeal0 @ SV17 )
        | ~ ( aIdeal0 @ SV30 )
        | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
            | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
        | ! [SY97: $i,SY98: $i] :
            ( ~ ( aElement0 @ SY97 )
            | ~ ( aElement0 @ SY98 )
            | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                      | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[180]) ).

thf(211,plain,
    ( ( ~ ( aElement0 @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[181]) ).

thf(212,plain,
    ( ( ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[181]) ).

thf(213,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(214,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(215,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(216,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(217,plain,
    ! [SV18: $i] :
      ( ( ~ ! [SY89: $i,SY90: $i] :
              ( ~ ( aElement0 @ SV18 )
              | ~ ( aElement0 @ SY89 )
              | ~ ( aElement0 @ SY90 )
              | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SY89 @ SY90 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SY89 ) @ ( sdtasdt0 @ SV18 @ SY90 ) ) ) )
        | ~ ! [SY91: $i,SY92: $i] :
              ( ~ ( aElement0 @ SV18 )
              | ~ ( aElement0 @ SY91 )
              | ~ ( aElement0 @ SY92 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY91 @ SY92 ) @ SV18 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY91 @ SV18 ) @ ( sdtasdt0 @ SY92 @ SV18 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(218,plain,
    ! [SV31: $i,SV19: $i] :
      ( ( ~ ( aSet0 @ SV19 )
        | ~ ( aSet0 @ SV31 )
        | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
            | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
        | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
            | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        | ( SV19 = SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(219,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( SV32 = sz00 )
        | ~ ( aElement0 @ SV20 )
        | ~ ( aElement0 @ SV32 )
        | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                        | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                  | ( SV20
                   != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
            | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                  = sz00 )
                | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(220,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(221,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(222,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(223,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(224,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(225,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(226,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xa @ SX0 )
             != sz00 )
            | ~ ( aElement0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(227,plain,
    ( ( ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(228,plain,
    ( ( ( xb = sz00 )
      = $false )
    | ( ( xa = sz00 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(229,plain,
    ! [SV2: $i] :
      ( ( ( aElement0 @ SV2 )
        = $false )
      | ( ( aElement0 @ ( smndt0 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[192]) ).

thf(230,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( ~ ( aElement0 @ SV3 )
          | ~ ( aElement0 @ SV21 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV21 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[193]) ).

thf(231,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( ~ ( aElement0 @ SV4 )
          | ~ ( aElement0 @ SV22 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV22 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[194]) ).

thf(232,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( ~ ( aElement0 @ SV5 )
          | ~ ( aElement0 @ SV23 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV5 @ SV23 )
          = ( sdtpldt0 @ SV23 @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[195]) ).

thf(233,plain,
    ! [SV33: $i,SV24: $i,SV6: $i] :
      ( ( ~ ( aElement0 @ SV6 )
        | ~ ( aElement0 @ SV24 )
        | ~ ( aElement0 @ SV33 )
        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[196]) ).

thf(234,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ( ~ ( aElement0 @ SV7 )
          | ~ ( aElement0 @ SV25 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV7 @ SV25 )
          = ( sdtasdt0 @ SV25 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[197]) ).

thf(235,plain,
    ! [SV34: $i,SV26: $i,SV8: $i] :
      ( ( ~ ( aElement0 @ SV8 )
        | ~ ( aElement0 @ SV26 )
        | ~ ( aElement0 @ SV34 )
        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(236,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( ~ ( aElement0 @ SV9 )
          | ~ ( aElement0 @ SV27 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
           != sz00 )
          | ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[199]) ).

thf(237,plain,
    ! [SV11: $i] :
      ( ( ( aSet0 @ SV11 )
        = $false )
      | ( ( ! [SY83: $i] :
              ( ~ ( aElementOf0 @ SY83 @ SV11 )
              | ( aElement0 @ SY83 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(238,plain,
    ! [SV28: $i,SV12: $i] :
      ( ( ( ~ ( aIdeal0 @ SV12 )
          | ~ ( aIdeal0 @ SV28 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[201]) ).

thf(239,plain,
    ! [SV29: $i,SV13: $i] :
      ( ( ( ~ ( aIdeal0 @ SV13 )
          | ~ ( aIdeal0 @ SV29 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SV29 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[202]) ).

thf(240,plain,
    ! [SV15: $i] :
      ( ( ( SV15 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV15 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[203]) ).

thf(241,plain,
    ! [SV35: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV35 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(242,plain,
    ! [SV16: $i] :
      ( ( ( aElement0 @ SV16 )
        = $false )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[205]) ).

thf(243,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i,SX2: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                          | ( ( sdtpldt0 @ SX1 @ SX2 )
                           != SX0 ) )
                      | ( aElementOf0 @ SX0 @ xI ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                          | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                           != SX0 ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xb @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xa @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElement0 @ SX1 )
                                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                  | ~ ( aSet0 @ xI ) )
                            | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[206]) ).

thf(244,plain,
    ( ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[207]) ).

thf(245,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                           != xa )
                                                          | ~ ( aElement0 @ sK12_W0 ) )
                                                    | ~ ( aElement0 @ xc ) )
                                              | ~ ( doDivides0 @ xc @ xa ) )
                                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                   != xb )
                                  | ~ ( aElement0 @ sK11_W0 ) ) )
                      | ~ ( doDivides0 @ xc @ xb ) )
                | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[208]) ).

thf(246,plain,
    ( ( aGcdOfAnd0 @ xc @ xa @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[209]) ).

thf(247,plain,
    ! [SV30: $i,SV17: $i] :
      ( ( ( ~ ( aIdeal0 @ SV17 )
          | ~ ( aIdeal0 @ SV30 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
          | ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[210]) ).

thf(248,plain,
    ( ( aElement0 @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[211]) ).

thf(249,plain,
    ( ( aElement0 @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[212]) ).

thf(250,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz10 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[213]) ).

thf(251,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[214]) ).

thf(252,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
            = ( smndt0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[215]) ).

thf(253,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( smndt0 @ SX0 )
            = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[216]) ).

thf(254,plain,
    ! [SV18: $i] :
      ( ( ~ ! [SY89: $i,SY90: $i] :
              ( ~ ( aElement0 @ SV18 )
              | ~ ( aElement0 @ SY89 )
              | ~ ( aElement0 @ SY90 )
              | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SY89 @ SY90 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SY89 ) @ ( sdtasdt0 @ SV18 @ SY90 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[217]) ).

thf(255,plain,
    ! [SV18: $i] :
      ( ( ~ ! [SY91: $i,SY92: $i] :
              ( ~ ( aElement0 @ SV18 )
              | ~ ( aElement0 @ SY91 )
              | ~ ( aElement0 @ SY92 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY91 @ SY92 ) @ SV18 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY91 @ SV18 ) @ ( sdtasdt0 @ SY92 @ SV18 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[217]) ).

thf(256,plain,
    ! [SV31: $i,SV19: $i] :
      ( ( ( ~ ( aSet0 @ SV19 )
          | ~ ( aSet0 @ SV31 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
          | ( SV19 = SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[218]) ).

thf(257,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ( SV32 = sz00 )
          | ~ ( aElement0 @ SV20 )
          | ~ ( aElement0 @ SV32 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                    | ( SV20
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[219]) ).

thf(258,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[220]) ).

thf(259,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[221]) ).

thf(260,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz00 )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[222]) ).

thf(261,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[223]) ).

thf(262,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ sz00 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[224]) ).

thf(263,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[225]) ).

thf(264,plain,
    ( ( ! [SX0: $i] :
          ( ( ( sdtasdt0 @ xa @ SX0 )
           != sz00 )
          | ~ ( aElement0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[226]) ).

thf(265,plain,
    ( ( ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[227]) ).

thf(266,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( ~ ( aElement0 @ SV3 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV21 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV21 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[230]) ).

thf(267,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( ~ ( aElement0 @ SV4 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV22 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV22 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[231]) ).

thf(268,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( ~ ( aElement0 @ SV5 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV23 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV5 @ SV23 )
          = ( sdtpldt0 @ SV23 @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(269,plain,
    ! [SV33: $i,SV24: $i,SV6: $i] :
      ( ( ( ~ ( aElement0 @ SV6 )
          | ~ ( aElement0 @ SV24 )
          | ~ ( aElement0 @ SV33 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[233]) ).

thf(270,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ( ~ ( aElement0 @ SV7 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV25 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV7 @ SV25 )
          = ( sdtasdt0 @ SV25 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[234]) ).

thf(271,plain,
    ! [SV34: $i,SV26: $i,SV8: $i] :
      ( ( ( ~ ( aElement0 @ SV8 )
          | ~ ( aElement0 @ SV26 )
          | ~ ( aElement0 @ SV34 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[235]) ).

thf(272,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( ~ ( aElement0 @ SV9 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV27 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
           != sz00 )
          | ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[236]) ).

thf(273,plain,
    ! [SV11: $i,SV36: $i] :
      ( ( ( ~ ( aElementOf0 @ SV36 @ SV11 )
          | ( aElement0 @ SV36 ) )
        = $true )
      | ( ( aSet0 @ SV11 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(274,plain,
    ! [SV28: $i,SV12: $i] :
      ( ( ( ~ ( aIdeal0 @ SV12 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV28 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[238]) ).

thf(275,plain,
    ! [SV29: $i,SV13: $i] :
      ( ( ( ~ ( aIdeal0 @ SV13 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV29 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SV29 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[239]) ).

thf(276,plain,
    ! [SV15: $i] :
      ( ( ( aElement0 @ SV15 )
        = $false )
      | ( ( SV15 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[240]) ).

thf(277,plain,
    ! [SV35: $i] :
      ( ( ( aNaturalNumber0 @ SV35 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[241]) ).

thf(278,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[243]) ).

thf(279,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[245]) ).

thf(280,plain,
    ! [SV30: $i,SV17: $i] :
      ( ( ( ~ ( aIdeal0 @ SV17 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV30 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
          | ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[247]) ).

thf(281,plain,
    ! [SV37: $i] :
      ( ( ~ ( aElement0 @ SV37 )
        | ( ( sdtasdt0 @ SV37 @ sz10 )
          = SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[250]) ).

thf(282,plain,
    ! [SV38: $i] :
      ( ( ~ ( aElement0 @ SV38 )
        | ( SV38
          = ( sdtasdt0 @ sz10 @ SV38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[251]) ).

thf(283,plain,
    ! [SV39: $i] :
      ( ( ~ ( aElement0 @ SV39 )
        | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV39 )
          = ( smndt0 @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[252]) ).

thf(284,plain,
    ! [SV40: $i] :
      ( ( ~ ( aElement0 @ SV40 )
        | ( ( smndt0 @ SV40 )
          = ( sdtasdt0 @ SV40 @ ( smndt0 @ sz10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[253]) ).

thf(285,plain,
    ! [SV18: $i] :
      ( ( ! [SY89: $i,SY90: $i] :
            ( ~ ( aElement0 @ SV18 )
            | ~ ( aElement0 @ SY89 )
            | ~ ( aElement0 @ SY90 )
            | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SY89 @ SY90 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SY89 ) @ ( sdtasdt0 @ SV18 @ SY90 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[254]) ).

thf(286,plain,
    ! [SV18: $i] :
      ( ( ! [SY91: $i,SY92: $i] :
            ( ~ ( aElement0 @ SV18 )
            | ~ ( aElement0 @ SY91 )
            | ~ ( aElement0 @ SY92 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SY91 @ SY92 ) @ SV18 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SY91 @ SV18 ) @ ( sdtasdt0 @ SY92 @ SV18 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[255]) ).

thf(287,plain,
    ! [SV31: $i,SV19: $i] :
      ( ( ( ~ ( aSet0 @ SV19 ) )
        = $true )
      | ( ( ~ ( aSet0 @ SV31 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
          | ( SV19 = SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[256]) ).

thf(288,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( SV32 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV20 )
          | ~ ( aElement0 @ SV32 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                    | ( SV20
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[257]) ).

thf(289,plain,
    ! [SV41: $i] :
      ( ( ~ ( aElement0 @ SV41 )
        | ( ( sdtpldt0 @ SV41 @ ( smndt0 @ SV41 ) )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[258]) ).

thf(290,plain,
    ! [SV42: $i] :
      ( ( ~ ( aElement0 @ SV42 )
        | ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV42 ) @ SV42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[259]) ).

thf(291,plain,
    ! [SV43: $i] :
      ( ( ~ ( aElement0 @ SV43 )
        | ( ( sdtasdt0 @ SV43 @ sz00 )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[260]) ).

thf(292,plain,
    ! [SV44: $i] :
      ( ( ~ ( aElement0 @ SV44 )
        | ( sz00
          = ( sdtasdt0 @ sz00 @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[261]) ).

thf(293,plain,
    ! [SV45: $i] :
      ( ( ~ ( aElement0 @ SV45 )
        | ( ( sdtpldt0 @ SV45 @ sz00 )
          = SV45 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[262]) ).

thf(294,plain,
    ! [SV46: $i] :
      ( ( ~ ( aElement0 @ SV46 )
        | ( SV46
          = ( sdtpldt0 @ sz00 @ SV46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[263]) ).

thf(295,plain,
    ! [SV47: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV47 )
         != sz00 )
        | ~ ( aElement0 @ SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[264]) ).

thf(296,plain,
    ( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[265]) ).

thf(297,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ( aElement0 @ SV3 )
        = $false )
      | ( ( ~ ( aElement0 @ SV21 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV21 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[266]) ).

thf(298,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ( aElement0 @ SV4 )
        = $false )
      | ( ( ~ ( aElement0 @ SV22 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV22 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[267]) ).

thf(299,plain,
    ! [SV23: $i,SV5: $i] :
      ( ( ( aElement0 @ SV5 )
        = $false )
      | ( ( ~ ( aElement0 @ SV23 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV5 @ SV23 )
          = ( sdtpldt0 @ SV23 @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[268]) ).

thf(300,plain,
    ! [SV33: $i,SV24: $i,SV6: $i] :
      ( ( ( ~ ( aElement0 @ SV6 )
          | ~ ( aElement0 @ SV24 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV33 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[269]) ).

thf(301,plain,
    ! [SV25: $i,SV7: $i] :
      ( ( ( aElement0 @ SV7 )
        = $false )
      | ( ( ~ ( aElement0 @ SV25 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV7 @ SV25 )
          = ( sdtasdt0 @ SV25 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[270]) ).

thf(302,plain,
    ! [SV34: $i,SV26: $i,SV8: $i] :
      ( ( ( ~ ( aElement0 @ SV8 )
          | ~ ( aElement0 @ SV26 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV34 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[271]) ).

thf(303,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( aElement0 @ SV9 )
        = $false )
      | ( ( ~ ( aElement0 @ SV27 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
           != sz00 )
          | ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(304,plain,
    ! [SV11: $i,SV36: $i] :
      ( ( ( ~ ( aElementOf0 @ SV36 @ SV11 ) )
        = $true )
      | ( ( aElement0 @ SV36 )
        = $true )
      | ( ( aSet0 @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[273]) ).

thf(305,plain,
    ! [SV28: $i,SV12: $i] :
      ( ( ( aIdeal0 @ SV12 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV28 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[274]) ).

thf(306,plain,
    ! [SV29: $i,SV13: $i] :
      ( ( ( aIdeal0 @ SV13 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV29 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SV29 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[275]) ).

thf(307,plain,
    ! [SV35: $i,SV48: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV48 ) )
        = $true )
      | ( ( aNaturalNumber0 @ SV35 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[277]) ).

thf(308,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[278]) ).

thf(309,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[278]) ).

thf(310,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[279]) ).

thf(311,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[279]) ).

thf(312,plain,
    ! [SV30: $i,SV17: $i] :
      ( ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV30 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
          | ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[280]) ).

thf(313,plain,
    ! [SV37: $i] :
      ( ( ( ~ ( aElement0 @ SV37 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV37 @ sz10 )
          = SV37 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[281]) ).

thf(314,plain,
    ! [SV38: $i] :
      ( ( ( ~ ( aElement0 @ SV38 ) )
        = $true )
      | ( ( SV38
          = ( sdtasdt0 @ sz10 @ SV38 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[282]) ).

thf(315,plain,
    ! [SV39: $i] :
      ( ( ( ~ ( aElement0 @ SV39 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV39 )
          = ( smndt0 @ SV39 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[283]) ).

thf(316,plain,
    ! [SV40: $i] :
      ( ( ( ~ ( aElement0 @ SV40 ) )
        = $true )
      | ( ( ( smndt0 @ SV40 )
          = ( sdtasdt0 @ SV40 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[284]) ).

thf(317,plain,
    ! [SV49: $i,SV18: $i] :
      ( ( ! [SY99: $i] :
            ( ~ ( aElement0 @ SV18 )
            | ~ ( aElement0 @ SV49 )
            | ~ ( aElement0 @ SY99 )
            | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SY99 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SY99 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(318,plain,
    ! [SV50: $i,SV18: $i] :
      ( ( ! [SY100: $i] :
            ( ~ ( aElement0 @ SV18 )
            | ~ ( aElement0 @ SV50 )
            | ~ ( aElement0 @ SY100 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SY100 ) @ SV18 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SY100 @ SV18 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[286]) ).

thf(319,plain,
    ! [SV31: $i,SV19: $i] :
      ( ( ( aSet0 @ SV19 )
        = $false )
      | ( ( ~ ( aSet0 @ SV31 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
          | ( SV19 = SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[287]) ).

thf(320,plain,
    ! [SV32: $i,SV20: $i] :
      ( ( ( ~ ( aElement0 @ SV20 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV32 ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                    | ( SV20
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[288]) ).

thf(321,plain,
    ! [SV41: $i] :
      ( ( ( ~ ( aElement0 @ SV41 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV41 @ ( smndt0 @ SV41 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[289]) ).

thf(322,plain,
    ! [SV42: $i] :
      ( ( ( ~ ( aElement0 @ SV42 ) )
        = $true )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV42 ) @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[290]) ).

thf(323,plain,
    ! [SV43: $i] :
      ( ( ( ~ ( aElement0 @ SV43 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV43 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[291]) ).

thf(324,plain,
    ! [SV44: $i] :
      ( ( ( ~ ( aElement0 @ SV44 ) )
        = $true )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV44 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[292]) ).

thf(325,plain,
    ! [SV45: $i] :
      ( ( ( ~ ( aElement0 @ SV45 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV45 @ sz00 )
          = SV45 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[293]) ).

thf(326,plain,
    ! [SV46: $i] :
      ( ( ( ~ ( aElement0 @ SV46 ) )
        = $true )
      | ( ( SV46
          = ( sdtpldt0 @ sz00 @ SV46 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[294]) ).

thf(327,plain,
    ! [SV47: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV47 )
           != sz00 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(328,plain,
    ! [SV3: $i,SV21: $i] :
      ( ( ( aElement0 @ SV21 )
        = $false )
      | ( ( aElement0 @ SV3 )
        = $false )
      | ( ( aElement0 @ ( sdtpldt0 @ SV3 @ SV21 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[297]) ).

thf(329,plain,
    ! [SV4: $i,SV22: $i] :
      ( ( ( aElement0 @ SV22 )
        = $false )
      | ( ( aElement0 @ SV4 )
        = $false )
      | ( ( aElement0 @ ( sdtasdt0 @ SV4 @ SV22 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[298]) ).

thf(330,plain,
    ! [SV5: $i,SV23: $i] :
      ( ( ( aElement0 @ SV23 )
        = $false )
      | ( ( aElement0 @ SV5 )
        = $false )
      | ( ( ( sdtpldt0 @ SV5 @ SV23 )
          = ( sdtpldt0 @ SV23 @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[299]) ).

thf(331,plain,
    ! [SV33: $i,SV24: $i,SV6: $i] :
      ( ( ( ~ ( aElement0 @ SV6 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV24 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV33 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[300]) ).

thf(332,plain,
    ! [SV7: $i,SV25: $i] :
      ( ( ( aElement0 @ SV25 )
        = $false )
      | ( ( aElement0 @ SV7 )
        = $false )
      | ( ( ( sdtasdt0 @ SV7 @ SV25 )
          = ( sdtasdt0 @ SV25 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[301]) ).

thf(333,plain,
    ! [SV34: $i,SV26: $i,SV8: $i] :
      ( ( ( ~ ( aElement0 @ SV8 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV26 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV34 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[302]) ).

thf(334,plain,
    ! [SV9: $i,SV27: $i] :
      ( ( ( aElement0 @ SV27 )
        = $false )
      | ( ( aElement0 @ SV9 )
        = $false )
      | ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
           != sz00 )
          | ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[303]) ).

thf(335,plain,
    ! [SV11: $i,SV36: $i] :
      ( ( ( aElementOf0 @ SV36 @ SV11 )
        = $false )
      | ( ( aElement0 @ SV36 )
        = $true )
      | ( ( aSet0 @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[304]) ).

thf(336,plain,
    ! [SV12: $i,SV28: $i] :
      ( ( ( aIdeal0 @ SV28 )
        = $false )
      | ( ( aIdeal0 @ SV12 )
        = $false )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV12 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[305]) ).

thf(337,plain,
    ! [SV13: $i,SV29: $i] :
      ( ( ( aIdeal0 @ SV29 )
        = $false )
      | ( ( aIdeal0 @ SV13 )
        = $false )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV13 @ SV29 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[306]) ).

thf(338,plain,
    ! [SV35: $i,SV48: $i] :
      ( ( ( aNaturalNumber0 @ SV48 )
        = $false )
      | ( ( aNaturalNumber0 @ SV35 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[307]) ).

thf(339,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i,SX2: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                    | ( ( sdtpldt0 @ SX1 @ SX2 )
                     != SX0 ) )
                | ( aElementOf0 @ SX0 @ xI ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                    | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                     != SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[308]) ).

thf(340,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xb @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                      | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xa @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElementOf0 @ SX1 @ xI )
                                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElement0 @ SX1 )
                                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                            | ~ ( aSet0 @ xI ) )
                      | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[309]) ).

thf(341,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[310]) ).

thf(342,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                     != xa )
                                                    | ~ ( aElement0 @ sK12_W0 ) )
                                              | ~ ( aElement0 @ xc ) )
                                        | ~ ( doDivides0 @ xc @ xa ) )
                                  | ~ ( aDivisorOf0 @ xc @ xa ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                             != xb )
                            | ~ ( aElement0 @ sK11_W0 ) ) )
                | ~ ( doDivides0 @ xc @ xb ) )
          | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[311]) ).

thf(343,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( aIdeal0 @ SV30 )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
          | ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[312]) ).

thf(344,plain,
    ! [SV37: $i] :
      ( ( ( aElement0 @ SV37 )
        = $false )
      | ( ( ( sdtasdt0 @ SV37 @ sz10 )
          = SV37 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[313]) ).

thf(345,plain,
    ! [SV38: $i] :
      ( ( ( aElement0 @ SV38 )
        = $false )
      | ( ( SV38
          = ( sdtasdt0 @ sz10 @ SV38 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[314]) ).

thf(346,plain,
    ! [SV39: $i] :
      ( ( ( aElement0 @ SV39 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV39 )
          = ( smndt0 @ SV39 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[315]) ).

thf(347,plain,
    ! [SV40: $i] :
      ( ( ( aElement0 @ SV40 )
        = $false )
      | ( ( ( smndt0 @ SV40 )
          = ( sdtasdt0 @ SV40 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[316]) ).

thf(348,plain,
    ! [SV51: $i,SV49: $i,SV18: $i] :
      ( ( ~ ( aElement0 @ SV18 )
        | ~ ( aElement0 @ SV49 )
        | ~ ( aElement0 @ SV51 )
        | ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[317]) ).

thf(349,plain,
    ! [SV52: $i,SV50: $i,SV18: $i] :
      ( ( ~ ( aElement0 @ SV18 )
        | ~ ( aElement0 @ SV50 )
        | ~ ( aElement0 @ SV52 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(350,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aSet0 @ SV31 )
        = $false )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
          | ( SV19 = SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[319]) ).

thf(351,plain,
    ! [SV32: $i,SV20: $i] :
      ( ( ( aElement0 @ SV20 )
        = $false )
      | ( ( ~ ( aElement0 @ SV32 ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                    | ( SV20
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[320]) ).

thf(352,plain,
    ! [SV41: $i] :
      ( ( ( aElement0 @ SV41 )
        = $false )
      | ( ( ( sdtpldt0 @ SV41 @ ( smndt0 @ SV41 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[321]) ).

thf(353,plain,
    ! [SV42: $i] :
      ( ( ( aElement0 @ SV42 )
        = $false )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV42 ) @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[322]) ).

thf(354,plain,
    ! [SV43: $i] :
      ( ( ( aElement0 @ SV43 )
        = $false )
      | ( ( ( sdtasdt0 @ SV43 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[323]) ).

thf(355,plain,
    ! [SV44: $i] :
      ( ( ( aElement0 @ SV44 )
        = $false )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV44 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[324]) ).

thf(356,plain,
    ! [SV45: $i] :
      ( ( ( aElement0 @ SV45 )
        = $false )
      | ( ( ( sdtpldt0 @ SV45 @ sz00 )
          = SV45 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[325]) ).

thf(357,plain,
    ! [SV46: $i] :
      ( ( ( aElement0 @ SV46 )
        = $false )
      | ( ( SV46
          = ( sdtpldt0 @ sz00 @ SV46 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[326]) ).

thf(358,plain,
    ! [SV47: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV47 )
          = sz00 )
        = $false )
      | ( ( ~ ( aElement0 @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[327]) ).

thf(359,plain,
    ! [SV33: $i,SV24: $i,SV6: $i] :
      ( ( ( aElement0 @ SV6 )
        = $false )
      | ( ( ~ ( aElement0 @ SV24 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV33 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(360,plain,
    ! [SV34: $i,SV26: $i,SV8: $i] :
      ( ( ( aElement0 @ SV8 )
        = $false )
      | ( ( ~ ( aElement0 @ SV26 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV34 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[333]) ).

thf(361,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
           != sz00 ) )
        = $true )
      | ( ( ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV9 )
        = $false )
      | ( ( aElement0 @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[334]) ).

thf(362,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(363,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(364,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[341]) ).

thf(365,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) )
      | ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[342]) ).

thf(366,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) ) )
        = $true )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(367,plain,
    ! [SV51: $i,SV49: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 )
          | ~ ( aElement0 @ SV49 )
          | ~ ( aElement0 @ SV51 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[348]) ).

thf(368,plain,
    ! [SV52: $i,SV50: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 )
          | ~ ( aElement0 @ SV50 )
          | ~ ( aElement0 @ SV52 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[349]) ).

thf(369,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[350]) ).

thf(370,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( aElement0 @ SV32 )
        = $false )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                    | ( SV20
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[351]) ).

thf(371,plain,
    ! [SV47: $i] :
      ( ( ( aElement0 @ SV47 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV47 )
          = sz00 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[358]) ).

thf(372,plain,
    ! [SV33: $i,SV6: $i,SV24: $i] :
      ( ( ( aElement0 @ SV24 )
        = $false )
      | ( ( aElement0 @ SV6 )
        = $false )
      | ( ( ~ ( aElement0 @ SV33 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[359]) ).

thf(373,plain,
    ! [SV34: $i,SV8: $i,SV26: $i] :
      ( ( ( aElement0 @ SV26 )
        = $false )
      | ( ( aElement0 @ SV8 )
        = $false )
      | ( ( ~ ( aElement0 @ SV34 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[360]) ).

thf(374,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( ( sdtasdt0 @ SV9 @ SV27 )
          = sz00 )
        = $false )
      | ( ( ( SV9 = sz00 )
          | ( SV27 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV9 )
        = $false )
      | ( ( aElement0 @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[361]) ).

thf(375,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[362]) ).

thf(376,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[362]) ).

thf(377,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[363]) ).

thf(378,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[363]) ).

thf(379,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[364]) ).

thf(380,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[364]) ).

thf(381,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[365]) ).

thf(382,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[365]) ).

thf(383,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
          | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
        = $false )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[366]) ).

thf(384,plain,
    ! [SV51: $i,SV49: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 )
          | ~ ( aElement0 @ SV49 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV51 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[367]) ).

thf(385,plain,
    ! [SV52: $i,SV50: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 )
          | ~ ( aElement0 @ SV50 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV52 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[368]) ).

thf(386,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[369]) ).

thf(387,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                | ( SV20
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
          | ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[370]) ).

thf(388,plain,
    ! [SV24: $i,SV6: $i,SV33: $i] :
      ( ( ( aElement0 @ SV33 )
        = $false )
      | ( ( aElement0 @ SV6 )
        = $false )
      | ( ( aElement0 @ SV24 )
        = $false )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV6 @ SV24 ) @ SV33 )
          = ( sdtpldt0 @ SV6 @ ( sdtpldt0 @ SV24 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[372]) ).

thf(389,plain,
    ! [SV26: $i,SV8: $i,SV34: $i] :
      ( ( ( aElement0 @ SV34 )
        = $false )
      | ( ( aElement0 @ SV8 )
        = $false )
      | ( ( aElement0 @ SV26 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV8 @ SV26 ) @ SV34 )
          = ( sdtasdt0 @ SV8 @ ( sdtasdt0 @ SV26 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[373]) ).

thf(390,plain,
    ! [SV27: $i,SV9: $i] :
      ( ( ( SV9 = sz00 )
        = $true )
      | ( ( SV27 = sz00 )
        = $true )
      | ( ( ( sdtasdt0 @ SV9 @ SV27 )
          = sz00 )
        = $false )
      | ( ( aElement0 @ SV9 )
        = $false )
      | ( ( aElement0 @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[374]) ).

thf(391,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i,SX2: $i] :
              ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SX1 @ SX2 )
               != SX0 ) )
          | ( aElementOf0 @ SX0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[375]) ).

thf(392,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
               != SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[376]) ).

thf(393,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xb @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[377]) ).

thf(394,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xa @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                      | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElementOf0 @ SX1 @ xI )
                                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElement0 @ SX1 )
                                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                      | ~ ( aSet0 @ xI ) )
                | ~ ( aIdeal0 @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[378]) ).

thf(395,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[379]) ).

thf(396,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[380]) ).

thf(397,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                               != xa )
                                              | ~ ( aElement0 @ sK12_W0 ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ( doDivides0 @ xc @ xa ) )
                            | ~ ( aDivisorOf0 @ xc @ xa ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                       != xb )
                      | ~ ( aElement0 @ sK11_W0 ) ) )
          | ~ ( doDivides0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[381]) ).

thf(398,plain,
    ( ( aDivisorOf0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[382]) ).

thf(399,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) ) )
        = $false )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[383]) ).

thf(400,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
        = $false )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[383]) ).

thf(401,plain,
    ! [SV51: $i,SV49: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV49 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV51 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[384]) ).

thf(402,plain,
    ! [SV52: $i,SV50: $i,SV18: $i] :
      ( ( ( ~ ( aElement0 @ SV18 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV50 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV52 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[385]) ).

thf(403,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
          | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[386]) ).

thf(404,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
                | ( SV20
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[387]) ).

thf(405,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( ( ( sK2_SY72 @ SV32 @ SV20 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[387]) ).

thf(406,plain,
    ! [SV53: $i] :
      ( ( ! [SY101: $i,SY102: $i] :
            ( ~ ( aElementOf0 @ SY101 @ ( slsdtgt0 @ xa ) )
            | ~ ( aElementOf0 @ SY102 @ ( slsdtgt0 @ xb ) )
            | ( ( sdtpldt0 @ SY101 @ SY102 )
             != SV53 ) )
        | ( aElementOf0 @ SV53 @ xI ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[391]) ).

thf(407,plain,
    ! [SV54: $i] :
      ( ( ~ ( aElementOf0 @ SV54 @ xI )
        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
            | ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
             != SV54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[392]) ).

thf(408,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[393]) ).

thf(409,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[394]) ).

thf(410,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[395]) ).

thf(411,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[396]) ).

thf(412,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) )
      | ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[397]) ).

thf(413,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[399]) ).

thf(414,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) ) )
        = $true )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[400]) ).

thf(415,plain,
    ! [SV51: $i,SV49: $i,SV18: $i] :
      ( ( ( aElement0 @ SV18 )
        = $false )
      | ( ( ~ ( aElement0 @ SV49 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV51 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[401]) ).

thf(416,plain,
    ! [SV52: $i,SV50: $i,SV18: $i] :
      ( ( ( aElement0 @ SV18 )
        = $false )
      | ( ( ~ ( aElement0 @ SV50 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV52 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[402]) ).

thf(417,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[403]) ).

thf(418,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[403]) ).

thf(419,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                    | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
              | ( SV20
               != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[404]) ).

thf(420,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ( ( sK2_SY72 @ SV32 @ SV20 )
            = sz00 )
          | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[405]) ).

thf(421,plain,
    ! [SV53: $i] :
      ( ( ( ! [SY101: $i,SY102: $i] :
              ( ~ ( aElementOf0 @ SY101 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY102 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SY101 @ SY102 )
               != SV53 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[406]) ).

thf(422,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( aElementOf0 @ SV54 @ xI ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
               != SV54 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[407]) ).

thf(423,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[408]) ).

thf(424,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[408]) ).

thf(425,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[409]) ).

thf(426,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[409]) ).

thf(427,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[410]) ).

thf(428,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[410]) ).

thf(429,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[411]) ).

thf(430,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[411]) ).

thf(431,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[412]) ).

thf(432,plain,
    ( ( ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[412]) ).

thf(433,plain,
    ! [SV17: $i,SV30: $i,SV55: $i] :
      ( ( ( ! [SY103: $i] :
              ( ~ ( aElement0 @ SV55 )
              | ~ ( aElement0 @ SY103 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY103 @ SV55 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY103 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY103 @ SV55 @ SV30 @ SV17 ) @ SY103 @ SV30 ) ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[413]) ).

thf(434,plain,
    ! [SV17: $i,SV30: $i] :
      ( ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( ! [SY97: $i,SY98: $i] :
              ( ~ ( aElement0 @ SY97 )
              | ~ ( aElement0 @ SY98 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY97 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY98 @ SY97 @ SV30 @ SV17 ) @ SY98 @ SV30 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[414]) ).

thf(435,plain,
    ! [SV51: $i,SV18: $i,SV49: $i] :
      ( ( ( aElement0 @ SV49 )
        = $false )
      | ( ( aElement0 @ SV18 )
        = $false )
      | ( ( ~ ( aElement0 @ SV51 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[415]) ).

thf(436,plain,
    ! [SV52: $i,SV18: $i,SV50: $i] :
      ( ( ( aElement0 @ SV50 )
        = $false )
      | ( ( aElement0 @ SV18 )
        = $false )
      | ( ( ~ ( aElement0 @ SV52 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[416]) ).

thf(437,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[417]) ).

thf(438,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[418]) ).

thf(439,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
          | ( SV20
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[419]) ).

thf(440,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ( sK2_SY72 @ SV32 @ SV20 )
          = sz00 )
        = $true )
      | ( ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) @ ( sbrdtbr0 @ SV32 ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[420]) ).

thf(441,plain,
    ! [SV53: $i,SV56: $i] :
      ( ( ( ! [SY104: $i] :
              ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY104 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SV56 @ SY104 )
               != SV53 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[421]) ).

thf(442,plain,
    ! [SV54: $i] :
      ( ( ( aElementOf0 @ SV54 @ xI )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
               != SV54 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[422]) ).

thf(443,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xb @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[423]) ).

thf(444,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
          | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[424]) ).

thf(445,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xa @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[425]) ).

thf(446,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ xI )
                                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElement0 @ SX1 )
                                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                | ~ ( aSet0 @ xI ) )
          | ~ ( aIdeal0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[426]) ).

thf(447,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[427]) ).

thf(448,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[428]) ).

thf(449,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[429]) ).

thf(450,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[430]) ).

thf(451,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                         != xa )
                                        | ~ ( aElement0 @ sK12_W0 ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ( doDivides0 @ xc @ xa ) )
                      | ~ ( aDivisorOf0 @ xc @ xa ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                 != xb )
                | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[431]) ).

thf(452,plain,
    ( ( doDivides0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[432]) ).

thf(453,plain,
    ! [SV17: $i,SV30: $i,SV57: $i,SV55: $i] :
      ( ( ( ~ ( aElement0 @ SV55 )
          | ~ ( aElement0 @ SV57 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[433]) ).

thf(454,plain,
    ! [SV17: $i,SV30: $i,SV58: $i] :
      ( ( ( ! [SY105: $i] :
              ( ~ ( aElement0 @ SV58 )
              | ~ ( aElement0 @ SY105 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY105 @ SV58 @ SV30 @ SV17 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY105 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY105 @ SV58 @ SV30 @ SV17 ) @ SY105 @ SV30 ) ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[434]) ).

thf(455,plain,
    ! [SV49: $i,SV18: $i,SV51: $i] :
      ( ( ( aElement0 @ SV51 )
        = $false )
      | ( ( aElement0 @ SV18 )
        = $false )
      | ( ( aElement0 @ SV49 )
        = $false )
      | ( ( ( sdtasdt0 @ SV18 @ ( sdtpldt0 @ SV49 @ SV51 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV18 @ SV49 ) @ ( sdtasdt0 @ SV18 @ SV51 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[435]) ).

thf(456,plain,
    ! [SV50: $i,SV18: $i,SV52: $i] :
      ( ( ( aElement0 @ SV52 )
        = $false )
      | ( ( aElement0 @ SV18 )
        = $false )
      | ( ( aElement0 @ SV50 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV50 @ SV52 ) @ SV18 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV50 @ SV18 ) @ ( sdtasdt0 @ SV52 @ SV18 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[436]) ).

thf(457,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[437]) ).

thf(458,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) ) )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[438]) ).

thf(459,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[439]) ).

thf(460,plain,
    ! [SV32: $i,SV20: $i] :
      ( ( ( ( SV20
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[439]) ).

thf(461,plain,
    ! [SV53: $i,SV59: $i,SV56: $i] :
      ( ( ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
          | ( ( sdtpldt0 @ SV56 @ SV59 )
           != SV53 ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[441]) ).

thf(462,plain,
    ! [SV54: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
          | ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
           != SV54 ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[442]) ).

thf(463,plain,
    ! [SV60: $i] :
      ( ( ! [SY106: $i] :
            ( ( ( sdtasdt0 @ xb @ SY106 )
             != SV60 )
            | ~ ( aElement0 @ SY106 ) )
        | ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[443]) ).

thf(464,plain,
    ! [SV61: $i] :
      ( ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
             != SV61 )
            | ~ ( aElement0 @ ( sK8_W1 @ SV61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[444]) ).

thf(465,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[445]) ).

thf(466,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) )
      | ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[446]) ).

thf(467,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[447]) ).

thf(468,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[448]) ).

thf(469,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[449]) ).

thf(470,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[450]) ).

thf(471,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[451]) ).

thf(472,plain,
    ! [SV17: $i,SV30: $i,SV57: $i,SV55: $i] :
      ( ( ( ~ ( aElement0 @ SV55 )
          | ~ ( aElement0 @ SV57 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[453]) ).

thf(473,plain,
    ! [SV17: $i,SV30: $i,SV62: $i,SV58: $i] :
      ( ( ( ~ ( aElement0 @ SV58 )
          | ~ ( aElement0 @ SV62 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[454]) ).

thf(474,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[457]) ).

thf(475,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[457]) ).

thf(476,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[458]) ).

thf(477,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
              | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[459]) ).

thf(478,plain,
    ! [SV32: $i,SV20: $i] :
      ( ( ( SV20
          = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV32 @ SV20 ) @ SV32 ) @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[460]) ).

thf(479,plain,
    ! [SV53: $i,SV59: $i,SV56: $i] :
      ( ( ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV56 @ SV59 )
           != SV53 ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[461]) ).

thf(480,plain,
    ! [SV54: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[462]) ).

thf(481,plain,
    ! [SV54: $i] :
      ( ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
           != SV54 ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[462]) ).

thf(482,plain,
    ! [SV60: $i] :
      ( ( ( ! [SY106: $i] :
              ( ( ( sdtasdt0 @ xb @ SY106 )
               != SV60 )
              | ~ ( aElement0 @ SY106 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[463]) ).

thf(483,plain,
    ! [SV61: $i] :
      ( ( ( ~ ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
               != SV61 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV61 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[464]) ).

thf(484,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[465]) ).

thf(485,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[465]) ).

thf(486,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[466]) ).

thf(487,plain,
    ( ( ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[466]) ).

thf(488,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[467]) ).

thf(489,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[467]) ).

thf(490,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[468]) ).

thf(491,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[468]) ).

thf(492,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[469]) ).

thf(493,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[469]) ).

thf(494,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[470]) ).

thf(495,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[470]) ).

thf(496,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[471]) ).

thf(497,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[471]) ).

thf(498,plain,
    ! [SV17: $i,SV30: $i,SV57: $i,SV55: $i] :
      ( ( ( ~ ( aElement0 @ SV55 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV57 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[472]) ).

thf(499,plain,
    ! [SV17: $i,SV30: $i,SV62: $i,SV58: $i] :
      ( ( ( ~ ( aElement0 @ SV58 )
          | ~ ( aElement0 @ SV62 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[473]) ).

thf(500,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[474]) ).

thf(501,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[475]) ).

thf(502,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[476]) ).

thf(503,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[476]) ).

thf(504,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
          | ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[477]) ).

thf(505,plain,
    ! [SV53: $i,SV59: $i,SV56: $i] :
      ( ( ( ~ ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV56 @ SV59 )
           != SV53 ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[479]) ).

thf(506,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $true )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[480]) ).

thf(507,plain,
    ! [SV54: $i] :
      ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV54 ) @ ( sK10_SY73 @ SV54 ) )
          = SV54 )
        = $true )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[481]) ).

thf(508,plain,
    ! [SV60: $i,SV63: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV63 )
           != SV60 )
          | ~ ( aElement0 @ SV63 ) )
        = $true )
      | ( ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[482]) ).

thf(509,plain,
    ! [SV61: $i] :
      ( ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
               != SV61 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV61 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[483]) ).

thf(510,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xa @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[484]) ).

thf(511,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
          | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[485]) ).

thf(512,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ xI )
                          | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElement0 @ SX1 )
                          | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
          | ~ ( aSet0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[486]) ).

thf(513,plain,
    ( ( aIdeal0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[487]) ).

thf(514,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[488]) ).

thf(515,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[489]) ).

thf(516,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[490]) ).

thf(517,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[491]) ).

thf(518,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[492]) ).

thf(519,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[493]) ).

thf(520,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[494]) ).

thf(521,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[495]) ).

thf(522,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                   != xa )
                                  | ~ ( aElement0 @ sK12_W0 ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ( doDivides0 @ xc @ xa ) )
                | ~ ( aDivisorOf0 @ xc @ xa ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[496]) ).

thf(523,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
           != xb )
          | ~ ( aElement0 @ sK11_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[497]) ).

thf(524,plain,
    ! [SV17: $i,SV30: $i,SV57: $i,SV55: $i] :
      ( ( ( aElement0 @ SV55 )
        = $false )
      | ( ( ~ ( aElement0 @ SV57 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[498]) ).

thf(525,plain,
    ! [SV17: $i,SV30: $i,SV62: $i,SV58: $i] :
      ( ( ( ~ ( aElement0 @ SV58 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV62 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[499]) ).

thf(526,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV19 )
        = $true )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[501]) ).

thf(527,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV31 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[502]) ).

thf(528,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[503]) ).

thf(529,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[504]) ).

thf(530,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( ~ ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) ) )
        = $false )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[504]) ).

thf(531,plain,
    ! [SV53: $i,SV59: $i,SV56: $i] :
      ( ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV56 @ SV59 )
           != SV53 ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[505]) ).

thf(532,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[506]) ).

thf(533,plain,
    ! [SV60: $i,SV63: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV63 )
           != SV60 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV63 ) )
        = $true )
      | ( ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[508]) ).

thf(534,plain,
    ! [SV61: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
           != SV61 )
          | ~ ( aElement0 @ ( sK8_W1 @ SV61 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[509]) ).

thf(535,plain,
    ! [SV64: $i] :
      ( ( ! [SY107: $i] :
            ( ( ( sdtasdt0 @ xa @ SY107 )
             != SV64 )
            | ~ ( aElement0 @ SY107 ) )
        | ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[510]) ).

thf(536,plain,
    ! [SV65: $i] :
      ( ( ~ ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
             != SV65 )
            | ~ ( aElement0 @ ( sK7_W1 @ SV65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[511]) ).

thf(537,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
      | ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[512]) ).

thf(538,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[514]) ).

thf(539,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[515]) ).

thf(540,plain,
    ! [SV66: $i] :
      ( ( ~ ( aDivisorOf0 @ SV66 @ xa )
        | ~ ( aDivisorOf0 @ SV66 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
             != xc )
            | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[516]) ).

thf(541,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[517]) ).

thf(542,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[518]) ).

thf(543,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[519]) ).

thf(544,plain,
    ! [SV67: $i] :
      ( ( ~ ( aDivisorOf0 @ SV67 @ xa )
        | ~ ( aDivisorOf0 @ SV67 @ xb )
        | ( doDivides0 @ SV67 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[520]) ).

thf(545,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[521]) ).

thf(546,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[522]) ).

thf(547,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb )
      | ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[523]) ).

thf(548,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[524]) ).

thf(549,plain,
    ! [SV17: $i,SV30: $i,SV62: $i,SV58: $i] :
      ( ( ( aElement0 @ SV58 )
        = $false )
      | ( ( ~ ( aElement0 @ SV62 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[525]) ).

thf(550,plain,
    ! [SV19: $i,SV31: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV31 @ SV19 ) @ SV19 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV31 @ SV19 ) @ SV31 )
        = $false )
      | ( ( SV19 = SV31 )
        = $true )
      | ( ( aSet0 @ SV19 )
        = $false )
      | ( ( aSet0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[528]) ).

thf(551,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( aElement0 @ ( sK1_W2 @ SV32 @ SV20 ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[529]) ).

thf(552,plain,
    ! [SV20: $i,SV32: $i] :
      ( ( ( aElement0 @ ( sK2_SY72 @ SV32 @ SV20 ) )
        = $true )
      | ( ( SV32 = sz00 )
        = $true )
      | ( ( aElement0 @ SV20 )
        = $false )
      | ( ( aElement0 @ SV32 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[530]) ).

thf(553,plain,
    ! [SV53: $i,SV56: $i,SV59: $i] :
      ( ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ( ( sdtpldt0 @ SV56 @ SV59 )
           != SV53 ) )
        = $true )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[531]) ).

thf(554,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[532]) ).

thf(555,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[532]) ).

thf(556,plain,
    ! [SV60: $i,SV63: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV63 )
          = SV60 )
        = $false )
      | ( ( ~ ( aElement0 @ SV63 ) )
        = $true )
      | ( ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[533]) ).

thf(557,plain,
    ! [SV61: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
           != SV61 ) )
        = $false )
      | ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[534]) ).

thf(558,plain,
    ! [SV61: $i] :
      ( ( ( ~ ( aElement0 @ ( sK8_W1 @ SV61 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[534]) ).

thf(559,plain,
    ! [SV64: $i] :
      ( ( ( ! [SY107: $i] :
              ( ( ( sdtasdt0 @ xa @ SY107 )
               != SV64 )
              | ~ ( aElement0 @ SY107 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[535]) ).

thf(560,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
               != SV65 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV65 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[536]) ).

thf(561,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[537]) ).

thf(562,plain,
    ( ( ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[537]) ).

thf(563,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[538]) ).

thf(564,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[538]) ).

thf(565,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[539]) ).

thf(566,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[539]) ).

thf(567,plain,
    ! [SV66: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV66 @ xa )
          | ~ ( aDivisorOf0 @ SV66 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[540]) ).

thf(568,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[541]) ).

thf(569,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[541]) ).

thf(570,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[542]) ).

thf(571,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[542]) ).

thf(572,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[543]) ).

thf(573,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[543]) ).

thf(574,plain,
    ! [SV67: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV67 @ xa )
          | ~ ( aDivisorOf0 @ SV67 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV67 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[544]) ).

thf(575,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[545]) ).

thf(576,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[545]) ).

thf(577,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[546]) ).

thf(578,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[546]) ).

thf(579,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[547]) ).

thf(580,plain,
    ( ( ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[547]) ).

thf(581,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[548]) ).

thf(582,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[549]) ).

thf(583,plain,
    ! [SV53: $i,SV59: $i,SV56: $i] :
      ( ( ( ( sdtpldt0 @ SV56 @ SV59 )
          = SV53 )
        = $false )
      | ( ( aElementOf0 @ SV56 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( aElementOf0 @ SV59 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV53 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[553]) ).

thf(584,plain,
    ! [SV54: $i] :
      ( ( ( aElementOf0 @ ( sK9_W1 @ SV54 ) @ ( slsdtgt0 @ xa ) )
        = $true )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[554]) ).

thf(585,plain,
    ! [SV54: $i] :
      ( ( ( aElementOf0 @ ( sK10_SY73 @ SV54 ) @ ( slsdtgt0 @ xb ) )
        = $true )
      | ( ( aElementOf0 @ SV54 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[555]) ).

thf(586,plain,
    ! [SV60: $i,SV63: $i] :
      ( ( ( aElement0 @ SV63 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV63 )
          = SV60 )
        = $false )
      | ( ( aElementOf0 @ SV60 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[556]) ).

thf(587,plain,
    ! [SV61: $i] :
      ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV61 ) )
          = SV61 )
        = $true )
      | ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[557]) ).

thf(588,plain,
    ! [SV61: $i] :
      ( ( ( aElement0 @ ( sK8_W1 @ SV61 ) )
        = $true )
      | ( ( aElementOf0 @ SV61 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[558]) ).

thf(589,plain,
    ! [SV64: $i,SV68: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV68 )
           != SV64 )
          | ~ ( aElement0 @ SV68 ) )
        = $true )
      | ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[559]) ).

thf(590,plain,
    ! [SV65: $i] :
      ( ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
               != SV65 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV65 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[560]) ).

thf(591,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ xI )
                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElement0 @ SX1 )
                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[561]) ).

thf(592,plain,
    ( ( aSet0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[562]) ).

thf(593,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[563]) ).

thf(594,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[564]) ).

thf(595,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[565]) ).

thf(596,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[566]) ).

thf(597,plain,
    ! [SV66: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV66 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV66 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[567]) ).

thf(598,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[568]) ).

thf(599,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[569]) ).

thf(600,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[570]) ).

thf(601,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[571]) ).

thf(602,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[572]) ).

thf(603,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[573]) ).

thf(604,plain,
    ! [SV67: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV67 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV67 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV67 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[574]) ).

thf(605,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[575]) ).

thf(606,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[576]) ).

thf(607,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                             != xa )
                            | ~ ( aElement0 @ sK12_W0 ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ( doDivides0 @ xc @ xa ) )
          | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[577]) ).

thf(608,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[578]) ).

thf(609,plain,
    ( ( ( sdtasdt0 @ xc @ sK11_W0 )
      = xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[579]) ).

thf(610,plain,
    ( ( aElement0 @ sK11_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[580]) ).

thf(611,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[581]) ).

thf(612,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[581]) ).

thf(613,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[582]) ).

thf(614,plain,
    ! [SV64: $i,SV68: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV68 )
           != SV64 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV68 ) )
        = $true )
      | ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[589]) ).

thf(615,plain,
    ! [SV65: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
           != SV65 )
          | ~ ( aElement0 @ ( sK7_W1 @ SV65 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[590]) ).

thf(616,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[591]) ).

thf(617,plain,
    ! [SV69: $i] :
      ( ( ~ ( aElement0 @ SV69 )
        | ! [SY108: $i] :
            ( ( ( sdtasdt0 @ SV69 @ SY108 )
             != xa )
            | ~ ( aElement0 @ SY108 ) )
        | ~ ( aDivisorOf0 @ SV69 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
             != xc )
            | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[593]) ).

thf(618,plain,
    ! [SV70: $i] :
      ( ( ~ ( aElement0 @ SV70 )
        | ~ ( doDivides0 @ SV70 @ xa )
        | ~ ( aDivisorOf0 @ SV70 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
             != xc )
            | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[594]) ).

thf(619,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[595]) ).

thf(620,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[596]) ).

thf(621,plain,
    ! [SV66: $i] :
      ( ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV66 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[597]) ).

thf(622,plain,
    ! [SV71: $i] :
      ( ( ~ ( aDivisorOf0 @ SV71 @ xa )
        | ! [SY109: $i] :
            ( ( ( sdtasdt0 @ SV71 @ SY109 )
             != xb )
            | ~ ( aElement0 @ SY109 ) )
        | ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
             != xc )
            | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[598]) ).

thf(623,plain,
    ! [SV72: $i] :
      ( ( ~ ( aDivisorOf0 @ SV72 @ xa )
        | ~ ( doDivides0 @ SV72 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
             != xc )
            | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[599]) ).

thf(624,plain,
    ! [SV73: $i] :
      ( ( ~ ( aElement0 @ SV73 )
        | ! [SY110: $i] :
            ( ( ( sdtasdt0 @ SV73 @ SY110 )
             != xa )
            | ~ ( aElement0 @ SY110 ) )
        | ~ ( aDivisorOf0 @ SV73 @ xb )
        | ( doDivides0 @ SV73 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[600]) ).

thf(625,plain,
    ! [SV74: $i] :
      ( ( ~ ( aElement0 @ SV74 )
        | ~ ( doDivides0 @ SV74 @ xa )
        | ~ ( aDivisorOf0 @ SV74 @ xb )
        | ( doDivides0 @ SV74 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[601]) ).

thf(626,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[602]) ).

thf(627,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[603]) ).

thf(628,plain,
    ! [SV67: $i] :
      ( ( ( aDivisorOf0 @ SV67 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV67 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV67 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[604]) ).

thf(629,plain,
    ! [SV75: $i] :
      ( ( ~ ( aDivisorOf0 @ SV75 @ xa )
        | ! [SY111: $i] :
            ( ( ( sdtasdt0 @ SV75 @ SY111 )
             != xb )
            | ~ ( aElement0 @ SY111 ) )
        | ( doDivides0 @ SV75 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[605]) ).

thf(630,plain,
    ! [SV76: $i] :
      ( ( ~ ( aDivisorOf0 @ SV76 @ xa )
        | ~ ( doDivides0 @ SV76 @ xb )
        | ( doDivides0 @ SV76 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[606]) ).

thf(631,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) )
      | ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[607]) ).

thf(632,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) ) )
        = $true )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[611]) ).

thf(633,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV57 @ SV30 )
        = $true )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[612]) ).

thf(634,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[613]) ).

thf(635,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[613]) ).

thf(636,plain,
    ! [SV64: $i,SV68: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV68 )
          = SV64 )
        = $false )
      | ( ( ~ ( aElement0 @ SV68 ) )
        = $true )
      | ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[614]) ).

thf(637,plain,
    ! [SV65: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
           != SV65 ) )
        = $false )
      | ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[615]) ).

thf(638,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( aElement0 @ ( sK7_W1 @ SV65 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[615]) ).

thf(639,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[616]) ).

thf(640,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[616]) ).

thf(641,plain,
    ! [SV69: $i] :
      ( ( ( ~ ( aElement0 @ SV69 )
          | ! [SY108: $i] :
              ( ( ( sdtasdt0 @ SV69 @ SY108 )
               != xa )
              | ~ ( aElement0 @ SY108 ) )
          | ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[617]) ).

thf(642,plain,
    ! [SV70: $i] :
      ( ( ( ~ ( aElement0 @ SV70 )
          | ~ ( doDivides0 @ SV70 @ xa )
          | ~ ( aDivisorOf0 @ SV70 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[618]) ).

thf(643,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[619]) ).

thf(644,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[619]) ).

thf(645,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[620]) ).

thf(646,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[620]) ).

thf(647,plain,
    ! [SV66: $i] :
      ( ( ( aDivisorOf0 @ SV66 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[621]) ).

thf(648,plain,
    ! [SV71: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV71 @ xa )
          | ! [SY109: $i] :
              ( ( ( sdtasdt0 @ SV71 @ SY109 )
               != xb )
              | ~ ( aElement0 @ SY109 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[622]) ).

thf(649,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV72 @ xa )
          | ~ ( doDivides0 @ SV72 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[623]) ).

thf(650,plain,
    ! [SV73: $i] :
      ( ( ( ~ ( aElement0 @ SV73 )
          | ! [SY110: $i] :
              ( ( ( sdtasdt0 @ SV73 @ SY110 )
               != xa )
              | ~ ( aElement0 @ SY110 ) )
          | ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[624]) ).

thf(651,plain,
    ! [SV74: $i] :
      ( ( ( ~ ( aElement0 @ SV74 )
          | ~ ( doDivides0 @ SV74 @ xa )
          | ~ ( aDivisorOf0 @ SV74 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[625]) ).

thf(652,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[626]) ).

thf(653,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[626]) ).

thf(654,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[627]) ).

thf(655,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[627]) ).

thf(656,plain,
    ! [SV67: $i] :
      ( ( ( aDivisorOf0 @ SV67 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV67 @ xa )
        = $false )
      | ( ( doDivides0 @ SV67 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[628]) ).

thf(657,plain,
    ! [SV75: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV75 @ xa )
          | ! [SY111: $i] :
              ( ( ( sdtasdt0 @ SV75 @ SY111 )
               != xb )
              | ~ ( aElement0 @ SY111 ) ) )
        = $true )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[629]) ).

thf(658,plain,
    ! [SV76: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV76 @ xa )
          | ~ ( doDivides0 @ SV76 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV76 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[630]) ).

thf(659,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[631]) ).

thf(660,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[631]) ).

thf(661,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[632]) ).

thf(662,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) ) )
        = $true )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[634]) ).

thf(663,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV62 @ SV30 )
        = $true )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[635]) ).

thf(664,plain,
    ! [SV64: $i,SV68: $i] :
      ( ( ( aElement0 @ SV68 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV68 )
          = SV64 )
        = $false )
      | ( ( aElementOf0 @ SV64 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[636]) ).

thf(665,plain,
    ! [SV65: $i] :
      ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV65 ) )
          = SV65 )
        = $true )
      | ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[637]) ).

thf(666,plain,
    ! [SV65: $i] :
      ( ( ( aElement0 @ ( sK7_W1 @ SV65 ) )
        = $true )
      | ( ( aElementOf0 @ SV65 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[638]) ).

thf(667,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElementOf0 @ SX1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[639]) ).

thf(668,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElement0 @ SX1 )
              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[640]) ).

thf(669,plain,
    ! [SV69: $i] :
      ( ( ( ~ ( aElement0 @ SV69 )
          | ! [SY108: $i] :
              ( ( ( sdtasdt0 @ SV69 @ SY108 )
               != xa )
              | ~ ( aElement0 @ SY108 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[641]) ).

thf(670,plain,
    ! [SV70: $i] :
      ( ( ( ~ ( aElement0 @ SV70 )
          | ~ ( doDivides0 @ SV70 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV70 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[642]) ).

thf(671,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[643]) ).

thf(672,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[644]) ).

thf(673,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[645]) ).

thf(674,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[646]) ).

thf(675,plain,
    ! [SV66: $i] :
      ( ( ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
           != xc )
          | ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[647]) ).

thf(676,plain,
    ! [SV71: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV71 @ xa ) )
        = $true )
      | ( ( ! [SY109: $i] :
              ( ( ( sdtasdt0 @ SV71 @ SY109 )
               != xb )
              | ~ ( aElement0 @ SY109 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[648]) ).

thf(677,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV72 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV72 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[649]) ).

thf(678,plain,
    ! [SV73: $i] :
      ( ( ( ~ ( aElement0 @ SV73 )
          | ! [SY110: $i] :
              ( ( ( sdtasdt0 @ SV73 @ SY110 )
               != xa )
              | ~ ( aElement0 @ SY110 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[650]) ).

thf(679,plain,
    ! [SV74: $i] :
      ( ( ( ~ ( aElement0 @ SV74 )
          | ~ ( doDivides0 @ SV74 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV74 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[651]) ).

thf(680,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[652]) ).

thf(681,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[653]) ).

thf(682,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[654]) ).

thf(683,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[655]) ).

thf(684,plain,
    ! [SV75: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV75 @ xa ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ( ( sdtasdt0 @ SV75 @ SY111 )
               != xb )
              | ~ ( aElement0 @ SY111 ) ) )
        = $true )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[657]) ).

thf(685,plain,
    ! [SV76: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV76 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV76 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV76 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[658]) ).

thf(686,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                       != xa )
                      | ~ ( aElement0 @ sK12_W0 ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ( doDivides0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[659]) ).

thf(687,plain,
    ( ( aDivisorOf0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[660]) ).

thf(688,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[661]) ).

thf(689,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 ) )
        = $false )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[661]) ).

thf(690,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[662]) ).

thf(691,plain,
    ! [SV77: $i] :
      ( ( ~ ( aElementOf0 @ SV77 @ xI )
        | ! [SY112: $i] :
            ( ~ ( aElementOf0 @ SY112 @ xI )
            | ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SY112 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[667]) ).

thf(692,plain,
    ! [SV78: $i] :
      ( ( ~ ( aElementOf0 @ SV78 @ xI )
        | ! [SY113: $i] :
            ( ~ ( aElement0 @ SY113 )
            | ( aElementOf0 @ ( sdtasdt0 @ SY113 @ SV78 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[668]) ).

thf(693,plain,
    ! [SV69: $i] :
      ( ( ( ~ ( aElement0 @ SV69 ) )
        = $true )
      | ( ( ! [SY108: $i] :
              ( ( ( sdtasdt0 @ SV69 @ SY108 )
               != xa )
              | ~ ( aElement0 @ SY108 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[669]) ).

thf(694,plain,
    ! [SV70: $i] :
      ( ( ( ~ ( aElement0 @ SV70 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV70 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV70 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[670]) ).

thf(695,plain,
    ! [SV79: $i] :
      ( ( ~ ( aElement0 @ SV79 )
        | ! [SY114: $i] :
            ( ( ( sdtasdt0 @ SV79 @ SY114 )
             != xa )
            | ~ ( aElement0 @ SY114 ) )
        | ! [SY115: $i] :
            ( ( ( sdtasdt0 @ SV79 @ SY115 )
             != xb )
            | ~ ( aElement0 @ SY115 ) )
        | ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
             != xc )
            | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[671]) ).

thf(696,plain,
    ! [SV80: $i] :
      ( ( ~ ( aElement0 @ SV80 )
        | ~ ( doDivides0 @ SV80 @ xa )
        | ! [SY116: $i] :
            ( ( ( sdtasdt0 @ SV80 @ SY116 )
             != xb )
            | ~ ( aElement0 @ SY116 ) )
        | ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
             != xc )
            | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[672]) ).

thf(697,plain,
    ! [SV81: $i] :
      ( ( ~ ( aElement0 @ SV81 )
        | ! [SY117: $i] :
            ( ( ( sdtasdt0 @ SV81 @ SY117 )
             != xa )
            | ~ ( aElement0 @ SY117 ) )
        | ~ ( doDivides0 @ SV81 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
             != xc )
            | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[673]) ).

thf(698,plain,
    ! [SV82: $i] :
      ( ( ~ ( aElement0 @ SV82 )
        | ~ ( doDivides0 @ SV82 @ xa )
        | ~ ( doDivides0 @ SV82 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
             != xc )
            | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[674]) ).

thf(699,plain,
    ! [SV66: $i] :
      ( ( ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[675]) ).

thf(700,plain,
    ! [SV66: $i] :
      ( ( ( ~ ( aElement0 @ ( sK15_W1 @ SV66 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[675]) ).

thf(701,plain,
    ! [SV71: $i] :
      ( ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ! [SY109: $i] :
              ( ( ( sdtasdt0 @ SV71 @ SY109 )
               != xb )
              | ~ ( aElement0 @ SY109 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[676]) ).

thf(702,plain,
    ! [SV72: $i] :
      ( ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV72 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[677]) ).

thf(703,plain,
    ! [SV73: $i] :
      ( ( ( ~ ( aElement0 @ SV73 ) )
        = $true )
      | ( ( ! [SY110: $i] :
              ( ( ( sdtasdt0 @ SV73 @ SY110 )
               != xa )
              | ~ ( aElement0 @ SY110 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[678]) ).

thf(704,plain,
    ! [SV74: $i] :
      ( ( ( ~ ( aElement0 @ SV74 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV74 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV74 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[679]) ).

thf(705,plain,
    ! [SV83: $i] :
      ( ( ~ ( aElement0 @ SV83 )
        | ! [SY118: $i] :
            ( ( ( sdtasdt0 @ SV83 @ SY118 )
             != xa )
            | ~ ( aElement0 @ SY118 ) )
        | ! [SY119: $i] :
            ( ( ( sdtasdt0 @ SV83 @ SY119 )
             != xb )
            | ~ ( aElement0 @ SY119 ) )
        | ( doDivides0 @ SV83 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[680]) ).

thf(706,plain,
    ! [SV84: $i] :
      ( ( ~ ( aElement0 @ SV84 )
        | ~ ( doDivides0 @ SV84 @ xa )
        | ! [SY120: $i] :
            ( ( ( sdtasdt0 @ SV84 @ SY120 )
             != xb )
            | ~ ( aElement0 @ SY120 ) )
        | ( doDivides0 @ SV84 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[681]) ).

thf(707,plain,
    ! [SV85: $i] :
      ( ( ~ ( aElement0 @ SV85 )
        | ! [SY121: $i] :
            ( ( ( sdtasdt0 @ SV85 @ SY121 )
             != xa )
            | ~ ( aElement0 @ SY121 ) )
        | ~ ( doDivides0 @ SV85 @ xb )
        | ( doDivides0 @ SV85 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[682]) ).

thf(708,plain,
    ! [SV86: $i] :
      ( ( ~ ( aElement0 @ SV86 )
        | ~ ( doDivides0 @ SV86 @ xa )
        | ~ ( doDivides0 @ SV86 @ xb )
        | ( doDivides0 @ SV86 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[683]) ).

thf(709,plain,
    ! [SV75: $i] :
      ( ( ( aDivisorOf0 @ SV75 @ xa )
        = $false )
      | ( ( ! [SY111: $i] :
              ( ( ( sdtasdt0 @ SV75 @ SY111 )
               != xb )
              | ~ ( aElement0 @ SY111 ) ) )
        = $true )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[684]) ).

thf(710,plain,
    ! [SV76: $i] :
      ( ( ( aDivisorOf0 @ SV76 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV76 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV76 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[685]) ).

thf(711,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[686]) ).

thf(712,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[688]) ).

thf(713,plain,
    ! [SV17: $i,SV30: $i,SV55: $i,SV57: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV57 @ SV55 @ SV30 @ SV17 ) @ SV55 @ SV17 )
        = $true )
      | ( ( aElement0 @ SV55 )
        = $false )
      | ( ( aElement0 @ SV57 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[689]) ).

thf(714,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[690]) ).

thf(715,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 ) )
        = $false )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[690]) ).

thf(716,plain,
    ! [SV77: $i] :
      ( ( ( ~ ( aElementOf0 @ SV77 @ xI ) )
        = $true )
      | ( ( ! [SY112: $i] :
              ( ~ ( aElementOf0 @ SY112 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SY112 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[691]) ).

thf(717,plain,
    ! [SV78: $i] :
      ( ( ( ~ ( aElementOf0 @ SV78 @ xI ) )
        = $true )
      | ( ( ! [SY113: $i] :
              ( ~ ( aElement0 @ SY113 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY113 @ SV78 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[692]) ).

thf(718,plain,
    ! [SV69: $i] :
      ( ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ! [SY108: $i] :
              ( ( ( sdtasdt0 @ SV69 @ SY108 )
               != xa )
              | ~ ( aElement0 @ SY108 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[693]) ).

thf(719,plain,
    ! [SV70: $i] :
      ( ( ( aElement0 @ SV70 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV70 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV70 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[694]) ).

thf(720,plain,
    ! [SV79: $i] :
      ( ( ( ~ ( aElement0 @ SV79 )
          | ! [SY114: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY114 )
               != xa )
              | ~ ( aElement0 @ SY114 ) )
          | ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[695]) ).

thf(721,plain,
    ! [SV80: $i] :
      ( ( ( ~ ( aElement0 @ SV80 )
          | ~ ( doDivides0 @ SV80 @ xa )
          | ! [SY116: $i] :
              ( ( ( sdtasdt0 @ SV80 @ SY116 )
               != xb )
              | ~ ( aElement0 @ SY116 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[696]) ).

thf(722,plain,
    ! [SV81: $i] :
      ( ( ( ~ ( aElement0 @ SV81 )
          | ! [SY117: $i] :
              ( ( ( sdtasdt0 @ SV81 @ SY117 )
               != xa )
              | ~ ( aElement0 @ SY117 ) )
          | ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[697]) ).

thf(723,plain,
    ! [SV82: $i] :
      ( ( ( ~ ( aElement0 @ SV82 )
          | ~ ( doDivides0 @ SV82 @ xa )
          | ~ ( doDivides0 @ SV82 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[698]) ).

thf(724,plain,
    ! [SV66: $i] :
      ( ( ( ( sdtasdt0 @ SV66 @ ( sK15_W1 @ SV66 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[699]) ).

thf(725,plain,
    ! [SV66: $i] :
      ( ( ( aElement0 @ ( sK15_W1 @ SV66 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV66 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV66 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[700]) ).

thf(726,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( ( sdtasdt0 @ SV71 @ SV87 )
           != xb )
          | ~ ( aElement0 @ SV87 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[701]) ).

thf(727,plain,
    ! [SV72: $i] :
      ( ( ( doDivides0 @ SV72 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[702]) ).

thf(728,plain,
    ! [SV73: $i] :
      ( ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ! [SY110: $i] :
              ( ( ( sdtasdt0 @ SV73 @ SY110 )
               != xa )
              | ~ ( aElement0 @ SY110 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[703]) ).

thf(729,plain,
    ! [SV74: $i] :
      ( ( ( aElement0 @ SV74 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV74 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV74 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[704]) ).

thf(730,plain,
    ! [SV83: $i] :
      ( ( ( ~ ( aElement0 @ SV83 )
          | ! [SY118: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY118 )
               != xa )
              | ~ ( aElement0 @ SY118 ) )
          | ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[705]) ).

thf(731,plain,
    ! [SV84: $i] :
      ( ( ( ~ ( aElement0 @ SV84 )
          | ~ ( doDivides0 @ SV84 @ xa )
          | ! [SY120: $i] :
              ( ( ( sdtasdt0 @ SV84 @ SY120 )
               != xb )
              | ~ ( aElement0 @ SY120 ) ) )
        = $true )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[706]) ).

thf(732,plain,
    ! [SV85: $i] :
      ( ( ( ~ ( aElement0 @ SV85 )
          | ! [SY121: $i] :
              ( ( ( sdtasdt0 @ SV85 @ SY121 )
               != xa )
              | ~ ( aElement0 @ SY121 ) )
          | ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[707]) ).

thf(733,plain,
    ! [SV86: $i] :
      ( ( ( ~ ( aElement0 @ SV86 )
          | ~ ( doDivides0 @ SV86 @ xa )
          | ~ ( doDivides0 @ SV86 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[708]) ).

thf(734,plain,
    ! [SV88: $i,SV75: $i] :
      ( ( ( ( ( sdtasdt0 @ SV75 @ SV88 )
           != xb )
          | ~ ( aElement0 @ SV88 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV75 @ xa )
        = $false )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[709]) ).

thf(735,plain,
    ! [SV76: $i] :
      ( ( ( doDivides0 @ SV76 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV76 @ xa )
        = $false )
      | ( ( doDivides0 @ SV76 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[710]) ).

thf(736,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[711]) ).

thf(737,plain,
    ( ( ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[711]) ).

thf(738,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) )
        = $true )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[714]) ).

thf(739,plain,
    ! [SV17: $i,SV30: $i,SV58: $i,SV62: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV62 @ SV58 @ SV30 @ SV17 ) @ SV58 @ SV17 )
        = $true )
      | ( ( aElement0 @ SV58 )
        = $false )
      | ( ( aElement0 @ SV62 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV30 @ SV17 ) @ ( sdtpldt1 @ SV17 @ SV30 ) )
        = $false )
      | ( ( aIdeal0 @ SV17 )
        = $false )
      | ( ( aIdeal0 @ SV30 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[715]) ).

thf(740,plain,
    ! [SV77: $i] :
      ( ( ( aElementOf0 @ SV77 @ xI )
        = $false )
      | ( ( ! [SY112: $i] :
              ( ~ ( aElementOf0 @ SY112 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SY112 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[716]) ).

thf(741,plain,
    ! [SV78: $i] :
      ( ( ( aElementOf0 @ SV78 @ xI )
        = $false )
      | ( ( ! [SY113: $i] :
              ( ~ ( aElement0 @ SY113 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY113 @ SV78 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[717]) ).

thf(742,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( ( sdtasdt0 @ SV69 @ SV89 )
           != xa )
          | ~ ( aElement0 @ SV89 ) )
        = $true )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[718]) ).

thf(743,plain,
    ! [SV70: $i] :
      ( ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV70 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[719]) ).

thf(744,plain,
    ! [SV79: $i] :
      ( ( ( ~ ( aElement0 @ SV79 )
          | ! [SY114: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY114 )
               != xa )
              | ~ ( aElement0 @ SY114 ) ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[720]) ).

thf(745,plain,
    ! [SV80: $i] :
      ( ( ( ~ ( aElement0 @ SV80 )
          | ~ ( doDivides0 @ SV80 @ xa ) )
        = $true )
      | ( ( ! [SY116: $i] :
              ( ( ( sdtasdt0 @ SV80 @ SY116 )
               != xb )
              | ~ ( aElement0 @ SY116 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[721]) ).

thf(746,plain,
    ! [SV81: $i] :
      ( ( ( ~ ( aElement0 @ SV81 )
          | ! [SY117: $i] :
              ( ( ( sdtasdt0 @ SV81 @ SY117 )
               != xa )
              | ~ ( aElement0 @ SY117 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[722]) ).

thf(747,plain,
    ! [SV82: $i] :
      ( ( ( ~ ( aElement0 @ SV82 )
          | ~ ( doDivides0 @ SV82 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV82 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[723]) ).

thf(748,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( ( sdtasdt0 @ SV71 @ SV87 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV87 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[726]) ).

thf(749,plain,
    ! [SV72: $i] :
      ( ( ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
           != xc )
          | ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( doDivides0 @ SV72 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[727]) ).

thf(750,plain,
    ! [SV90: $i,SV73: $i] :
      ( ( ( ( ( sdtasdt0 @ SV73 @ SV90 )
           != xa )
          | ~ ( aElement0 @ SV90 ) )
        = $true )
      | ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[728]) ).

thf(751,plain,
    ! [SV74: $i] :
      ( ( ( doDivides0 @ SV74 @ xa )
        = $false )
      | ( ( aElement0 @ SV74 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV74 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[729]) ).

thf(752,plain,
    ! [SV83: $i] :
      ( ( ( ~ ( aElement0 @ SV83 )
          | ! [SY118: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY118 )
               != xa )
              | ~ ( aElement0 @ SY118 ) ) )
        = $true )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[730]) ).

thf(753,plain,
    ! [SV84: $i] :
      ( ( ( ~ ( aElement0 @ SV84 )
          | ~ ( doDivides0 @ SV84 @ xa ) )
        = $true )
      | ( ( ! [SY120: $i] :
              ( ( ( sdtasdt0 @ SV84 @ SY120 )
               != xb )
              | ~ ( aElement0 @ SY120 ) ) )
        = $true )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[731]) ).

thf(754,plain,
    ! [SV85: $i] :
      ( ( ( ~ ( aElement0 @ SV85 )
          | ! [SY121: $i] :
              ( ( ( sdtasdt0 @ SV85 @ SY121 )
               != xa )
              | ~ ( aElement0 @ SY121 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[732]) ).

thf(755,plain,
    ! [SV86: $i] :
      ( ( ( ~ ( aElement0 @ SV86 )
          | ~ ( doDivides0 @ SV86 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV86 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[733]) ).

thf(756,plain,
    ! [SV88: $i,SV75: $i] :
      ( ( ( ( ( sdtasdt0 @ SV75 @ SV88 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV88 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV75 @ xa )
        = $false )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[734]) ).

thf(757,plain,
    ( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                 != xa )
                | ~ ( aElement0 @ sK12_W0 ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[736]) ).

thf(758,plain,
    ( ( doDivides0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[737]) ).

thf(759,plain,
    ! [SV77: $i,SV91: $i] :
      ( ( ( ~ ( aElementOf0 @ SV91 @ xI )
          | ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SV91 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV77 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[740]) ).

thf(760,plain,
    ! [SV78: $i,SV92: $i] :
      ( ( ( ~ ( aElement0 @ SV92 )
          | ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV78 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV78 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[741]) ).

thf(761,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( ( sdtasdt0 @ SV69 @ SV89 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV89 ) )
        = $true )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[742]) ).

thf(762,plain,
    ! [SV70: $i] :
      ( ( ( aDivisorOf0 @ SV70 @ xb )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[743]) ).

thf(763,plain,
    ! [SV79: $i] :
      ( ( ( ~ ( aElement0 @ SV79 ) )
        = $true )
      | ( ( ! [SY114: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY114 )
               != xa )
              | ~ ( aElement0 @ SY114 ) ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[744]) ).

thf(764,plain,
    ! [SV80: $i] :
      ( ( ( ~ ( aElement0 @ SV80 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV80 @ xa ) )
        = $true )
      | ( ( ! [SY116: $i] :
              ( ( ( sdtasdt0 @ SV80 @ SY116 )
               != xb )
              | ~ ( aElement0 @ SY116 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[745]) ).

thf(765,plain,
    ! [SV81: $i] :
      ( ( ( ~ ( aElement0 @ SV81 ) )
        = $true )
      | ( ( ! [SY117: $i] :
              ( ( ( sdtasdt0 @ SV81 @ SY117 )
               != xa )
              | ~ ( aElement0 @ SY117 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[746]) ).

thf(766,plain,
    ! [SV82: $i] :
      ( ( ( ~ ( aElement0 @ SV82 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV82 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV82 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[747]) ).

thf(767,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV87 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[748]) ).

thf(768,plain,
    ! [SV72: $i] :
      ( ( ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( doDivides0 @ SV72 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[749]) ).

thf(769,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( aElement0 @ ( sK13_W1 @ SV72 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( doDivides0 @ SV72 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[749]) ).

thf(770,plain,
    ! [SV90: $i,SV73: $i] :
      ( ( ( ( ( sdtasdt0 @ SV73 @ SV90 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV90 ) )
        = $true )
      | ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[750]) ).

thf(771,plain,
    ! [SV74: $i] :
      ( ( ( aDivisorOf0 @ SV74 @ xb )
        = $false )
      | ( ( aElement0 @ SV74 )
        = $false )
      | ( ( doDivides0 @ SV74 @ xa )
        = $false )
      | ( ( doDivides0 @ SV74 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[751]) ).

thf(772,plain,
    ! [SV83: $i] :
      ( ( ( ~ ( aElement0 @ SV83 ) )
        = $true )
      | ( ( ! [SY118: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY118 )
               != xa )
              | ~ ( aElement0 @ SY118 ) ) )
        = $true )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[752]) ).

thf(773,plain,
    ! [SV84: $i] :
      ( ( ( ~ ( aElement0 @ SV84 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV84 @ xa ) )
        = $true )
      | ( ( ! [SY120: $i] :
              ( ( ( sdtasdt0 @ SV84 @ SY120 )
               != xb )
              | ~ ( aElement0 @ SY120 ) ) )
        = $true )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[753]) ).

thf(774,plain,
    ! [SV85: $i] :
      ( ( ( ~ ( aElement0 @ SV85 ) )
        = $true )
      | ( ( ! [SY121: $i] :
              ( ( ( sdtasdt0 @ SV85 @ SY121 )
               != xa )
              | ~ ( aElement0 @ SY121 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[754]) ).

thf(775,plain,
    ! [SV86: $i] :
      ( ( ( ~ ( aElement0 @ SV86 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV86 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV86 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[755]) ).

thf(776,plain,
    ! [SV88: $i,SV75: $i] :
      ( ( ( ( sdtasdt0 @ SV75 @ SV88 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV88 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV75 @ xa )
        = $false )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[756]) ).

thf(777,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[757]) ).

thf(778,plain,
    ! [SV77: $i,SV91: $i] :
      ( ( ( ~ ( aElementOf0 @ SV91 @ xI ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SV91 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV77 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[759]) ).

thf(779,plain,
    ! [SV78: $i,SV92: $i] :
      ( ( ( ~ ( aElement0 @ SV92 ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV78 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV78 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[760]) ).

thf(780,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV89 ) )
        = $true )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[761]) ).

thf(781,plain,
    ! [SV70: $i] :
      ( ( ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
           != xc )
          | ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) )
        = $false )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( aDivisorOf0 @ SV70 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[762]) ).

thf(782,plain,
    ! [SV79: $i] :
      ( ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ! [SY114: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY114 )
               != xa )
              | ~ ( aElement0 @ SY114 ) ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[763]) ).

thf(783,plain,
    ! [SV80: $i] :
      ( ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV80 @ xa ) )
        = $true )
      | ( ( ! [SY116: $i] :
              ( ( ( sdtasdt0 @ SV80 @ SY116 )
               != xb )
              | ~ ( aElement0 @ SY116 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[764]) ).

thf(784,plain,
    ! [SV81: $i] :
      ( ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ! [SY117: $i] :
              ( ( ( sdtasdt0 @ SV81 @ SY117 )
               != xa )
              | ~ ( aElement0 @ SY117 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[765]) ).

thf(785,plain,
    ! [SV82: $i] :
      ( ( ( aElement0 @ SV82 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV82 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV82 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[766]) ).

thf(786,plain,
    ! [SV71: $i,SV87: $i] :
      ( ( ( aElement0 @ SV87 )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[767]) ).

thf(787,plain,
    ! [SV72: $i] :
      ( ( ( ( sdtasdt0 @ SV72 @ ( sK13_W1 @ SV72 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( doDivides0 @ SV72 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[768]) ).

thf(788,plain,
    ! [SV72: $i] :
      ( ( ( aElement0 @ ( sK13_W1 @ SV72 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV72 @ xa )
        = $false )
      | ( ( doDivides0 @ SV72 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[769]) ).

thf(789,plain,
    ! [SV90: $i,SV73: $i] :
      ( ( ( ( sdtasdt0 @ SV73 @ SV90 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV90 ) )
        = $true )
      | ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[770]) ).

thf(790,plain,
    ! [SV83: $i] :
      ( ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ! [SY118: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY118 )
               != xa )
              | ~ ( aElement0 @ SY118 ) ) )
        = $true )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[772]) ).

thf(791,plain,
    ! [SV84: $i] :
      ( ( ( aElement0 @ SV84 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV84 @ xa ) )
        = $true )
      | ( ( ! [SY120: $i] :
              ( ( ( sdtasdt0 @ SV84 @ SY120 )
               != xb )
              | ~ ( aElement0 @ SY120 ) ) )
        = $true )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[773]) ).

thf(792,plain,
    ! [SV85: $i] :
      ( ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ! [SY121: $i] :
              ( ( ( sdtasdt0 @ SV85 @ SY121 )
               != xa )
              | ~ ( aElement0 @ SY121 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[774]) ).

thf(793,plain,
    ! [SV86: $i] :
      ( ( ( aElement0 @ SV86 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV86 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV86 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[775]) ).

thf(794,plain,
    ! [SV75: $i,SV88: $i] :
      ( ( ( aElement0 @ SV88 )
        = $false )
      | ( ( ( sdtasdt0 @ SV75 @ SV88 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV75 @ xa )
        = $false )
      | ( ( doDivides0 @ SV75 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[776]) ).

thf(795,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[777]) ).

thf(796,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[777]) ).

thf(797,plain,
    ! [SV77: $i,SV91: $i] :
      ( ( ( aElementOf0 @ SV91 @ xI )
        = $false )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV77 @ SV91 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV77 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[778]) ).

thf(798,plain,
    ! [SV78: $i,SV92: $i] :
      ( ( ( aElement0 @ SV92 )
        = $false )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV92 @ SV78 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV78 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[779]) ).

thf(799,plain,
    ! [SV69: $i,SV89: $i] :
      ( ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV69 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[780]) ).

thf(800,plain,
    ! [SV70: $i] :
      ( ( ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( aDivisorOf0 @ SV70 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[781]) ).

thf(801,plain,
    ! [SV70: $i] :
      ( ( ( ~ ( aElement0 @ ( sK20_W1 @ SV70 ) ) )
        = $false )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( aDivisorOf0 @ SV70 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[781]) ).

thf(802,plain,
    ! [SV93: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ SV93 )
           != xa )
          | ~ ( aElement0 @ SV93 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[782]) ).

thf(803,plain,
    ! [SV80: $i] :
      ( ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ! [SY116: $i] :
              ( ( ( sdtasdt0 @ SV80 @ SY116 )
               != xb )
              | ~ ( aElement0 @ SY116 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[783]) ).

thf(804,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( ( sdtasdt0 @ SV81 @ SV94 )
           != xa )
          | ~ ( aElement0 @ SV94 ) )
        = $true )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[784]) ).

thf(805,plain,
    ! [SV82: $i] :
      ( ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV82 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[785]) ).

thf(806,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
           != xc )
          | ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV87 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[786]) ).

thf(807,plain,
    ! [SV73: $i,SV90: $i] :
      ( ( ( aElement0 @ SV90 )
        = $false )
      | ( ( ( sdtasdt0 @ SV73 @ SV90 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV73 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[789]) ).

thf(808,plain,
    ! [SV95: $i,SV83: $i] :
      ( ( ( ( ( sdtasdt0 @ SV83 @ SV95 )
           != xa )
          | ~ ( aElement0 @ SV95 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[790]) ).

thf(809,plain,
    ! [SV84: $i] :
      ( ( ( doDivides0 @ SV84 @ xa )
        = $false )
      | ( ( aElement0 @ SV84 )
        = $false )
      | ( ( ! [SY120: $i] :
              ( ( ( sdtasdt0 @ SV84 @ SY120 )
               != xb )
              | ~ ( aElement0 @ SY120 ) ) )
        = $true )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[791]) ).

thf(810,plain,
    ! [SV96: $i,SV85: $i] :
      ( ( ( ( ( sdtasdt0 @ SV85 @ SV96 )
           != xa )
          | ~ ( aElement0 @ SV96 ) )
        = $true )
      | ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[792]) ).

thf(811,plain,
    ! [SV86: $i] :
      ( ( ( doDivides0 @ SV86 @ xa )
        = $false )
      | ( ( aElement0 @ SV86 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV86 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[793]) ).

thf(812,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
           != xa )
          | ~ ( aElement0 @ sK12_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[795]) ).

thf(813,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[796]) ).

thf(814,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( aDivisorOf0 @ SV69 @ xb )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[799]) ).

thf(815,plain,
    ! [SV70: $i] :
      ( ( ( ( sdtasdt0 @ SV70 @ ( sK20_W1 @ SV70 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( aDivisorOf0 @ SV70 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[800]) ).

thf(816,plain,
    ! [SV70: $i] :
      ( ( ( aElement0 @ ( sK20_W1 @ SV70 ) )
        = $true )
      | ( ( doDivides0 @ SV70 @ xa )
        = $false )
      | ( ( aElement0 @ SV70 )
        = $false )
      | ( ( aDivisorOf0 @ SV70 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[801]) ).

thf(817,plain,
    ! [SV93: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ SV93 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV93 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[802]) ).

thf(818,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( ( sdtasdt0 @ SV80 @ SV97 )
           != xb )
          | ~ ( aElement0 @ SV97 ) )
        = $true )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[803]) ).

thf(819,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( ( sdtasdt0 @ SV81 @ SV94 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV94 ) )
        = $true )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[804]) ).

thf(820,plain,
    ! [SV82: $i] :
      ( ( ( doDivides0 @ SV82 @ xb )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[805]) ).

thf(821,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV87 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[806]) ).

thf(822,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ~ ( aElement0 @ ( sK14_W1 @ SV71 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV87 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[806]) ).

thf(823,plain,
    ! [SV90: $i,SV73: $i] :
      ( ( ( aDivisorOf0 @ SV73 @ xb )
        = $false )
      | ( ( aElement0 @ SV73 )
        = $false )
      | ( ( ( sdtasdt0 @ SV73 @ SV90 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV90 )
        = $false )
      | ( ( doDivides0 @ SV73 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[807]) ).

thf(824,plain,
    ! [SV95: $i,SV83: $i] :
      ( ( ( ( ( sdtasdt0 @ SV83 @ SV95 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV95 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[808]) ).

thf(825,plain,
    ! [SV98: $i,SV84: $i] :
      ( ( ( ( ( sdtasdt0 @ SV84 @ SV98 )
           != xb )
          | ~ ( aElement0 @ SV98 ) )
        = $true )
      | ( ( aElement0 @ SV84 )
        = $false )
      | ( ( doDivides0 @ SV84 @ xa )
        = $false )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[809]) ).

thf(826,plain,
    ! [SV96: $i,SV85: $i] :
      ( ( ( ( ( sdtasdt0 @ SV85 @ SV96 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV96 ) )
        = $true )
      | ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[810]) ).

thf(827,plain,
    ! [SV86: $i] :
      ( ( ( doDivides0 @ SV86 @ xb )
        = $false )
      | ( ( aElement0 @ SV86 )
        = $false )
      | ( ( doDivides0 @ SV86 @ xa )
        = $false )
      | ( ( doDivides0 @ SV86 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[811]) ).

thf(828,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa )
      | ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[812]) ).

thf(829,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
           != xc )
          | ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) )
        = $false )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( aDivisorOf0 @ SV69 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[814]) ).

thf(830,plain,
    ! [SV93: $i,SV79: $i] :
      ( ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV93 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[817]) ).

thf(831,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( ( sdtasdt0 @ SV80 @ SV97 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV97 ) )
        = $true )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[818]) ).

thf(832,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV94 ) )
        = $true )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[819]) ).

thf(833,plain,
    ! [SV82: $i] :
      ( ( ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
           != xc )
          | ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) )
        = $false )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[820]) ).

thf(834,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( ( sdtasdt0 @ SV71 @ ( sK14_W1 @ SV71 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV87 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[821]) ).

thf(835,plain,
    ! [SV87: $i,SV71: $i] :
      ( ( ( aElement0 @ ( sK14_W1 @ SV71 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV71 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV71 @ SV87 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV87 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[822]) ).

thf(836,plain,
    ! [SV95: $i,SV83: $i] :
      ( ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV95 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[824]) ).

thf(837,plain,
    ! [SV98: $i,SV84: $i] :
      ( ( ( ( ( sdtasdt0 @ SV84 @ SV98 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV98 ) )
        = $true )
      | ( ( aElement0 @ SV84 )
        = $false )
      | ( ( doDivides0 @ SV84 @ xa )
        = $false )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[825]) ).

thf(838,plain,
    ! [SV96: $i,SV85: $i] :
      ( ( ( ( sdtasdt0 @ SV85 @ SV96 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV96 ) )
        = $true )
      | ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[826]) ).

thf(839,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[828]) ).

thf(840,plain,
    ( ( ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[828]) ).

thf(841,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( aDivisorOf0 @ SV69 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[829]) ).

thf(842,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ~ ( aElement0 @ ( sK21_W1 @ SV69 ) ) )
        = $false )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( aDivisorOf0 @ SV69 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[829]) ).

thf(843,plain,
    ! [SV79: $i,SV93: $i] :
      ( ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ( ( sdtasdt0 @ SV79 @ SY115 )
               != xb )
              | ~ ( aElement0 @ SY115 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[830]) ).

thf(844,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV97 ) )
        = $true )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[831]) ).

thf(845,plain,
    ! [SV81: $i,SV94: $i] :
      ( ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV81 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[832]) ).

thf(846,plain,
    ! [SV82: $i] :
      ( ( ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[833]) ).

thf(847,plain,
    ! [SV82: $i] :
      ( ( ( ~ ( aElement0 @ ( sK16_W1 @ SV82 ) ) )
        = $false )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[833]) ).

thf(848,plain,
    ! [SV83: $i,SV95: $i] :
      ( ( ( aElement0 @ SV95 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ! [SY119: $i] :
              ( ( ( sdtasdt0 @ SV83 @ SY119 )
               != xb )
              | ~ ( aElement0 @ SY119 ) ) )
        = $true )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[836]) ).

thf(849,plain,
    ! [SV98: $i,SV84: $i] :
      ( ( ( ( sdtasdt0 @ SV84 @ SV98 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV98 ) )
        = $true )
      | ( ( aElement0 @ SV84 )
        = $false )
      | ( ( doDivides0 @ SV84 @ xa )
        = $false )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[837]) ).

thf(850,plain,
    ! [SV85: $i,SV96: $i] :
      ( ( ( aElement0 @ SV96 )
        = $false )
      | ( ( ( sdtasdt0 @ SV85 @ SV96 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV85 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[838]) ).

thf(851,plain,
    ( ( ( sdtasdt0 @ xc @ sK12_W0 )
      = xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[839]) ).

thf(852,plain,
    ( ( aElement0 @ sK12_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[840]) ).

thf(853,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( ( sdtasdt0 @ SV69 @ ( sK21_W1 @ SV69 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( aDivisorOf0 @ SV69 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[841]) ).

thf(854,plain,
    ! [SV89: $i,SV69: $i] :
      ( ( ( aElement0 @ ( sK21_W1 @ SV69 ) )
        = $true )
      | ( ( aElement0 @ SV89 )
        = $false )
      | ( ( ( sdtasdt0 @ SV69 @ SV89 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV69 )
        = $false )
      | ( ( aDivisorOf0 @ SV69 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[842]) ).

thf(855,plain,
    ! [SV93: $i,SV99: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ SV99 )
           != xb )
          | ~ ( aElement0 @ SV99 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[843]) ).

thf(856,plain,
    ! [SV80: $i,SV97: $i] :
      ( ( ( aElement0 @ SV97 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[844]) ).

thf(857,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( doDivides0 @ SV81 @ xb )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[845]) ).

thf(858,plain,
    ! [SV82: $i] :
      ( ( ( ( sdtasdt0 @ SV82 @ ( sK16_W1 @ SV82 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[846]) ).

thf(859,plain,
    ! [SV82: $i] :
      ( ( ( aElement0 @ ( sK16_W1 @ SV82 ) )
        = $true )
      | ( ( doDivides0 @ SV82 @ xa )
        = $false )
      | ( ( aElement0 @ SV82 )
        = $false )
      | ( ( doDivides0 @ SV82 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[847]) ).

thf(860,plain,
    ! [SV95: $i,SV100: $i,SV83: $i] :
      ( ( ( ( ( sdtasdt0 @ SV83 @ SV100 )
           != xb )
          | ~ ( aElement0 @ SV100 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV95 )
        = $false )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[848]) ).

thf(861,plain,
    ! [SV84: $i,SV98: $i] :
      ( ( ( aElement0 @ SV98 )
        = $false )
      | ( ( ( sdtasdt0 @ SV84 @ SV98 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV84 )
        = $false )
      | ( ( doDivides0 @ SV84 @ xa )
        = $false )
      | ( ( doDivides0 @ SV84 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[849]) ).

thf(862,plain,
    ! [SV96: $i,SV85: $i] :
      ( ( ( doDivides0 @ SV85 @ xb )
        = $false )
      | ( ( aElement0 @ SV85 )
        = $false )
      | ( ( ( sdtasdt0 @ SV85 @ SV96 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV96 )
        = $false )
      | ( ( doDivides0 @ SV85 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[850]) ).

thf(863,plain,
    ! [SV93: $i,SV99: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ SV99 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV99 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[855]) ).

thf(864,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
           != xc )
          | ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV97 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[856]) ).

thf(865,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
           != xc )
          | ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) )
        = $false )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( doDivides0 @ SV81 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[857]) ).

thf(866,plain,
    ! [SV95: $i,SV100: $i,SV83: $i] :
      ( ( ( ( ( sdtasdt0 @ SV83 @ SV100 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV100 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV95 )
        = $false )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[860]) ).

thf(867,plain,
    ! [SV93: $i,SV99: $i,SV79: $i] :
      ( ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV99 ) )
        = $true )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[863]) ).

thf(868,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV97 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[864]) ).

thf(869,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ~ ( aElement0 @ ( sK18_W1 @ SV80 ) ) )
        = $false )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV97 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[864]) ).

thf(870,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( doDivides0 @ SV81 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[865]) ).

thf(871,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ~ ( aElement0 @ ( sK17_W1 @ SV81 ) ) )
        = $false )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( doDivides0 @ SV81 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[865]) ).

thf(872,plain,
    ! [SV95: $i,SV100: $i,SV83: $i] :
      ( ( ( ( sdtasdt0 @ SV83 @ SV100 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV100 ) )
        = $true )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV95 )
        = $false )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[866]) ).

thf(873,plain,
    ! [SV93: $i,SV79: $i,SV99: $i] :
      ( ( ( aElement0 @ SV99 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[867]) ).

thf(874,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( ( sdtasdt0 @ SV80 @ ( sK18_W1 @ SV80 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV97 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[868]) ).

thf(875,plain,
    ! [SV97: $i,SV80: $i] :
      ( ( ( aElement0 @ ( sK18_W1 @ SV80 ) )
        = $true )
      | ( ( doDivides0 @ SV80 @ xa )
        = $false )
      | ( ( aElement0 @ SV80 )
        = $false )
      | ( ( ( sdtasdt0 @ SV80 @ SV97 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV97 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[869]) ).

thf(876,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( ( sdtasdt0 @ SV81 @ ( sK17_W1 @ SV81 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( doDivides0 @ SV81 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[870]) ).

thf(877,plain,
    ! [SV94: $i,SV81: $i] :
      ( ( ( aElement0 @ ( sK17_W1 @ SV81 ) )
        = $true )
      | ( ( aElement0 @ SV94 )
        = $false )
      | ( ( ( sdtasdt0 @ SV81 @ SV94 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV81 )
        = $false )
      | ( ( doDivides0 @ SV81 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[871]) ).

thf(878,plain,
    ! [SV95: $i,SV83: $i,SV100: $i] :
      ( ( ( aElement0 @ SV100 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV100 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV83 )
        = $false )
      | ( ( ( sdtasdt0 @ SV83 @ SV95 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV95 )
        = $false )
      | ( ( doDivides0 @ SV83 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[872]) ).

thf(879,plain,
    ! [SV99: $i,SV93: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
           != xc )
          | ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV99 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[873]) ).

thf(880,plain,
    ! [SV99: $i,SV93: $i,SV79: $i] :
      ( ( ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV99 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[879]) ).

thf(881,plain,
    ! [SV99: $i,SV93: $i,SV79: $i] :
      ( ( ( ~ ( aElement0 @ ( sK19_W1 @ SV79 ) ) )
        = $false )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV99 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[879]) ).

thf(882,plain,
    ! [SV99: $i,SV93: $i,SV79: $i] :
      ( ( ( ( sdtasdt0 @ SV79 @ ( sK19_W1 @ SV79 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV99 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[880]) ).

thf(883,plain,
    ! [SV99: $i,SV93: $i,SV79: $i] :
      ( ( ( aElement0 @ ( sK19_W1 @ SV79 ) )
        = $true )
      | ( ( aElement0 @ SV93 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV93 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV79 )
        = $false )
      | ( ( ( sdtasdt0 @ SV79 @ SV99 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV99 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[881]) ).

thf(884,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[117,883,882,878,877,876,875,874,862,861,859,858,854,853,852,851,835,834,827,823,816,815,813,798,797,794,788,787,771,758,739,738,735,725,724,713,712,687,666,665,664,663,656,633,610,609,608,592,588,587,586,585,584,583,552,551,550,527,526,513,507,500,478,456,455,452,440,398,390,389,388,371,357,356,355,354,353,352,347,346,345,344,338,337,336,335,332,330,329,328,296,276,249,248,246,244,242,229,228,174,170,169,160,118]) ).

thf(885,plain,
    ( ( ( aElement0 @ xa )
      & ( aElement0 @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(886,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(887,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK21_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK21_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK20_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK20_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK19_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK19_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK18_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK18_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK17_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK17_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK16_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK16_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK15_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK15_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK14_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK14_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK13_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK13_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ( ( sdtasdt0 @ xc @ sK12_W0 )
        = xa )
      & ( aElement0 @ sK12_W0 )
      & ( aElement0 @ xc )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ( ( sdtasdt0 @ xc @ sK11_W0 )
        = xb )
      & ( aElement0 @ sK11_W0 )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(888,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ W1 @ W2 )
               != W0 ) )
          | ( aElementOf0 @ W0 @ xI ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ( ( aElementOf0 @ ( sK9_W1 @ W0 ) @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ ( sK10_SY73 @ W0 ) @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ ( sK9_W1 @ W0 ) @ ( sK10_SY73 @ W0 ) )
              = W0 ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xb @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
          | ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK8_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xa @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
          | ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK7_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElement0 @ W1 )
              | ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
      & ( aSet0 @ xI )
      & ( aIdeal0 @ xI )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(889,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(890,plain,
    ( ( aElement0 @ sz00 )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(891,plain,
    ( ( aElement0 @ sz10 )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(892,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(893,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(894,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(895,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(896,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(897,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtpldt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(898,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(899,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(900,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(901,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz10 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtasdt0 @ sz10 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(902,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(903,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
            = ( smndt0 @ W0 ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( smndt0 @ W0 )
            = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(904,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz00 )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(905,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
           != sz00 )
          | ( W0 = sz00 )
          | ( W1 = sz00 ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(906,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(907,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(908,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aSet0 @ W0 )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ W0 )
              | ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(909,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aSet0 @ W0 )
          | ~ ( aSet0 @ W1 )
          | ( ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W0 )
            & ~ ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W1 ) )
          | ( ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W1 )
            & ~ ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W0 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(910,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(911,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(912,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( ( aElement0 @ ( sK4_W2 @ W1 @ W0 ) )
            & ~ ( aElementOf0 @ ( sK4_W2 @ W1 @ W0 ) @ ( sdtpldt1 @ W0 @ W1 ) ) )
          | ! [W2: $i,W3: $i] :
              ( ~ ( aElement0 @ W2 )
              | ~ ( aElement0 @ W3 )
              | ( ( aElement0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W3 @ W1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(913,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(914,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(915,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(916,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( W1 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( aElement0 @ ( sK1_W2 @ W1 @ W0 ) )
            & ( aElement0 @ ( sK2_SY72 @ W1 @ W0 ) )
            & ( W0
              = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 ) @ ( sK2_SY72 @ W1 @ W0 ) ) )
            & ( ( ( sK2_SY72 @ W1 @ W0 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ W1 @ W0 ) ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(917,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(918,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xa @ W0 )
           != xa )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(919,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz00 )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[904]) ).

thf(920,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aIdeal0 @ SX0 )
          | ~ ( aIdeal0 @ SX1 )
          | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SX1 @ SX0 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SX1 @ SX0 ) @ ( sdtpldt1 @ SX0 @ SX1 ) ) )
          | ! [SX2: $i,SX3: $i] :
              ( ~ ( aElement0 @ SX2 )
              | ~ ( aElement0 @ SX3 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[912]) ).

thf(921,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ sz00 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[897]) ).

thf(922,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                                 != xa )
                                                                | ~ ( aElement0 @ sK12_W0 ) )
                                                          | ~ ( aElement0 @ xc ) )
                                                    | ~ ( doDivides0 @ xc @ xa ) )
                                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                         != xb )
                                        | ~ ( aElement0 @ sK11_W0 ) ) )
                            | ~ ( doDivides0 @ xc @ xb ) )
                      | ~ ( aDivisorOf0 @ xc @ xb ) ) )
          | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[887]) ).

thf(923,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[898]) ).

thf(924,plain,
    ( ( ~ ( ~ ( aElement0 @ xa )
          | ~ ( aElement0 @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[885]) ).

thf(925,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( sdtasdt0 @ xa @ SX0 )
                 != xa )
                | ~ ( aElement0 @ SX0 ) )
          | ~ ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[918]) ).

thf(926,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aSet0 @ SX0 )
          | ~ ( aSet0 @ SX1 )
          | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[909]) ).

thf(927,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i,SX2: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                                | ( ( sdtpldt0 @ SX1 @ SX2 )
                                 != SX0 ) )
                            | ( aElementOf0 @ SX0 @ xI ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                                 != SX0 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xb @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ xa @ SX1 )
                                             != SX0 )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                             != SX0 )
                                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElement0 @ SX1 )
                                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                        | ~ ( aSet0 @ xI ) )
                                  | ~ ( aIdeal0 @ xI ) ) ) ) )
          | ( xI
           != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[888]) ).

thf(928,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
                  = ( smndt0 @ SX0 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( smndt0 @ SX0 )
                  = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[903]) ).

thf(929,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[902]) ).

thf(930,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 = sz00 )
          | ~ ( aElement0 @ SX0 )
          | ~ ( aElement0 @ SX1 )
          | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SX1 @ SX0 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) )
                    | ( SX0
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 ) @ ( sK2_SY72 @ SX1 @ SX0 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SX1 @ SX0 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[916]) ).

thf(931,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz10 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[901]) ).

thf(932,plain,
    ( ( ( ( xa != sz00 ) )
      = $true )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[886]) ).

thf(933,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[889]) ).

thf(934,plain,
    ! [SV102: $i] :
      ( ( ~ ( aElement0 @ SV102 )
        | ( aElement0 @ ( smndt0 @ SV102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[892]) ).

thf(935,plain,
    ! [SV103: $i] :
      ( ( ! [SY122: $i] :
            ( ~ ( aElement0 @ SV103 )
            | ~ ( aElement0 @ SY122 )
            | ( aElement0 @ ( sdtpldt0 @ SV103 @ SY122 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[893]) ).

thf(936,plain,
    ! [SV104: $i] :
      ( ( ! [SY123: $i] :
            ( ~ ( aElement0 @ SV104 )
            | ~ ( aElement0 @ SY123 )
            | ( aElement0 @ ( sdtasdt0 @ SV104 @ SY123 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[894]) ).

thf(937,plain,
    ! [SV105: $i] :
      ( ( ! [SY124: $i] :
            ( ~ ( aElement0 @ SV105 )
            | ~ ( aElement0 @ SY124 )
            | ( ( sdtpldt0 @ SV105 @ SY124 )
              = ( sdtpldt0 @ SY124 @ SV105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[895]) ).

thf(938,plain,
    ! [SV106: $i] :
      ( ( ! [SY125: $i,SY126: $i] :
            ( ~ ( aElement0 @ SV106 )
            | ~ ( aElement0 @ SY125 )
            | ~ ( aElement0 @ SY126 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SY125 ) @ SY126 )
              = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SY125 @ SY126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[896]) ).

thf(939,plain,
    ! [SV107: $i] :
      ( ( ! [SY127: $i] :
            ( ~ ( aElement0 @ SV107 )
            | ~ ( aElement0 @ SY127 )
            | ( ( sdtasdt0 @ SV107 @ SY127 )
              = ( sdtasdt0 @ SY127 @ SV107 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[899]) ).

thf(940,plain,
    ! [SV108: $i] :
      ( ( ! [SY128: $i,SY129: $i] :
            ( ~ ( aElement0 @ SV108 )
            | ~ ( aElement0 @ SY128 )
            | ~ ( aElement0 @ SY129 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SY128 ) @ SY129 )
              = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SY128 @ SY129 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[900]) ).

thf(941,plain,
    ! [SV109: $i] :
      ( ( ! [SY130: $i] :
            ( ~ ( aElement0 @ SV109 )
            | ~ ( aElement0 @ SY130 )
            | ( ( sdtasdt0 @ SV109 @ SY130 )
             != sz00 )
            | ( SV109 = sz00 )
            | ( SY130 = sz00 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[905]) ).

thf(942,plain,
    ( ( sz10 = sz00 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[906]) ).

thf(943,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[907]) ).

thf(944,plain,
    ! [SV111: $i] :
      ( ( ~ ( aSet0 @ SV111 )
        | ! [SY131: $i] :
            ( ~ ( aElementOf0 @ SY131 @ SV111 )
            | ( aElement0 @ SY131 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[908]) ).

thf(945,plain,
    ! [SV112: $i] :
      ( ( ! [SY132: $i] :
            ( ~ ( aIdeal0 @ SV112 )
            | ~ ( aIdeal0 @ SY132 )
            | ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SY132 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[910]) ).

thf(946,plain,
    ! [SV113: $i] :
      ( ( ! [SY133: $i] :
            ( ~ ( aIdeal0 @ SV113 )
            | ~ ( aIdeal0 @ SY133 )
            | ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SY133 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[911]) ).

thf(947,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[913]) ).

thf(948,plain,
    ! [SV115: $i] :
      ( ( ( SV115 = sz00 )
        | ~ ( aElement0 @ SV115 )
        | ( aNaturalNumber0 @ ( sbrdtbr0 @ SV115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[914]) ).

thf(949,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 )
        | ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[915]) ).

thf(950,plain,
    ! [SV116: $i] :
      ( ( ~ ( aElement0 @ SV116 )
        | ( aIdeal0 @ ( slsdtgt0 @ SV116 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[917]) ).

thf(951,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[919]) ).

thf(952,plain,
    ! [SV117: $i] :
      ( ( ! [SY134: $i] :
            ( ~ ( aIdeal0 @ SV117 )
            | ~ ( aIdeal0 @ SY134 )
            | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SY134 @ SV117 ) )
                | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SY134 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SY134 ) ) )
            | ! [SY135: $i,SY136: $i] :
                ( ~ ( aElement0 @ SY135 )
                | ~ ( aElement0 @ SY136 )
                | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY136 @ SY135 @ SY134 @ SV117 ) )
                          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY136 @ SY135 @ SY134 @ SV117 ) @ SY135 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY136 @ SY135 @ SY134 @ SV117 ) @ SY136 @ SY134 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[920]) ).

thf(953,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[921]) ).

thf(954,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) )
      | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[922]) ).

thf(955,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[923]) ).

thf(956,plain,
    ( ( ~ ( aElement0 @ xa )
      | ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[924]) ).

thf(957,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xa @ SX0 )
             != xa )
            | ~ ( aElement0 @ SX0 ) )
      | ~ ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[925]) ).

thf(958,plain,
    ! [SV118: $i] :
      ( ( ! [SY137: $i] :
            ( ~ ( aSet0 @ SV118 )
            | ~ ( aSet0 @ SY137 )
            | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SY137 @ SV118 ) @ SV118 )
                | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SY137 @ SV118 ) @ SY137 ) )
            | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SY137 @ SV118 ) @ SY137 )
                | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SY137 @ SV118 ) @ SV118 ) )
            | ( SV118 = SY137 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[926]) ).

thf(959,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) )
      | ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[927]) ).

thf(960,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[928]) ).

thf(961,plain,
    ! [SV119: $i] :
      ( ( ~ ( ~ ! [SY138: $i,SY139: $i] :
                  ( ~ ( aElement0 @ SV119 )
                  | ~ ( aElement0 @ SY138 )
                  | ~ ( aElement0 @ SY139 )
                  | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SY138 @ SY139 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SY138 ) @ ( sdtasdt0 @ SV119 @ SY139 ) ) ) )
            | ~ ! [SY140: $i,SY141: $i] :
                  ( ~ ( aElement0 @ SV119 )
                  | ~ ( aElement0 @ SY140 )
                  | ~ ( aElement0 @ SY141 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SY140 @ SY141 ) @ SV119 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SY140 @ SV119 ) @ ( sdtasdt0 @ SY141 @ SV119 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[929]) ).

thf(962,plain,
    ! [SV120: $i] :
      ( ( ! [SY142: $i] :
            ( ( SY142 = sz00 )
            | ~ ( aElement0 @ SV120 )
            | ~ ( aElement0 @ SY142 )
            | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SY142 @ SV120 ) )
                            | ~ ( aElement0 @ ( sK2_SY72 @ SY142 @ SV120 ) ) )
                      | ( SV120
                       != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SY142 @ SV120 ) @ SY142 ) @ ( sK2_SY72 @ SY142 @ SV120 ) ) ) )
                | ~ ( ( ( sK2_SY72 @ SY142 @ SV120 )
                      = sz00 )
                    | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SY142 @ SV120 ) ) @ ( sbrdtbr0 @ SY142 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[930]) ).

thf(963,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[931]) ).

thf(964,plain,
    ( ( ( xa = sz00 )
      = $false )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[932]) ).

thf(965,plain,
    ! [SV102: $i] :
      ( ( ( ~ ( aElement0 @ SV102 ) )
        = $true )
      | ( ( aElement0 @ ( smndt0 @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[934]) ).

thf(966,plain,
    ! [SV121: $i,SV103: $i] :
      ( ( ~ ( aElement0 @ SV103 )
        | ~ ( aElement0 @ SV121 )
        | ( aElement0 @ ( sdtpldt0 @ SV103 @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[935]) ).

thf(967,plain,
    ! [SV122: $i,SV104: $i] :
      ( ( ~ ( aElement0 @ SV104 )
        | ~ ( aElement0 @ SV122 )
        | ( aElement0 @ ( sdtasdt0 @ SV104 @ SV122 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[936]) ).

thf(968,plain,
    ! [SV123: $i,SV105: $i] :
      ( ( ~ ( aElement0 @ SV105 )
        | ~ ( aElement0 @ SV123 )
        | ( ( sdtpldt0 @ SV105 @ SV123 )
          = ( sdtpldt0 @ SV123 @ SV105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[937]) ).

thf(969,plain,
    ! [SV124: $i,SV106: $i] :
      ( ( ! [SY143: $i] :
            ( ~ ( aElement0 @ SV106 )
            | ~ ( aElement0 @ SV124 )
            | ~ ( aElement0 @ SY143 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SY143 )
              = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SY143 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[938]) ).

thf(970,plain,
    ! [SV125: $i,SV107: $i] :
      ( ( ~ ( aElement0 @ SV107 )
        | ~ ( aElement0 @ SV125 )
        | ( ( sdtasdt0 @ SV107 @ SV125 )
          = ( sdtasdt0 @ SV125 @ SV107 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[939]) ).

thf(971,plain,
    ! [SV126: $i,SV108: $i] :
      ( ( ! [SY144: $i] :
            ( ~ ( aElement0 @ SV108 )
            | ~ ( aElement0 @ SV126 )
            | ~ ( aElement0 @ SY144 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SY144 )
              = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SY144 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[940]) ).

thf(972,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ~ ( aElement0 @ SV109 )
        | ~ ( aElement0 @ SV127 )
        | ( ( sdtasdt0 @ SV109 @ SV127 )
         != sz00 )
        | ( SV109 = sz00 )
        | ( SV127 = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[941]) ).

thf(973,plain,
    ! [SV111: $i] :
      ( ( ( ~ ( aSet0 @ SV111 ) )
        = $true )
      | ( ( ! [SY131: $i] :
              ( ~ ( aElementOf0 @ SY131 @ SV111 )
              | ( aElement0 @ SY131 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[944]) ).

thf(974,plain,
    ! [SV128: $i,SV112: $i] :
      ( ( ~ ( aIdeal0 @ SV112 )
        | ~ ( aIdeal0 @ SV128 )
        | ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SV128 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[945]) ).

thf(975,plain,
    ! [SV129: $i,SV113: $i] :
      ( ( ~ ( aIdeal0 @ SV113 )
        | ~ ( aIdeal0 @ SV129 )
        | ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SV129 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[946]) ).

thf(976,plain,
    ! [SV115: $i] :
      ( ( ( ( SV115 = sz00 )
          | ~ ( aElement0 @ SV115 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV115 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[948]) ).

thf(977,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[949]) ).

thf(978,plain,
    ! [SV116: $i] :
      ( ( ( ~ ( aElement0 @ SV116 ) )
        = $true )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV116 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[950]) ).

thf(979,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[951]) ).

thf(980,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[951]) ).

thf(981,plain,
    ! [SV130: $i,SV117: $i] :
      ( ( ~ ( aIdeal0 @ SV117 )
        | ~ ( aIdeal0 @ SV130 )
        | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
            | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
        | ! [SY145: $i,SY146: $i] :
            ( ~ ( aElement0 @ SY145 )
            | ~ ( aElement0 @ SY146 )
            | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                      | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[952]) ).

thf(982,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[953]) ).

thf(983,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[953]) ).

thf(984,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[954]) ).

thf(985,plain,
    ( ( ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[954]) ).

thf(986,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[955]) ).

thf(987,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[955]) ).

thf(988,plain,
    ( ( ~ ( aElement0 @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[956]) ).

thf(989,plain,
    ( ( ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[956]) ).

thf(990,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xa @ SX0 )
             != xa )
            | ~ ( aElement0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[957]) ).

thf(991,plain,
    ( ( ~ ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[957]) ).

thf(992,plain,
    ! [SV131: $i,SV118: $i] :
      ( ( ~ ( aSet0 @ SV118 )
        | ~ ( aSet0 @ SV131 )
        | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
            | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
        | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
            | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        | ( SV118 = SV131 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[958]) ).

thf(993,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[959]) ).

thf(994,plain,
    ( ( ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[959]) ).

thf(995,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[960]) ).

thf(996,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[960]) ).

thf(997,plain,
    ! [SV119: $i] :
      ( ( ~ ! [SY138: $i,SY139: $i] :
              ( ~ ( aElement0 @ SV119 )
              | ~ ( aElement0 @ SY138 )
              | ~ ( aElement0 @ SY139 )
              | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SY138 @ SY139 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SY138 ) @ ( sdtasdt0 @ SV119 @ SY139 ) ) ) )
        | ~ ! [SY140: $i,SY141: $i] :
              ( ~ ( aElement0 @ SV119 )
              | ~ ( aElement0 @ SY140 )
              | ~ ( aElement0 @ SY141 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY140 @ SY141 ) @ SV119 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY140 @ SV119 ) @ ( sdtasdt0 @ SY141 @ SV119 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[961]) ).

thf(998,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( SV132 = sz00 )
        | ~ ( aElement0 @ SV120 )
        | ~ ( aElement0 @ SV132 )
        | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                        | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                  | ( SV120
                   != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
            | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                  = sz00 )
                | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[962]) ).

thf(999,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[963]) ).

thf(1000,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[963]) ).

thf(1001,plain,
    ( ( ( xb = sz00 )
      = $false )
    | ( ( xa = sz00 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[964]) ).

thf(1002,plain,
    ! [SV102: $i] :
      ( ( ( aElement0 @ SV102 )
        = $false )
      | ( ( aElement0 @ ( smndt0 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[965]) ).

thf(1003,plain,
    ! [SV121: $i,SV103: $i] :
      ( ( ( ~ ( aElement0 @ SV103 )
          | ~ ( aElement0 @ SV121 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV103 @ SV121 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[966]) ).

thf(1004,plain,
    ! [SV122: $i,SV104: $i] :
      ( ( ( ~ ( aElement0 @ SV104 )
          | ~ ( aElement0 @ SV122 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV104 @ SV122 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[967]) ).

thf(1005,plain,
    ! [SV123: $i,SV105: $i] :
      ( ( ( ~ ( aElement0 @ SV105 )
          | ~ ( aElement0 @ SV123 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV105 @ SV123 )
          = ( sdtpldt0 @ SV123 @ SV105 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[968]) ).

thf(1006,plain,
    ! [SV133: $i,SV124: $i,SV106: $i] :
      ( ( ~ ( aElement0 @ SV106 )
        | ~ ( aElement0 @ SV124 )
        | ~ ( aElement0 @ SV133 )
        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[969]) ).

thf(1007,plain,
    ! [SV125: $i,SV107: $i] :
      ( ( ( ~ ( aElement0 @ SV107 )
          | ~ ( aElement0 @ SV125 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV107 @ SV125 )
          = ( sdtasdt0 @ SV125 @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[970]) ).

thf(1008,plain,
    ! [SV134: $i,SV126: $i,SV108: $i] :
      ( ( ~ ( aElement0 @ SV108 )
        | ~ ( aElement0 @ SV126 )
        | ~ ( aElement0 @ SV134 )
        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[971]) ).

thf(1009,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( ~ ( aElement0 @ SV109 )
          | ~ ( aElement0 @ SV127 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
           != sz00 )
          | ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[972]) ).

thf(1010,plain,
    ! [SV111: $i] :
      ( ( ( aSet0 @ SV111 )
        = $false )
      | ( ( ! [SY131: $i] :
              ( ~ ( aElementOf0 @ SY131 @ SV111 )
              | ( aElement0 @ SY131 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[973]) ).

thf(1011,plain,
    ! [SV128: $i,SV112: $i] :
      ( ( ( ~ ( aIdeal0 @ SV112 )
          | ~ ( aIdeal0 @ SV128 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SV128 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[974]) ).

thf(1012,plain,
    ! [SV129: $i,SV113: $i] :
      ( ( ( ~ ( aIdeal0 @ SV113 )
          | ~ ( aIdeal0 @ SV129 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SV129 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[975]) ).

thf(1013,plain,
    ! [SV115: $i] :
      ( ( ( SV115 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV115 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV115 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[976]) ).

thf(1014,plain,
    ! [SV135: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV135 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[977]) ).

thf(1015,plain,
    ! [SV116: $i] :
      ( ( ( aElement0 @ SV116 )
        = $false )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV116 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[978]) ).

thf(1016,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz00 )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[979]) ).

thf(1017,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[980]) ).

thf(1018,plain,
    ! [SV130: $i,SV117: $i] :
      ( ( ( ~ ( aIdeal0 @ SV117 )
          | ~ ( aIdeal0 @ SV130 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
          | ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[981]) ).

thf(1019,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ sz00 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[982]) ).

thf(1020,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[983]) ).

thf(1021,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                           != xa )
                                                          | ~ ( aElement0 @ sK12_W0 ) )
                                                    | ~ ( aElement0 @ xc ) )
                                              | ~ ( doDivides0 @ xc @ xa ) )
                                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                   != xb )
                                  | ~ ( aElement0 @ sK11_W0 ) ) )
                      | ~ ( doDivides0 @ xc @ xb ) )
                | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[984]) ).

thf(1022,plain,
    ( ( aGcdOfAnd0 @ xc @ xa @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[985]) ).

thf(1023,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[986]) ).

thf(1024,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[987]) ).

thf(1025,plain,
    ( ( aElement0 @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[988]) ).

thf(1026,plain,
    ( ( aElement0 @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[989]) ).

thf(1027,plain,
    ( ( ! [SX0: $i] :
          ( ( ( sdtasdt0 @ xa @ SX0 )
           != xa )
          | ~ ( aElement0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[990]) ).

thf(1028,plain,
    ( ( ~ ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[991]) ).

thf(1029,plain,
    ! [SV131: $i,SV118: $i] :
      ( ( ( ~ ( aSet0 @ SV118 )
          | ~ ( aSet0 @ SV131 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
          | ( SV118 = SV131 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[992]) ).

thf(1030,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i,SX2: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                          | ( ( sdtpldt0 @ SX1 @ SX2 )
                           != SX0 ) )
                      | ( aElementOf0 @ SX0 @ xI ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                          | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                           != SX0 ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xb @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xa @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElement0 @ SX1 )
                                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                  | ~ ( aSet0 @ xI ) )
                            | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[993]) ).

thf(1031,plain,
    ( ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[994]) ).

thf(1032,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
            = ( smndt0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[995]) ).

thf(1033,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( smndt0 @ SX0 )
            = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[996]) ).

thf(1034,plain,
    ! [SV119: $i] :
      ( ( ~ ! [SY138: $i,SY139: $i] :
              ( ~ ( aElement0 @ SV119 )
              | ~ ( aElement0 @ SY138 )
              | ~ ( aElement0 @ SY139 )
              | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SY138 @ SY139 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SY138 ) @ ( sdtasdt0 @ SV119 @ SY139 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[997]) ).

thf(1035,plain,
    ! [SV119: $i] :
      ( ( ~ ! [SY140: $i,SY141: $i] :
              ( ~ ( aElement0 @ SV119 )
              | ~ ( aElement0 @ SY140 )
              | ~ ( aElement0 @ SY141 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY140 @ SY141 ) @ SV119 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY140 @ SV119 ) @ ( sdtasdt0 @ SY141 @ SV119 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[997]) ).

thf(1036,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ( SV132 = sz00 )
          | ~ ( aElement0 @ SV120 )
          | ~ ( aElement0 @ SV132 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                    | ( SV120
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[998]) ).

thf(1037,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz10 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[999]) ).

thf(1038,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1000]) ).

thf(1039,plain,
    ! [SV121: $i,SV103: $i] :
      ( ( ( ~ ( aElement0 @ SV103 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV121 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV103 @ SV121 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1003]) ).

thf(1040,plain,
    ! [SV122: $i,SV104: $i] :
      ( ( ( ~ ( aElement0 @ SV104 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV122 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV104 @ SV122 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1004]) ).

thf(1041,plain,
    ! [SV123: $i,SV105: $i] :
      ( ( ( ~ ( aElement0 @ SV105 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV123 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV105 @ SV123 )
          = ( sdtpldt0 @ SV123 @ SV105 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1005]) ).

thf(1042,plain,
    ! [SV133: $i,SV124: $i,SV106: $i] :
      ( ( ( ~ ( aElement0 @ SV106 )
          | ~ ( aElement0 @ SV124 )
          | ~ ( aElement0 @ SV133 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1006]) ).

thf(1043,plain,
    ! [SV125: $i,SV107: $i] :
      ( ( ( ~ ( aElement0 @ SV107 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV125 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV107 @ SV125 )
          = ( sdtasdt0 @ SV125 @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1007]) ).

thf(1044,plain,
    ! [SV134: $i,SV126: $i,SV108: $i] :
      ( ( ( ~ ( aElement0 @ SV108 )
          | ~ ( aElement0 @ SV126 )
          | ~ ( aElement0 @ SV134 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1008]) ).

thf(1045,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( ~ ( aElement0 @ SV109 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV127 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
           != sz00 )
          | ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1009]) ).

thf(1046,plain,
    ! [SV111: $i,SV136: $i] :
      ( ( ( ~ ( aElementOf0 @ SV136 @ SV111 )
          | ( aElement0 @ SV136 ) )
        = $true )
      | ( ( aSet0 @ SV111 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1010]) ).

thf(1047,plain,
    ! [SV128: $i,SV112: $i] :
      ( ( ( ~ ( aIdeal0 @ SV112 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV128 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SV128 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1011]) ).

thf(1048,plain,
    ! [SV129: $i,SV113: $i] :
      ( ( ( ~ ( aIdeal0 @ SV113 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV129 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SV129 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1012]) ).

thf(1049,plain,
    ! [SV115: $i] :
      ( ( ( aElement0 @ SV115 )
        = $false )
      | ( ( SV115 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV115 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1013]) ).

thf(1050,plain,
    ! [SV135: $i] :
      ( ( ( aNaturalNumber0 @ SV135 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1014]) ).

thf(1051,plain,
    ! [SV137: $i] :
      ( ( ~ ( aElement0 @ SV137 )
        | ( ( sdtasdt0 @ SV137 @ sz00 )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1016]) ).

thf(1052,plain,
    ! [SV138: $i] :
      ( ( ~ ( aElement0 @ SV138 )
        | ( sz00
          = ( sdtasdt0 @ sz00 @ SV138 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1017]) ).

thf(1053,plain,
    ! [SV130: $i,SV117: $i] :
      ( ( ( ~ ( aIdeal0 @ SV117 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV130 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
          | ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1018]) ).

thf(1054,plain,
    ! [SV139: $i] :
      ( ( ~ ( aElement0 @ SV139 )
        | ( ( sdtpldt0 @ SV139 @ sz00 )
          = SV139 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1019]) ).

thf(1055,plain,
    ! [SV140: $i] :
      ( ( ~ ( aElement0 @ SV140 )
        | ( SV140
          = ( sdtpldt0 @ sz00 @ SV140 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1020]) ).

thf(1056,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1021]) ).

thf(1057,plain,
    ! [SV141: $i] :
      ( ( ~ ( aElement0 @ SV141 )
        | ( ( sdtpldt0 @ SV141 @ ( smndt0 @ SV141 ) )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1023]) ).

thf(1058,plain,
    ! [SV142: $i] :
      ( ( ~ ( aElement0 @ SV142 )
        | ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV142 ) @ SV142 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1024]) ).

thf(1059,plain,
    ! [SV143: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV143 )
         != xa )
        | ~ ( aElement0 @ SV143 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1027]) ).

thf(1060,plain,
    ( ( aElementOf0 @ xa @ ( slsdtgt0 @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1028]) ).

thf(1061,plain,
    ! [SV131: $i,SV118: $i] :
      ( ( ( ~ ( aSet0 @ SV118 ) )
        = $true )
      | ( ( ~ ( aSet0 @ SV131 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
          | ( SV118 = SV131 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1029]) ).

thf(1062,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1030]) ).

thf(1063,plain,
    ! [SV144: $i] :
      ( ( ~ ( aElement0 @ SV144 )
        | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV144 )
          = ( smndt0 @ SV144 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1032]) ).

thf(1064,plain,
    ! [SV145: $i] :
      ( ( ~ ( aElement0 @ SV145 )
        | ( ( smndt0 @ SV145 )
          = ( sdtasdt0 @ SV145 @ ( smndt0 @ sz10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1033]) ).

thf(1065,plain,
    ! [SV119: $i] :
      ( ( ! [SY138: $i,SY139: $i] :
            ( ~ ( aElement0 @ SV119 )
            | ~ ( aElement0 @ SY138 )
            | ~ ( aElement0 @ SY139 )
            | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SY138 @ SY139 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SY138 ) @ ( sdtasdt0 @ SV119 @ SY139 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1034]) ).

thf(1066,plain,
    ! [SV119: $i] :
      ( ( ! [SY140: $i,SY141: $i] :
            ( ~ ( aElement0 @ SV119 )
            | ~ ( aElement0 @ SY140 )
            | ~ ( aElement0 @ SY141 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SY140 @ SY141 ) @ SV119 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SY140 @ SV119 ) @ ( sdtasdt0 @ SY141 @ SV119 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1035]) ).

thf(1067,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( SV132 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV120 )
          | ~ ( aElement0 @ SV132 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                    | ( SV120
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1036]) ).

thf(1068,plain,
    ! [SV146: $i] :
      ( ( ~ ( aElement0 @ SV146 )
        | ( ( sdtasdt0 @ SV146 @ sz10 )
          = SV146 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1037]) ).

thf(1069,plain,
    ! [SV147: $i] :
      ( ( ~ ( aElement0 @ SV147 )
        | ( SV147
          = ( sdtasdt0 @ sz10 @ SV147 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1038]) ).

thf(1070,plain,
    ! [SV121: $i,SV103: $i] :
      ( ( ( aElement0 @ SV103 )
        = $false )
      | ( ( ~ ( aElement0 @ SV121 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV103 @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1039]) ).

thf(1071,plain,
    ! [SV122: $i,SV104: $i] :
      ( ( ( aElement0 @ SV104 )
        = $false )
      | ( ( ~ ( aElement0 @ SV122 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV104 @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1040]) ).

thf(1072,plain,
    ! [SV123: $i,SV105: $i] :
      ( ( ( aElement0 @ SV105 )
        = $false )
      | ( ( ~ ( aElement0 @ SV123 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV105 @ SV123 )
          = ( sdtpldt0 @ SV123 @ SV105 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1041]) ).

thf(1073,plain,
    ! [SV133: $i,SV124: $i,SV106: $i] :
      ( ( ( ~ ( aElement0 @ SV106 )
          | ~ ( aElement0 @ SV124 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV133 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1042]) ).

thf(1074,plain,
    ! [SV125: $i,SV107: $i] :
      ( ( ( aElement0 @ SV107 )
        = $false )
      | ( ( ~ ( aElement0 @ SV125 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV107 @ SV125 )
          = ( sdtasdt0 @ SV125 @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1043]) ).

thf(1075,plain,
    ! [SV134: $i,SV126: $i,SV108: $i] :
      ( ( ( ~ ( aElement0 @ SV108 )
          | ~ ( aElement0 @ SV126 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV134 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1044]) ).

thf(1076,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( aElement0 @ SV109 )
        = $false )
      | ( ( ~ ( aElement0 @ SV127 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
           != sz00 )
          | ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1045]) ).

thf(1077,plain,
    ! [SV111: $i,SV136: $i] :
      ( ( ( ~ ( aElementOf0 @ SV136 @ SV111 ) )
        = $true )
      | ( ( aElement0 @ SV136 )
        = $true )
      | ( ( aSet0 @ SV111 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1046]) ).

thf(1078,plain,
    ! [SV128: $i,SV112: $i] :
      ( ( ( aIdeal0 @ SV112 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV128 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SV128 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1047]) ).

thf(1079,plain,
    ! [SV129: $i,SV113: $i] :
      ( ( ( aIdeal0 @ SV113 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV129 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SV129 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1048]) ).

thf(1080,plain,
    ! [SV135: $i,SV148: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV148 ) )
        = $true )
      | ( ( aNaturalNumber0 @ SV135 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1050]) ).

thf(1081,plain,
    ! [SV137: $i] :
      ( ( ( ~ ( aElement0 @ SV137 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV137 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1051]) ).

thf(1082,plain,
    ! [SV138: $i] :
      ( ( ( ~ ( aElement0 @ SV138 ) )
        = $true )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV138 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1052]) ).

thf(1083,plain,
    ! [SV130: $i,SV117: $i] :
      ( ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV130 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
          | ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1053]) ).

thf(1084,plain,
    ! [SV139: $i] :
      ( ( ( ~ ( aElement0 @ SV139 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV139 @ sz00 )
          = SV139 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1054]) ).

thf(1085,plain,
    ! [SV140: $i] :
      ( ( ( ~ ( aElement0 @ SV140 ) )
        = $true )
      | ( ( SV140
          = ( sdtpldt0 @ sz00 @ SV140 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1055]) ).

thf(1086,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1056]) ).

thf(1087,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1056]) ).

thf(1088,plain,
    ! [SV141: $i] :
      ( ( ( ~ ( aElement0 @ SV141 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV141 @ ( smndt0 @ SV141 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1057]) ).

thf(1089,plain,
    ! [SV142: $i] :
      ( ( ( ~ ( aElement0 @ SV142 ) )
        = $true )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV142 ) @ SV142 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1058]) ).

thf(1090,plain,
    ! [SV143: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV143 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV143 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1059]) ).

thf(1091,plain,
    ! [SV131: $i,SV118: $i] :
      ( ( ( aSet0 @ SV118 )
        = $false )
      | ( ( ~ ( aSet0 @ SV131 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
          | ( SV118 = SV131 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1061]) ).

thf(1092,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1062]) ).

thf(1093,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1062]) ).

thf(1094,plain,
    ! [SV144: $i] :
      ( ( ( ~ ( aElement0 @ SV144 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV144 )
          = ( smndt0 @ SV144 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1063]) ).

thf(1095,plain,
    ! [SV145: $i] :
      ( ( ( ~ ( aElement0 @ SV145 ) )
        = $true )
      | ( ( ( smndt0 @ SV145 )
          = ( sdtasdt0 @ SV145 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1064]) ).

thf(1096,plain,
    ! [SV149: $i,SV119: $i] :
      ( ( ! [SY147: $i] :
            ( ~ ( aElement0 @ SV119 )
            | ~ ( aElement0 @ SV149 )
            | ~ ( aElement0 @ SY147 )
            | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SY147 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SY147 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1065]) ).

thf(1097,plain,
    ! [SV150: $i,SV119: $i] :
      ( ( ! [SY148: $i] :
            ( ~ ( aElement0 @ SV119 )
            | ~ ( aElement0 @ SV150 )
            | ~ ( aElement0 @ SY148 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SY148 ) @ SV119 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SY148 @ SV119 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1066]) ).

thf(1098,plain,
    ! [SV132: $i,SV120: $i] :
      ( ( ( ~ ( aElement0 @ SV120 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV132 ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                    | ( SV120
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1067]) ).

thf(1099,plain,
    ! [SV146: $i] :
      ( ( ( ~ ( aElement0 @ SV146 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV146 @ sz10 )
          = SV146 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1068]) ).

thf(1100,plain,
    ! [SV147: $i] :
      ( ( ( ~ ( aElement0 @ SV147 ) )
        = $true )
      | ( ( SV147
          = ( sdtasdt0 @ sz10 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1069]) ).

thf(1101,plain,
    ! [SV103: $i,SV121: $i] :
      ( ( ( aElement0 @ SV121 )
        = $false )
      | ( ( aElement0 @ SV103 )
        = $false )
      | ( ( aElement0 @ ( sdtpldt0 @ SV103 @ SV121 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1070]) ).

thf(1102,plain,
    ! [SV104: $i,SV122: $i] :
      ( ( ( aElement0 @ SV122 )
        = $false )
      | ( ( aElement0 @ SV104 )
        = $false )
      | ( ( aElement0 @ ( sdtasdt0 @ SV104 @ SV122 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1071]) ).

thf(1103,plain,
    ! [SV105: $i,SV123: $i] :
      ( ( ( aElement0 @ SV123 )
        = $false )
      | ( ( aElement0 @ SV105 )
        = $false )
      | ( ( ( sdtpldt0 @ SV105 @ SV123 )
          = ( sdtpldt0 @ SV123 @ SV105 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1072]) ).

thf(1104,plain,
    ! [SV133: $i,SV124: $i,SV106: $i] :
      ( ( ( ~ ( aElement0 @ SV106 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV124 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV133 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1073]) ).

thf(1105,plain,
    ! [SV107: $i,SV125: $i] :
      ( ( ( aElement0 @ SV125 )
        = $false )
      | ( ( aElement0 @ SV107 )
        = $false )
      | ( ( ( sdtasdt0 @ SV107 @ SV125 )
          = ( sdtasdt0 @ SV125 @ SV107 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1074]) ).

thf(1106,plain,
    ! [SV134: $i,SV126: $i,SV108: $i] :
      ( ( ( ~ ( aElement0 @ SV108 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV126 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV134 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1075]) ).

thf(1107,plain,
    ! [SV109: $i,SV127: $i] :
      ( ( ( aElement0 @ SV127 )
        = $false )
      | ( ( aElement0 @ SV109 )
        = $false )
      | ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
           != sz00 )
          | ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1076]) ).

thf(1108,plain,
    ! [SV111: $i,SV136: $i] :
      ( ( ( aElementOf0 @ SV136 @ SV111 )
        = $false )
      | ( ( aElement0 @ SV136 )
        = $true )
      | ( ( aSet0 @ SV111 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1077]) ).

thf(1109,plain,
    ! [SV112: $i,SV128: $i] :
      ( ( ( aIdeal0 @ SV128 )
        = $false )
      | ( ( aIdeal0 @ SV112 )
        = $false )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV112 @ SV128 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1078]) ).

thf(1110,plain,
    ! [SV113: $i,SV129: $i] :
      ( ( ( aIdeal0 @ SV129 )
        = $false )
      | ( ( aIdeal0 @ SV113 )
        = $false )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV113 @ SV129 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1079]) ).

thf(1111,plain,
    ! [SV135: $i,SV148: $i] :
      ( ( ( aNaturalNumber0 @ SV148 )
        = $false )
      | ( ( aNaturalNumber0 @ SV135 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1080]) ).

thf(1112,plain,
    ! [SV137: $i] :
      ( ( ( aElement0 @ SV137 )
        = $false )
      | ( ( ( sdtasdt0 @ SV137 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1081]) ).

thf(1113,plain,
    ! [SV138: $i] :
      ( ( ( aElement0 @ SV138 )
        = $false )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV138 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1082]) ).

thf(1114,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( aIdeal0 @ SV130 )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
          | ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1083]) ).

thf(1115,plain,
    ! [SV139: $i] :
      ( ( ( aElement0 @ SV139 )
        = $false )
      | ( ( ( sdtpldt0 @ SV139 @ sz00 )
          = SV139 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1084]) ).

thf(1116,plain,
    ! [SV140: $i] :
      ( ( ( aElement0 @ SV140 )
        = $false )
      | ( ( SV140
          = ( sdtpldt0 @ sz00 @ SV140 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1085]) ).

thf(1117,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1086]) ).

thf(1118,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                     != xa )
                                                    | ~ ( aElement0 @ sK12_W0 ) )
                                              | ~ ( aElement0 @ xc ) )
                                        | ~ ( doDivides0 @ xc @ xa ) )
                                  | ~ ( aDivisorOf0 @ xc @ xa ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                             != xb )
                            | ~ ( aElement0 @ sK11_W0 ) ) )
                | ~ ( doDivides0 @ xc @ xb ) )
          | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1087]) ).

thf(1119,plain,
    ! [SV141: $i] :
      ( ( ( aElement0 @ SV141 )
        = $false )
      | ( ( ( sdtpldt0 @ SV141 @ ( smndt0 @ SV141 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1088]) ).

thf(1120,plain,
    ! [SV142: $i] :
      ( ( ( aElement0 @ SV142 )
        = $false )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV142 ) @ SV142 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1089]) ).

thf(1121,plain,
    ! [SV143: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV143 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV143 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1090]) ).

thf(1122,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aSet0 @ SV131 )
        = $false )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
          | ( SV118 = SV131 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1091]) ).

thf(1123,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i,SX2: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                    | ( ( sdtpldt0 @ SX1 @ SX2 )
                     != SX0 ) )
                | ( aElementOf0 @ SX0 @ xI ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                    | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                     != SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1092]) ).

thf(1124,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xb @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                      | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xa @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElementOf0 @ SX1 @ xI )
                                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElement0 @ SX1 )
                                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                            | ~ ( aSet0 @ xI ) )
                      | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1093]) ).

thf(1125,plain,
    ! [SV144: $i] :
      ( ( ( aElement0 @ SV144 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV144 )
          = ( smndt0 @ SV144 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1094]) ).

thf(1126,plain,
    ! [SV145: $i] :
      ( ( ( aElement0 @ SV145 )
        = $false )
      | ( ( ( smndt0 @ SV145 )
          = ( sdtasdt0 @ SV145 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1095]) ).

thf(1127,plain,
    ! [SV151: $i,SV149: $i,SV119: $i] :
      ( ( ~ ( aElement0 @ SV119 )
        | ~ ( aElement0 @ SV149 )
        | ~ ( aElement0 @ SV151 )
        | ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1096]) ).

thf(1128,plain,
    ! [SV152: $i,SV150: $i,SV119: $i] :
      ( ( ~ ( aElement0 @ SV119 )
        | ~ ( aElement0 @ SV150 )
        | ~ ( aElement0 @ SV152 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1097]) ).

thf(1129,plain,
    ! [SV132: $i,SV120: $i] :
      ( ( ( aElement0 @ SV120 )
        = $false )
      | ( ( ~ ( aElement0 @ SV132 ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                    | ( SV120
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1098]) ).

thf(1130,plain,
    ! [SV146: $i] :
      ( ( ( aElement0 @ SV146 )
        = $false )
      | ( ( ( sdtasdt0 @ SV146 @ sz10 )
          = SV146 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1099]) ).

thf(1131,plain,
    ! [SV147: $i] :
      ( ( ( aElement0 @ SV147 )
        = $false )
      | ( ( SV147
          = ( sdtasdt0 @ sz10 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1100]) ).

thf(1132,plain,
    ! [SV133: $i,SV124: $i,SV106: $i] :
      ( ( ( aElement0 @ SV106 )
        = $false )
      | ( ( ~ ( aElement0 @ SV124 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV133 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1104]) ).

thf(1133,plain,
    ! [SV134: $i,SV126: $i,SV108: $i] :
      ( ( ( aElement0 @ SV108 )
        = $false )
      | ( ( ~ ( aElement0 @ SV126 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV134 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1106]) ).

thf(1134,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
           != sz00 ) )
        = $true )
      | ( ( ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV109 )
        = $false )
      | ( ( aElement0 @ SV127 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1107]) ).

thf(1135,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) ) )
        = $true )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1114]) ).

thf(1136,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1117]) ).

thf(1137,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) )
      | ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1118]) ).

thf(1138,plain,
    ! [SV143: $i] :
      ( ( ( aElement0 @ SV143 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV143 )
          = xa )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1121]) ).

thf(1139,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1122]) ).

thf(1140,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1123]) ).

thf(1141,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1124]) ).

thf(1142,plain,
    ! [SV151: $i,SV149: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 )
          | ~ ( aElement0 @ SV149 )
          | ~ ( aElement0 @ SV151 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1127]) ).

thf(1143,plain,
    ! [SV152: $i,SV150: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 )
          | ~ ( aElement0 @ SV150 )
          | ~ ( aElement0 @ SV152 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1128]) ).

thf(1144,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( aElement0 @ SV132 )
        = $false )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                    | ( SV120
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1129]) ).

thf(1145,plain,
    ! [SV133: $i,SV106: $i,SV124: $i] :
      ( ( ( aElement0 @ SV124 )
        = $false )
      | ( ( aElement0 @ SV106 )
        = $false )
      | ( ( ~ ( aElement0 @ SV133 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1132]) ).

thf(1146,plain,
    ! [SV134: $i,SV108: $i,SV126: $i] :
      ( ( ( aElement0 @ SV126 )
        = $false )
      | ( ( aElement0 @ SV108 )
        = $false )
      | ( ( ~ ( aElement0 @ SV134 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1133]) ).

thf(1147,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( ( sdtasdt0 @ SV109 @ SV127 )
          = sz00 )
        = $false )
      | ( ( ( SV109 = sz00 )
          | ( SV127 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV109 )
        = $false )
      | ( ( aElement0 @ SV127 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1134]) ).

thf(1148,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
          | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
        = $false )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1135]) ).

thf(1149,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1136]) ).

thf(1150,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1136]) ).

thf(1151,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1137]) ).

thf(1152,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1137]) ).

thf(1153,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1139]) ).

thf(1154,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1140]) ).

thf(1155,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1140]) ).

thf(1156,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1141]) ).

thf(1157,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1141]) ).

thf(1158,plain,
    ! [SV151: $i,SV149: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 )
          | ~ ( aElement0 @ SV149 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV151 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1142]) ).

thf(1159,plain,
    ! [SV152: $i,SV150: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 )
          | ~ ( aElement0 @ SV150 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV152 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1143]) ).

thf(1160,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                | ( SV120
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
          | ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1144]) ).

thf(1161,plain,
    ! [SV124: $i,SV106: $i,SV133: $i] :
      ( ( ( aElement0 @ SV133 )
        = $false )
      | ( ( aElement0 @ SV106 )
        = $false )
      | ( ( aElement0 @ SV124 )
        = $false )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV106 @ SV124 ) @ SV133 )
          = ( sdtpldt0 @ SV106 @ ( sdtpldt0 @ SV124 @ SV133 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1145]) ).

thf(1162,plain,
    ! [SV126: $i,SV108: $i,SV134: $i] :
      ( ( ( aElement0 @ SV134 )
        = $false )
      | ( ( aElement0 @ SV108 )
        = $false )
      | ( ( aElement0 @ SV126 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV108 @ SV126 ) @ SV134 )
          = ( sdtasdt0 @ SV108 @ ( sdtasdt0 @ SV126 @ SV134 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1146]) ).

thf(1163,plain,
    ! [SV127: $i,SV109: $i] :
      ( ( ( SV109 = sz00 )
        = $true )
      | ( ( SV127 = sz00 )
        = $true )
      | ( ( ( sdtasdt0 @ SV109 @ SV127 )
          = sz00 )
        = $false )
      | ( ( aElement0 @ SV109 )
        = $false )
      | ( ( aElement0 @ SV127 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1147]) ).

thf(1164,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) ) )
        = $false )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1148]) ).

thf(1165,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
        = $false )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1148]) ).

thf(1166,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1149]) ).

thf(1167,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1150]) ).

thf(1168,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                               != xa )
                                              | ~ ( aElement0 @ sK12_W0 ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ( doDivides0 @ xc @ xa ) )
                            | ~ ( aDivisorOf0 @ xc @ xa ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                       != xb )
                      | ~ ( aElement0 @ sK11_W0 ) ) )
          | ~ ( doDivides0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1151]) ).

thf(1169,plain,
    ( ( aDivisorOf0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1152]) ).

thf(1170,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
          | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1153]) ).

thf(1171,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i,SX2: $i] :
              ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SX1 @ SX2 )
               != SX0 ) )
          | ( aElementOf0 @ SX0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1154]) ).

thf(1172,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
               != SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1155]) ).

thf(1173,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xb @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1156]) ).

thf(1174,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xa @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                      | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElementOf0 @ SX1 @ xI )
                                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElement0 @ SX1 )
                                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                      | ~ ( aSet0 @ xI ) )
                | ~ ( aIdeal0 @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1157]) ).

thf(1175,plain,
    ! [SV151: $i,SV149: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV149 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV151 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1158]) ).

thf(1176,plain,
    ! [SV152: $i,SV150: $i,SV119: $i] :
      ( ( ( ~ ( aElement0 @ SV119 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV150 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV152 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1159]) ).

thf(1177,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
                | ( SV120
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1160]) ).

thf(1178,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( ( ( sK2_SY72 @ SV132 @ SV120 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1160]) ).

thf(1179,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1164]) ).

thf(1180,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) ) )
        = $true )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1165]) ).

thf(1181,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1166]) ).

thf(1182,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1167]) ).

thf(1183,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) )
      | ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1168]) ).

thf(1184,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1170]) ).

thf(1185,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1170]) ).

thf(1186,plain,
    ! [SV153: $i] :
      ( ( ! [SY149: $i,SY150: $i] :
            ( ~ ( aElementOf0 @ SY149 @ ( slsdtgt0 @ xa ) )
            | ~ ( aElementOf0 @ SY150 @ ( slsdtgt0 @ xb ) )
            | ( ( sdtpldt0 @ SY149 @ SY150 )
             != SV153 ) )
        | ( aElementOf0 @ SV153 @ xI ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1171]) ).

thf(1187,plain,
    ! [SV154: $i] :
      ( ( ~ ( aElementOf0 @ SV154 @ xI )
        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
            | ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
             != SV154 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1172]) ).

thf(1188,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1173]) ).

thf(1189,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1174]) ).

thf(1190,plain,
    ! [SV151: $i,SV149: $i,SV119: $i] :
      ( ( ( aElement0 @ SV119 )
        = $false )
      | ( ( ~ ( aElement0 @ SV149 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV151 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1175]) ).

thf(1191,plain,
    ! [SV152: $i,SV150: $i,SV119: $i] :
      ( ( ( aElement0 @ SV119 )
        = $false )
      | ( ( ~ ( aElement0 @ SV150 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV152 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1176]) ).

thf(1192,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                    | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
              | ( SV120
               != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1177]) ).

thf(1193,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ( ( sK2_SY72 @ SV132 @ SV120 )
            = sz00 )
          | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1178]) ).

thf(1194,plain,
    ! [SV117: $i,SV130: $i,SV155: $i] :
      ( ( ( ! [SY151: $i] :
              ( ~ ( aElement0 @ SV155 )
              | ~ ( aElement0 @ SY151 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY151 @ SV155 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY151 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY151 @ SV155 @ SV130 @ SV117 ) @ SY151 @ SV130 ) ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1179]) ).

thf(1195,plain,
    ! [SV117: $i,SV130: $i] :
      ( ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( ! [SY145: $i,SY146: $i] :
              ( ~ ( aElement0 @ SY145 )
              | ~ ( aElement0 @ SY146 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY145 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY146 @ SY145 @ SV130 @ SV117 ) @ SY146 @ SV130 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1180]) ).

thf(1196,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1181]) ).

thf(1197,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1181]) ).

thf(1198,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1182]) ).

thf(1199,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1182]) ).

thf(1200,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1183]) ).

thf(1201,plain,
    ( ( ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1183]) ).

thf(1202,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1184]) ).

thf(1203,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1185]) ).

thf(1204,plain,
    ! [SV153: $i] :
      ( ( ( ! [SY149: $i,SY150: $i] :
              ( ~ ( aElementOf0 @ SY149 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY150 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SY149 @ SY150 )
               != SV153 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1186]) ).

thf(1205,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( aElementOf0 @ SV154 @ xI ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
               != SV154 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1187]) ).

thf(1206,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1188]) ).

thf(1207,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1188]) ).

thf(1208,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1189]) ).

thf(1209,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1189]) ).

thf(1210,plain,
    ! [SV151: $i,SV119: $i,SV149: $i] :
      ( ( ( aElement0 @ SV149 )
        = $false )
      | ( ( aElement0 @ SV119 )
        = $false )
      | ( ( ~ ( aElement0 @ SV151 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1190]) ).

thf(1211,plain,
    ! [SV152: $i,SV119: $i,SV150: $i] :
      ( ( ( aElement0 @ SV150 )
        = $false )
      | ( ( aElement0 @ SV119 )
        = $false )
      | ( ( ~ ( aElement0 @ SV152 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1191]) ).

thf(1212,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
          | ( SV120
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1192]) ).

thf(1213,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ( sK2_SY72 @ SV132 @ SV120 )
          = sz00 )
        = $true )
      | ( ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) @ ( sbrdtbr0 @ SV132 ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1193]) ).

thf(1214,plain,
    ! [SV117: $i,SV130: $i,SV156: $i,SV155: $i] :
      ( ( ( ~ ( aElement0 @ SV155 )
          | ~ ( aElement0 @ SV156 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1194]) ).

thf(1215,plain,
    ! [SV117: $i,SV130: $i,SV157: $i] :
      ( ( ( ! [SY152: $i] :
              ( ~ ( aElement0 @ SV157 )
              | ~ ( aElement0 @ SY152 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY152 @ SV157 @ SV130 @ SV117 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY152 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY152 @ SV157 @ SV130 @ SV117 ) @ SY152 @ SV130 ) ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1195]) ).

thf(1216,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1196]) ).

thf(1217,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1197]) ).

thf(1218,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1198]) ).

thf(1219,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1199]) ).

thf(1220,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                         != xa )
                                        | ~ ( aElement0 @ sK12_W0 ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ( doDivides0 @ xc @ xa ) )
                      | ~ ( aDivisorOf0 @ xc @ xa ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                 != xb )
                | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1200]) ).

thf(1221,plain,
    ( ( doDivides0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1201]) ).

thf(1222,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1202]) ).

thf(1223,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) ) )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1203]) ).

thf(1224,plain,
    ! [SV153: $i,SV158: $i] :
      ( ( ( ! [SY153: $i] :
              ( ~ ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY153 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SV158 @ SY153 )
               != SV153 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1204]) ).

thf(1225,plain,
    ! [SV154: $i] :
      ( ( ( aElementOf0 @ SV154 @ xI )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
               != SV154 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1205]) ).

thf(1226,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xb @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1206]) ).

thf(1227,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
          | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1207]) ).

thf(1228,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xa @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1208]) ).

thf(1229,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ xI )
                                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElement0 @ SX1 )
                                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                | ~ ( aSet0 @ xI ) )
          | ~ ( aIdeal0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1209]) ).

thf(1230,plain,
    ! [SV149: $i,SV119: $i,SV151: $i] :
      ( ( ( aElement0 @ SV151 )
        = $false )
      | ( ( aElement0 @ SV119 )
        = $false )
      | ( ( aElement0 @ SV149 )
        = $false )
      | ( ( ( sdtasdt0 @ SV119 @ ( sdtpldt0 @ SV149 @ SV151 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV119 @ SV149 ) @ ( sdtasdt0 @ SV119 @ SV151 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1210]) ).

thf(1231,plain,
    ! [SV150: $i,SV119: $i,SV152: $i] :
      ( ( ( aElement0 @ SV152 )
        = $false )
      | ( ( aElement0 @ SV119 )
        = $false )
      | ( ( aElement0 @ SV150 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV150 @ SV152 ) @ SV119 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV150 @ SV119 ) @ ( sdtasdt0 @ SV152 @ SV119 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1211]) ).

thf(1232,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1212]) ).

thf(1233,plain,
    ! [SV132: $i,SV120: $i] :
      ( ( ( ( SV120
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1212]) ).

thf(1234,plain,
    ! [SV117: $i,SV130: $i,SV156: $i,SV155: $i] :
      ( ( ( ~ ( aElement0 @ SV155 )
          | ~ ( aElement0 @ SV156 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1214]) ).

thf(1235,plain,
    ! [SV117: $i,SV130: $i,SV159: $i,SV157: $i] :
      ( ( ( ~ ( aElement0 @ SV157 )
          | ~ ( aElement0 @ SV159 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1215]) ).

thf(1236,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1216]) ).

thf(1237,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1217]) ).

thf(1238,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1218]) ).

thf(1239,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1219]) ).

thf(1240,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1220]) ).

thf(1241,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1222]) ).

thf(1242,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1222]) ).

thf(1243,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1223]) ).

thf(1244,plain,
    ! [SV153: $i,SV160: $i,SV158: $i] :
      ( ( ( ~ ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) )
          | ( ( sdtpldt0 @ SV158 @ SV160 )
           != SV153 ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1224]) ).

thf(1245,plain,
    ! [SV154: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
          | ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
           != SV154 ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1225]) ).

thf(1246,plain,
    ! [SV161: $i] :
      ( ( ! [SY154: $i] :
            ( ( ( sdtasdt0 @ xb @ SY154 )
             != SV161 )
            | ~ ( aElement0 @ SY154 ) )
        | ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1226]) ).

thf(1247,plain,
    ! [SV162: $i] :
      ( ( ~ ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
             != SV162 )
            | ~ ( aElement0 @ ( sK8_W1 @ SV162 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1227]) ).

thf(1248,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1228]) ).

thf(1249,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) )
      | ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1229]) ).

thf(1250,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
              | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1232]) ).

thf(1251,plain,
    ! [SV132: $i,SV120: $i] :
      ( ( ( SV120
          = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV132 @ SV120 ) @ SV132 ) @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1233]) ).

thf(1252,plain,
    ! [SV117: $i,SV130: $i,SV156: $i,SV155: $i] :
      ( ( ( ~ ( aElement0 @ SV155 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV156 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1234]) ).

thf(1253,plain,
    ! [SV117: $i,SV130: $i,SV159: $i,SV157: $i] :
      ( ( ( ~ ( aElement0 @ SV157 )
          | ~ ( aElement0 @ SV159 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1235]) ).

thf(1254,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1236]) ).

thf(1255,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1236]) ).

thf(1256,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1237]) ).

thf(1257,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1237]) ).

thf(1258,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1238]) ).

thf(1259,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1238]) ).

thf(1260,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1239]) ).

thf(1261,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1239]) ).

thf(1262,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1240]) ).

thf(1263,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1240]) ).

thf(1264,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1241]) ).

thf(1265,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1242]) ).

thf(1266,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1243]) ).

thf(1267,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1243]) ).

thf(1268,plain,
    ! [SV153: $i,SV160: $i,SV158: $i] :
      ( ( ( ~ ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV158 @ SV160 )
           != SV153 ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1244]) ).

thf(1269,plain,
    ! [SV154: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1245]) ).

thf(1270,plain,
    ! [SV154: $i] :
      ( ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
           != SV154 ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1245]) ).

thf(1271,plain,
    ! [SV161: $i] :
      ( ( ( ! [SY154: $i] :
              ( ( ( sdtasdt0 @ xb @ SY154 )
               != SV161 )
              | ~ ( aElement0 @ SY154 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1246]) ).

thf(1272,plain,
    ! [SV162: $i] :
      ( ( ( ~ ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
               != SV162 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV162 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1247]) ).

thf(1273,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1248]) ).

thf(1274,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1248]) ).

thf(1275,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1249]) ).

thf(1276,plain,
    ( ( ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1249]) ).

thf(1277,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
          | ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1250]) ).

thf(1278,plain,
    ! [SV117: $i,SV130: $i,SV156: $i,SV155: $i] :
      ( ( ( aElement0 @ SV155 )
        = $false )
      | ( ( ~ ( aElement0 @ SV156 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1252]) ).

thf(1279,plain,
    ! [SV117: $i,SV130: $i,SV159: $i,SV157: $i] :
      ( ( ( ~ ( aElement0 @ SV157 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV159 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1253]) ).

thf(1280,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1254]) ).

thf(1281,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1255]) ).

thf(1282,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1256]) ).

thf(1283,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1257]) ).

thf(1284,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1258]) ).

thf(1285,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1259]) ).

thf(1286,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1260]) ).

thf(1287,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1261]) ).

thf(1288,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                   != xa )
                                  | ~ ( aElement0 @ sK12_W0 ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ( doDivides0 @ xc @ xa ) )
                | ~ ( aDivisorOf0 @ xc @ xa ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1262]) ).

thf(1289,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
           != xb )
          | ~ ( aElement0 @ sK11_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1263]) ).

thf(1290,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV118 )
        = $true )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1265]) ).

thf(1291,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV131 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1266]) ).

thf(1292,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1267]) ).

thf(1293,plain,
    ! [SV153: $i,SV160: $i,SV158: $i] :
      ( ( ( ~ ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV158 @ SV160 )
           != SV153 ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1268]) ).

thf(1294,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $true )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1269]) ).

thf(1295,plain,
    ! [SV154: $i] :
      ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV154 ) @ ( sK10_SY73 @ SV154 ) )
          = SV154 )
        = $true )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1270]) ).

thf(1296,plain,
    ! [SV161: $i,SV163: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV163 )
           != SV161 )
          | ~ ( aElement0 @ SV163 ) )
        = $true )
      | ( ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1271]) ).

thf(1297,plain,
    ! [SV162: $i] :
      ( ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
               != SV162 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV162 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1272]) ).

thf(1298,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xa @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1273]) ).

thf(1299,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
          | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1274]) ).

thf(1300,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ xI )
                          | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElement0 @ SX1 )
                          | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
          | ~ ( aSet0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1275]) ).

thf(1301,plain,
    ( ( aIdeal0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1276]) ).

thf(1302,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1277]) ).

thf(1303,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( ~ ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) ) )
        = $false )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1277]) ).

thf(1304,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1278]) ).

thf(1305,plain,
    ! [SV117: $i,SV130: $i,SV159: $i,SV157: $i] :
      ( ( ( aElement0 @ SV157 )
        = $false )
      | ( ( ~ ( aElement0 @ SV159 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1279]) ).

thf(1306,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1280]) ).

thf(1307,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1281]) ).

thf(1308,plain,
    ! [SV164: $i] :
      ( ( ~ ( aDivisorOf0 @ SV164 @ xa )
        | ~ ( aDivisorOf0 @ SV164 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
             != xc )
            | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1282]) ).

thf(1309,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1283]) ).

thf(1310,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1284]) ).

thf(1311,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1285]) ).

thf(1312,plain,
    ! [SV165: $i] :
      ( ( ~ ( aDivisorOf0 @ SV165 @ xa )
        | ~ ( aDivisorOf0 @ SV165 @ xb )
        | ( doDivides0 @ SV165 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1286]) ).

thf(1313,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1287]) ).

thf(1314,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1288]) ).

thf(1315,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb )
      | ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1289]) ).

thf(1316,plain,
    ! [SV118: $i,SV131: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV131 @ SV118 ) @ SV118 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV131 @ SV118 ) @ SV131 )
        = $false )
      | ( ( SV118 = SV131 )
        = $true )
      | ( ( aSet0 @ SV118 )
        = $false )
      | ( ( aSet0 @ SV131 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1292]) ).

thf(1317,plain,
    ! [SV153: $i,SV160: $i,SV158: $i] :
      ( ( ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV158 @ SV160 )
           != SV153 ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1293]) ).

thf(1318,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1294]) ).

thf(1319,plain,
    ! [SV161: $i,SV163: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV163 )
           != SV161 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV163 ) )
        = $true )
      | ( ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1296]) ).

thf(1320,plain,
    ! [SV162: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
           != SV162 )
          | ~ ( aElement0 @ ( sK8_W1 @ SV162 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1297]) ).

thf(1321,plain,
    ! [SV166: $i] :
      ( ( ! [SY155: $i] :
            ( ( ( sdtasdt0 @ xa @ SY155 )
             != SV166 )
            | ~ ( aElement0 @ SY155 ) )
        | ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1298]) ).

thf(1322,plain,
    ! [SV167: $i] :
      ( ( ~ ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
             != SV167 )
            | ~ ( aElement0 @ ( sK7_W1 @ SV167 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1299]) ).

thf(1323,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
      | ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1300]) ).

thf(1324,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( aElement0 @ ( sK1_W2 @ SV132 @ SV120 ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1302]) ).

thf(1325,plain,
    ! [SV120: $i,SV132: $i] :
      ( ( ( aElement0 @ ( sK2_SY72 @ SV132 @ SV120 ) )
        = $true )
      | ( ( SV132 = sz00 )
        = $true )
      | ( ( aElement0 @ SV120 )
        = $false )
      | ( ( aElement0 @ SV132 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1303]) ).

thf(1326,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1304]) ).

thf(1327,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1305]) ).

thf(1328,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1306]) ).

thf(1329,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1306]) ).

thf(1330,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1307]) ).

thf(1331,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1307]) ).

thf(1332,plain,
    ! [SV164: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV164 @ xa )
          | ~ ( aDivisorOf0 @ SV164 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1308]) ).

thf(1333,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1309]) ).

thf(1334,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1309]) ).

thf(1335,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1310]) ).

thf(1336,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1310]) ).

thf(1337,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1311]) ).

thf(1338,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1311]) ).

thf(1339,plain,
    ! [SV165: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV165 @ xa )
          | ~ ( aDivisorOf0 @ SV165 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV165 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1312]) ).

thf(1340,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1313]) ).

thf(1341,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1313]) ).

thf(1342,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1314]) ).

thf(1343,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1314]) ).

thf(1344,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1315]) ).

thf(1345,plain,
    ( ( ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1315]) ).

thf(1346,plain,
    ! [SV153: $i,SV158: $i,SV160: $i] :
      ( ( ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ( ( sdtpldt0 @ SV158 @ SV160 )
           != SV153 ) )
        = $true )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1317]) ).

thf(1347,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1318]) ).

thf(1348,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1318]) ).

thf(1349,plain,
    ! [SV161: $i,SV163: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV163 )
          = SV161 )
        = $false )
      | ( ( ~ ( aElement0 @ SV163 ) )
        = $true )
      | ( ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1319]) ).

thf(1350,plain,
    ! [SV162: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
           != SV162 ) )
        = $false )
      | ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1320]) ).

thf(1351,plain,
    ! [SV162: $i] :
      ( ( ( ~ ( aElement0 @ ( sK8_W1 @ SV162 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1320]) ).

thf(1352,plain,
    ! [SV166: $i] :
      ( ( ( ! [SY155: $i] :
              ( ( ( sdtasdt0 @ xa @ SY155 )
               != SV166 )
              | ~ ( aElement0 @ SY155 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1321]) ).

thf(1353,plain,
    ! [SV167: $i] :
      ( ( ( ~ ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
               != SV167 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV167 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1322]) ).

thf(1354,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1323]) ).

thf(1355,plain,
    ( ( ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1323]) ).

thf(1356,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1326]) ).

thf(1357,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1326]) ).

thf(1358,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1327]) ).

thf(1359,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1328]) ).

thf(1360,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1329]) ).

thf(1361,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1330]) ).

thf(1362,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1331]) ).

thf(1363,plain,
    ! [SV164: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV164 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV164 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1332]) ).

thf(1364,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1333]) ).

thf(1365,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1334]) ).

thf(1366,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1335]) ).

thf(1367,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1336]) ).

thf(1368,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1337]) ).

thf(1369,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1338]) ).

thf(1370,plain,
    ! [SV165: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV165 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV165 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV165 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1339]) ).

thf(1371,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1340]) ).

thf(1372,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1341]) ).

thf(1373,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                             != xa )
                            | ~ ( aElement0 @ sK12_W0 ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ( doDivides0 @ xc @ xa ) )
          | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1342]) ).

thf(1374,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1343]) ).

thf(1375,plain,
    ( ( ( sdtasdt0 @ xc @ sK11_W0 )
      = xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1344]) ).

thf(1376,plain,
    ( ( aElement0 @ sK11_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1345]) ).

thf(1377,plain,
    ! [SV153: $i,SV160: $i,SV158: $i] :
      ( ( ( ( sdtpldt0 @ SV158 @ SV160 )
          = SV153 )
        = $false )
      | ( ( aElementOf0 @ SV158 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( aElementOf0 @ SV160 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV153 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1346]) ).

thf(1378,plain,
    ! [SV154: $i] :
      ( ( ( aElementOf0 @ ( sK9_W1 @ SV154 ) @ ( slsdtgt0 @ xa ) )
        = $true )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1347]) ).

thf(1379,plain,
    ! [SV154: $i] :
      ( ( ( aElementOf0 @ ( sK10_SY73 @ SV154 ) @ ( slsdtgt0 @ xb ) )
        = $true )
      | ( ( aElementOf0 @ SV154 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1348]) ).

thf(1380,plain,
    ! [SV161: $i,SV163: $i] :
      ( ( ( aElement0 @ SV163 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV163 )
          = SV161 )
        = $false )
      | ( ( aElementOf0 @ SV161 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1349]) ).

thf(1381,plain,
    ! [SV162: $i] :
      ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV162 ) )
          = SV162 )
        = $true )
      | ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1350]) ).

thf(1382,plain,
    ! [SV162: $i] :
      ( ( ( aElement0 @ ( sK8_W1 @ SV162 ) )
        = $true )
      | ( ( aElementOf0 @ SV162 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1351]) ).

thf(1383,plain,
    ! [SV166: $i,SV168: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV168 )
           != SV166 )
          | ~ ( aElement0 @ SV168 ) )
        = $true )
      | ( ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1352]) ).

thf(1384,plain,
    ! [SV167: $i] :
      ( ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
               != SV167 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV167 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1353]) ).

thf(1385,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ xI )
                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElement0 @ SX1 )
                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1354]) ).

thf(1386,plain,
    ( ( aSet0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1355]) ).

thf(1387,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) ) )
        = $true )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1356]) ).

thf(1388,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV156 @ SV130 )
        = $true )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1357]) ).

thf(1389,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1358]) ).

thf(1390,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1358]) ).

thf(1391,plain,
    ! [SV169: $i] :
      ( ( ~ ( aElement0 @ SV169 )
        | ! [SY156: $i] :
            ( ( ( sdtasdt0 @ SV169 @ SY156 )
             != xa )
            | ~ ( aElement0 @ SY156 ) )
        | ~ ( aDivisorOf0 @ SV169 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
             != xc )
            | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1359]) ).

thf(1392,plain,
    ! [SV170: $i] :
      ( ( ~ ( aElement0 @ SV170 )
        | ~ ( doDivides0 @ SV170 @ xa )
        | ~ ( aDivisorOf0 @ SV170 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
             != xc )
            | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1360]) ).

thf(1393,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1361]) ).

thf(1394,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1362]) ).

thf(1395,plain,
    ! [SV164: $i] :
      ( ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV164 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1363]) ).

thf(1396,plain,
    ! [SV171: $i] :
      ( ( ~ ( aDivisorOf0 @ SV171 @ xa )
        | ! [SY157: $i] :
            ( ( ( sdtasdt0 @ SV171 @ SY157 )
             != xb )
            | ~ ( aElement0 @ SY157 ) )
        | ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
             != xc )
            | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1364]) ).

thf(1397,plain,
    ! [SV172: $i] :
      ( ( ~ ( aDivisorOf0 @ SV172 @ xa )
        | ~ ( doDivides0 @ SV172 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
             != xc )
            | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1365]) ).

thf(1398,plain,
    ! [SV173: $i] :
      ( ( ~ ( aElement0 @ SV173 )
        | ! [SY158: $i] :
            ( ( ( sdtasdt0 @ SV173 @ SY158 )
             != xa )
            | ~ ( aElement0 @ SY158 ) )
        | ~ ( aDivisorOf0 @ SV173 @ xb )
        | ( doDivides0 @ SV173 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1366]) ).

thf(1399,plain,
    ! [SV174: $i] :
      ( ( ~ ( aElement0 @ SV174 )
        | ~ ( doDivides0 @ SV174 @ xa )
        | ~ ( aDivisorOf0 @ SV174 @ xb )
        | ( doDivides0 @ SV174 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1367]) ).

thf(1400,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1368]) ).

thf(1401,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1369]) ).

thf(1402,plain,
    ! [SV165: $i] :
      ( ( ( aDivisorOf0 @ SV165 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV165 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV165 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1370]) ).

thf(1403,plain,
    ! [SV175: $i] :
      ( ( ~ ( aDivisorOf0 @ SV175 @ xa )
        | ! [SY159: $i] :
            ( ( ( sdtasdt0 @ SV175 @ SY159 )
             != xb )
            | ~ ( aElement0 @ SY159 ) )
        | ( doDivides0 @ SV175 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1371]) ).

thf(1404,plain,
    ! [SV176: $i] :
      ( ( ~ ( aDivisorOf0 @ SV176 @ xa )
        | ~ ( doDivides0 @ SV176 @ xb )
        | ( doDivides0 @ SV176 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1372]) ).

thf(1405,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) )
      | ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1373]) ).

thf(1406,plain,
    ! [SV166: $i,SV168: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV168 )
           != SV166 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV168 ) )
        = $true )
      | ( ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1383]) ).

thf(1407,plain,
    ! [SV167: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
           != SV167 )
          | ~ ( aElement0 @ ( sK7_W1 @ SV167 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1384]) ).

thf(1408,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1385]) ).

thf(1409,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1387]) ).

thf(1410,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) ) )
        = $true )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1389]) ).

thf(1411,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV159 @ SV130 )
        = $true )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1390]) ).

thf(1412,plain,
    ! [SV169: $i] :
      ( ( ( ~ ( aElement0 @ SV169 )
          | ! [SY156: $i] :
              ( ( ( sdtasdt0 @ SV169 @ SY156 )
               != xa )
              | ~ ( aElement0 @ SY156 ) )
          | ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1391]) ).

thf(1413,plain,
    ! [SV170: $i] :
      ( ( ( ~ ( aElement0 @ SV170 )
          | ~ ( doDivides0 @ SV170 @ xa )
          | ~ ( aDivisorOf0 @ SV170 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1392]) ).

thf(1414,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1393]) ).

thf(1415,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1393]) ).

thf(1416,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1394]) ).

thf(1417,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1394]) ).

thf(1418,plain,
    ! [SV164: $i] :
      ( ( ( aDivisorOf0 @ SV164 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1395]) ).

thf(1419,plain,
    ! [SV171: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV171 @ xa )
          | ! [SY157: $i] :
              ( ( ( sdtasdt0 @ SV171 @ SY157 )
               != xb )
              | ~ ( aElement0 @ SY157 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1396]) ).

thf(1420,plain,
    ! [SV172: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV172 @ xa )
          | ~ ( doDivides0 @ SV172 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1397]) ).

thf(1421,plain,
    ! [SV173: $i] :
      ( ( ( ~ ( aElement0 @ SV173 )
          | ! [SY158: $i] :
              ( ( ( sdtasdt0 @ SV173 @ SY158 )
               != xa )
              | ~ ( aElement0 @ SY158 ) )
          | ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1398]) ).

thf(1422,plain,
    ! [SV174: $i] :
      ( ( ( ~ ( aElement0 @ SV174 )
          | ~ ( doDivides0 @ SV174 @ xa )
          | ~ ( aDivisorOf0 @ SV174 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1399]) ).

thf(1423,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1400]) ).

thf(1424,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1400]) ).

thf(1425,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1401]) ).

thf(1426,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1401]) ).

thf(1427,plain,
    ! [SV165: $i] :
      ( ( ( aDivisorOf0 @ SV165 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV165 @ xa )
        = $false )
      | ( ( doDivides0 @ SV165 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1402]) ).

thf(1428,plain,
    ! [SV175: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV175 @ xa )
          | ! [SY159: $i] :
              ( ( ( sdtasdt0 @ SV175 @ SY159 )
               != xb )
              | ~ ( aElement0 @ SY159 ) ) )
        = $true )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1403]) ).

thf(1429,plain,
    ! [SV176: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV176 @ xa )
          | ~ ( doDivides0 @ SV176 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV176 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1404]) ).

thf(1430,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1405]) ).

thf(1431,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1405]) ).

thf(1432,plain,
    ! [SV166: $i,SV168: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV168 )
          = SV166 )
        = $false )
      | ( ( ~ ( aElement0 @ SV168 ) )
        = $true )
      | ( ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1406]) ).

thf(1433,plain,
    ! [SV167: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
           != SV167 ) )
        = $false )
      | ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1407]) ).

thf(1434,plain,
    ! [SV167: $i] :
      ( ( ( ~ ( aElement0 @ ( sK7_W1 @ SV167 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1407]) ).

thf(1435,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1408]) ).

thf(1436,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1408]) ).

thf(1437,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1409]) ).

thf(1438,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 ) )
        = $false )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1409]) ).

thf(1439,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1410]) ).

thf(1440,plain,
    ! [SV169: $i] :
      ( ( ( ~ ( aElement0 @ SV169 )
          | ! [SY156: $i] :
              ( ( ( sdtasdt0 @ SV169 @ SY156 )
               != xa )
              | ~ ( aElement0 @ SY156 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1412]) ).

thf(1441,plain,
    ! [SV170: $i] :
      ( ( ( ~ ( aElement0 @ SV170 )
          | ~ ( doDivides0 @ SV170 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV170 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1413]) ).

thf(1442,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1414]) ).

thf(1443,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1415]) ).

thf(1444,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1416]) ).

thf(1445,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1417]) ).

thf(1446,plain,
    ! [SV164: $i] :
      ( ( ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
           != xc )
          | ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1418]) ).

thf(1447,plain,
    ! [SV171: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV171 @ xa ) )
        = $true )
      | ( ( ! [SY157: $i] :
              ( ( ( sdtasdt0 @ SV171 @ SY157 )
               != xb )
              | ~ ( aElement0 @ SY157 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1419]) ).

thf(1448,plain,
    ! [SV172: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV172 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV172 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1420]) ).

thf(1449,plain,
    ! [SV173: $i] :
      ( ( ( ~ ( aElement0 @ SV173 )
          | ! [SY158: $i] :
              ( ( ( sdtasdt0 @ SV173 @ SY158 )
               != xa )
              | ~ ( aElement0 @ SY158 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1421]) ).

thf(1450,plain,
    ! [SV174: $i] :
      ( ( ( ~ ( aElement0 @ SV174 )
          | ~ ( doDivides0 @ SV174 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV174 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1422]) ).

thf(1451,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1423]) ).

thf(1452,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1424]) ).

thf(1453,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1425]) ).

thf(1454,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1426]) ).

thf(1455,plain,
    ! [SV175: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV175 @ xa ) )
        = $true )
      | ( ( ! [SY159: $i] :
              ( ( ( sdtasdt0 @ SV175 @ SY159 )
               != xb )
              | ~ ( aElement0 @ SY159 ) ) )
        = $true )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1428]) ).

thf(1456,plain,
    ! [SV176: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV176 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV176 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV176 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1429]) ).

thf(1457,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                       != xa )
                      | ~ ( aElement0 @ sK12_W0 ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ( doDivides0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1430]) ).

thf(1458,plain,
    ( ( aDivisorOf0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1431]) ).

thf(1459,plain,
    ! [SV166: $i,SV168: $i] :
      ( ( ( aElement0 @ SV168 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV168 )
          = SV166 )
        = $false )
      | ( ( aElementOf0 @ SV166 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1432]) ).

thf(1460,plain,
    ! [SV167: $i] :
      ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV167 ) )
          = SV167 )
        = $true )
      | ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1433]) ).

thf(1461,plain,
    ! [SV167: $i] :
      ( ( ( aElement0 @ ( sK7_W1 @ SV167 ) )
        = $true )
      | ( ( aElementOf0 @ SV167 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1434]) ).

thf(1462,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElementOf0 @ SX1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1435]) ).

thf(1463,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElement0 @ SX1 )
              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1436]) ).

thf(1464,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1437]) ).

thf(1465,plain,
    ! [SV117: $i,SV130: $i,SV155: $i,SV156: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV156 @ SV155 @ SV130 @ SV117 ) @ SV155 @ SV117 )
        = $true )
      | ( ( aElement0 @ SV155 )
        = $false )
      | ( ( aElement0 @ SV156 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1438]) ).

thf(1466,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1439]) ).

thf(1467,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 ) )
        = $false )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1439]) ).

thf(1468,plain,
    ! [SV169: $i] :
      ( ( ( ~ ( aElement0 @ SV169 ) )
        = $true )
      | ( ( ! [SY156: $i] :
              ( ( ( sdtasdt0 @ SV169 @ SY156 )
               != xa )
              | ~ ( aElement0 @ SY156 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1440]) ).

thf(1469,plain,
    ! [SV170: $i] :
      ( ( ( ~ ( aElement0 @ SV170 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV170 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV170 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1441]) ).

thf(1470,plain,
    ! [SV177: $i] :
      ( ( ~ ( aElement0 @ SV177 )
        | ! [SY160: $i] :
            ( ( ( sdtasdt0 @ SV177 @ SY160 )
             != xa )
            | ~ ( aElement0 @ SY160 ) )
        | ! [SY161: $i] :
            ( ( ( sdtasdt0 @ SV177 @ SY161 )
             != xb )
            | ~ ( aElement0 @ SY161 ) )
        | ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
             != xc )
            | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1442]) ).

thf(1471,plain,
    ! [SV178: $i] :
      ( ( ~ ( aElement0 @ SV178 )
        | ~ ( doDivides0 @ SV178 @ xa )
        | ! [SY162: $i] :
            ( ( ( sdtasdt0 @ SV178 @ SY162 )
             != xb )
            | ~ ( aElement0 @ SY162 ) )
        | ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
             != xc )
            | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1443]) ).

thf(1472,plain,
    ! [SV179: $i] :
      ( ( ~ ( aElement0 @ SV179 )
        | ! [SY163: $i] :
            ( ( ( sdtasdt0 @ SV179 @ SY163 )
             != xa )
            | ~ ( aElement0 @ SY163 ) )
        | ~ ( doDivides0 @ SV179 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
             != xc )
            | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1444]) ).

thf(1473,plain,
    ! [SV180: $i] :
      ( ( ~ ( aElement0 @ SV180 )
        | ~ ( doDivides0 @ SV180 @ xa )
        | ~ ( doDivides0 @ SV180 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
             != xc )
            | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1445]) ).

thf(1474,plain,
    ! [SV164: $i] :
      ( ( ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1446]) ).

thf(1475,plain,
    ! [SV164: $i] :
      ( ( ( ~ ( aElement0 @ ( sK15_W1 @ SV164 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1446]) ).

thf(1476,plain,
    ! [SV171: $i] :
      ( ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ! [SY157: $i] :
              ( ( ( sdtasdt0 @ SV171 @ SY157 )
               != xb )
              | ~ ( aElement0 @ SY157 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1447]) ).

thf(1477,plain,
    ! [SV172: $i] :
      ( ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV172 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1448]) ).

thf(1478,plain,
    ! [SV173: $i] :
      ( ( ( ~ ( aElement0 @ SV173 ) )
        = $true )
      | ( ( ! [SY158: $i] :
              ( ( ( sdtasdt0 @ SV173 @ SY158 )
               != xa )
              | ~ ( aElement0 @ SY158 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1449]) ).

thf(1479,plain,
    ! [SV174: $i] :
      ( ( ( ~ ( aElement0 @ SV174 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV174 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV174 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1450]) ).

thf(1480,plain,
    ! [SV181: $i] :
      ( ( ~ ( aElement0 @ SV181 )
        | ! [SY164: $i] :
            ( ( ( sdtasdt0 @ SV181 @ SY164 )
             != xa )
            | ~ ( aElement0 @ SY164 ) )
        | ! [SY165: $i] :
            ( ( ( sdtasdt0 @ SV181 @ SY165 )
             != xb )
            | ~ ( aElement0 @ SY165 ) )
        | ( doDivides0 @ SV181 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1451]) ).

thf(1481,plain,
    ! [SV182: $i] :
      ( ( ~ ( aElement0 @ SV182 )
        | ~ ( doDivides0 @ SV182 @ xa )
        | ! [SY166: $i] :
            ( ( ( sdtasdt0 @ SV182 @ SY166 )
             != xb )
            | ~ ( aElement0 @ SY166 ) )
        | ( doDivides0 @ SV182 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1452]) ).

thf(1482,plain,
    ! [SV183: $i] :
      ( ( ~ ( aElement0 @ SV183 )
        | ! [SY167: $i] :
            ( ( ( sdtasdt0 @ SV183 @ SY167 )
             != xa )
            | ~ ( aElement0 @ SY167 ) )
        | ~ ( doDivides0 @ SV183 @ xb )
        | ( doDivides0 @ SV183 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1453]) ).

thf(1483,plain,
    ! [SV184: $i] :
      ( ( ~ ( aElement0 @ SV184 )
        | ~ ( doDivides0 @ SV184 @ xa )
        | ~ ( doDivides0 @ SV184 @ xb )
        | ( doDivides0 @ SV184 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1454]) ).

thf(1484,plain,
    ! [SV175: $i] :
      ( ( ( aDivisorOf0 @ SV175 @ xa )
        = $false )
      | ( ( ! [SY159: $i] :
              ( ( ( sdtasdt0 @ SV175 @ SY159 )
               != xb )
              | ~ ( aElement0 @ SY159 ) ) )
        = $true )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1455]) ).

thf(1485,plain,
    ! [SV176: $i] :
      ( ( ( aDivisorOf0 @ SV176 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV176 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV176 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1456]) ).

thf(1486,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1457]) ).

thf(1487,plain,
    ! [SV185: $i] :
      ( ( ~ ( aElementOf0 @ SV185 @ xI )
        | ! [SY168: $i] :
            ( ~ ( aElementOf0 @ SY168 @ xI )
            | ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SY168 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1462]) ).

thf(1488,plain,
    ! [SV186: $i] :
      ( ( ~ ( aElementOf0 @ SV186 @ xI )
        | ! [SY169: $i] :
            ( ~ ( aElement0 @ SY169 )
            | ( aElementOf0 @ ( sdtasdt0 @ SY169 @ SV186 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1463]) ).

thf(1489,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) )
        = $true )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1466]) ).

thf(1490,plain,
    ! [SV117: $i,SV130: $i,SV157: $i,SV159: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV159 @ SV157 @ SV130 @ SV117 ) @ SV157 @ SV117 )
        = $true )
      | ( ( aElement0 @ SV157 )
        = $false )
      | ( ( aElement0 @ SV159 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV130 @ SV117 ) @ ( sdtpldt1 @ SV117 @ SV130 ) )
        = $false )
      | ( ( aIdeal0 @ SV117 )
        = $false )
      | ( ( aIdeal0 @ SV130 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1467]) ).

thf(1491,plain,
    ! [SV169: $i] :
      ( ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ! [SY156: $i] :
              ( ( ( sdtasdt0 @ SV169 @ SY156 )
               != xa )
              | ~ ( aElement0 @ SY156 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1468]) ).

thf(1492,plain,
    ! [SV170: $i] :
      ( ( ( aElement0 @ SV170 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV170 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV170 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1469]) ).

thf(1493,plain,
    ! [SV177: $i] :
      ( ( ( ~ ( aElement0 @ SV177 )
          | ! [SY160: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY160 )
               != xa )
              | ~ ( aElement0 @ SY160 ) )
          | ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1470]) ).

thf(1494,plain,
    ! [SV178: $i] :
      ( ( ( ~ ( aElement0 @ SV178 )
          | ~ ( doDivides0 @ SV178 @ xa )
          | ! [SY162: $i] :
              ( ( ( sdtasdt0 @ SV178 @ SY162 )
               != xb )
              | ~ ( aElement0 @ SY162 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1471]) ).

thf(1495,plain,
    ! [SV179: $i] :
      ( ( ( ~ ( aElement0 @ SV179 )
          | ! [SY163: $i] :
              ( ( ( sdtasdt0 @ SV179 @ SY163 )
               != xa )
              | ~ ( aElement0 @ SY163 ) )
          | ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1472]) ).

thf(1496,plain,
    ! [SV180: $i] :
      ( ( ( ~ ( aElement0 @ SV180 )
          | ~ ( doDivides0 @ SV180 @ xa )
          | ~ ( doDivides0 @ SV180 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1473]) ).

thf(1497,plain,
    ! [SV164: $i] :
      ( ( ( ( sdtasdt0 @ SV164 @ ( sK15_W1 @ SV164 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1474]) ).

thf(1498,plain,
    ! [SV164: $i] :
      ( ( ( aElement0 @ ( sK15_W1 @ SV164 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV164 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV164 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1475]) ).

thf(1499,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( ( sdtasdt0 @ SV171 @ SV187 )
           != xb )
          | ~ ( aElement0 @ SV187 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1476]) ).

thf(1500,plain,
    ! [SV172: $i] :
      ( ( ( doDivides0 @ SV172 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1477]) ).

thf(1501,plain,
    ! [SV173: $i] :
      ( ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ! [SY158: $i] :
              ( ( ( sdtasdt0 @ SV173 @ SY158 )
               != xa )
              | ~ ( aElement0 @ SY158 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1478]) ).

thf(1502,plain,
    ! [SV174: $i] :
      ( ( ( aElement0 @ SV174 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV174 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV174 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1479]) ).

thf(1503,plain,
    ! [SV181: $i] :
      ( ( ( ~ ( aElement0 @ SV181 )
          | ! [SY164: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY164 )
               != xa )
              | ~ ( aElement0 @ SY164 ) )
          | ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1480]) ).

thf(1504,plain,
    ! [SV182: $i] :
      ( ( ( ~ ( aElement0 @ SV182 )
          | ~ ( doDivides0 @ SV182 @ xa )
          | ! [SY166: $i] :
              ( ( ( sdtasdt0 @ SV182 @ SY166 )
               != xb )
              | ~ ( aElement0 @ SY166 ) ) )
        = $true )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1481]) ).

thf(1505,plain,
    ! [SV183: $i] :
      ( ( ( ~ ( aElement0 @ SV183 )
          | ! [SY167: $i] :
              ( ( ( sdtasdt0 @ SV183 @ SY167 )
               != xa )
              | ~ ( aElement0 @ SY167 ) )
          | ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1482]) ).

thf(1506,plain,
    ! [SV184: $i] :
      ( ( ( ~ ( aElement0 @ SV184 )
          | ~ ( doDivides0 @ SV184 @ xa )
          | ~ ( doDivides0 @ SV184 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1483]) ).

thf(1507,plain,
    ! [SV188: $i,SV175: $i] :
      ( ( ( ( ( sdtasdt0 @ SV175 @ SV188 )
           != xb )
          | ~ ( aElement0 @ SV188 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV175 @ xa )
        = $false )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1484]) ).

thf(1508,plain,
    ! [SV176: $i] :
      ( ( ( doDivides0 @ SV176 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV176 @ xa )
        = $false )
      | ( ( doDivides0 @ SV176 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1485]) ).

thf(1509,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1486]) ).

thf(1510,plain,
    ( ( ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1486]) ).

thf(1511,plain,
    ! [SV185: $i] :
      ( ( ( ~ ( aElementOf0 @ SV185 @ xI ) )
        = $true )
      | ( ( ! [SY168: $i] :
              ( ~ ( aElementOf0 @ SY168 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SY168 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1487]) ).

thf(1512,plain,
    ! [SV186: $i] :
      ( ( ( ~ ( aElementOf0 @ SV186 @ xI ) )
        = $true )
      | ( ( ! [SY169: $i] :
              ( ~ ( aElement0 @ SY169 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY169 @ SV186 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1488]) ).

thf(1513,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( ( sdtasdt0 @ SV169 @ SV189 )
           != xa )
          | ~ ( aElement0 @ SV189 ) )
        = $true )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1491]) ).

thf(1514,plain,
    ! [SV170: $i] :
      ( ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV170 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1492]) ).

thf(1515,plain,
    ! [SV177: $i] :
      ( ( ( ~ ( aElement0 @ SV177 )
          | ! [SY160: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY160 )
               != xa )
              | ~ ( aElement0 @ SY160 ) ) )
        = $true )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1493]) ).

thf(1516,plain,
    ! [SV178: $i] :
      ( ( ( ~ ( aElement0 @ SV178 )
          | ~ ( doDivides0 @ SV178 @ xa ) )
        = $true )
      | ( ( ! [SY162: $i] :
              ( ( ( sdtasdt0 @ SV178 @ SY162 )
               != xb )
              | ~ ( aElement0 @ SY162 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1494]) ).

thf(1517,plain,
    ! [SV179: $i] :
      ( ( ( ~ ( aElement0 @ SV179 )
          | ! [SY163: $i] :
              ( ( ( sdtasdt0 @ SV179 @ SY163 )
               != xa )
              | ~ ( aElement0 @ SY163 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1495]) ).

thf(1518,plain,
    ! [SV180: $i] :
      ( ( ( ~ ( aElement0 @ SV180 )
          | ~ ( doDivides0 @ SV180 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV180 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1496]) ).

thf(1519,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( ( sdtasdt0 @ SV171 @ SV187 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV187 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1499]) ).

thf(1520,plain,
    ! [SV172: $i] :
      ( ( ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
           != xc )
          | ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( doDivides0 @ SV172 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1500]) ).

thf(1521,plain,
    ! [SV190: $i,SV173: $i] :
      ( ( ( ( ( sdtasdt0 @ SV173 @ SV190 )
           != xa )
          | ~ ( aElement0 @ SV190 ) )
        = $true )
      | ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1501]) ).

thf(1522,plain,
    ! [SV174: $i] :
      ( ( ( doDivides0 @ SV174 @ xa )
        = $false )
      | ( ( aElement0 @ SV174 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV174 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1502]) ).

thf(1523,plain,
    ! [SV181: $i] :
      ( ( ( ~ ( aElement0 @ SV181 )
          | ! [SY164: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY164 )
               != xa )
              | ~ ( aElement0 @ SY164 ) ) )
        = $true )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1503]) ).

thf(1524,plain,
    ! [SV182: $i] :
      ( ( ( ~ ( aElement0 @ SV182 )
          | ~ ( doDivides0 @ SV182 @ xa ) )
        = $true )
      | ( ( ! [SY166: $i] :
              ( ( ( sdtasdt0 @ SV182 @ SY166 )
               != xb )
              | ~ ( aElement0 @ SY166 ) ) )
        = $true )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1504]) ).

thf(1525,plain,
    ! [SV183: $i] :
      ( ( ( ~ ( aElement0 @ SV183 )
          | ! [SY167: $i] :
              ( ( ( sdtasdt0 @ SV183 @ SY167 )
               != xa )
              | ~ ( aElement0 @ SY167 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1505]) ).

thf(1526,plain,
    ! [SV184: $i] :
      ( ( ( ~ ( aElement0 @ SV184 )
          | ~ ( doDivides0 @ SV184 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV184 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1506]) ).

thf(1527,plain,
    ! [SV188: $i,SV175: $i] :
      ( ( ( ( ( sdtasdt0 @ SV175 @ SV188 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV188 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV175 @ xa )
        = $false )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1507]) ).

thf(1528,plain,
    ( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                 != xa )
                | ~ ( aElement0 @ sK12_W0 ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1509]) ).

thf(1529,plain,
    ( ( doDivides0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1510]) ).

thf(1530,plain,
    ! [SV185: $i] :
      ( ( ( aElementOf0 @ SV185 @ xI )
        = $false )
      | ( ( ! [SY168: $i] :
              ( ~ ( aElementOf0 @ SY168 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SY168 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1511]) ).

thf(1531,plain,
    ! [SV186: $i] :
      ( ( ( aElementOf0 @ SV186 @ xI )
        = $false )
      | ( ( ! [SY169: $i] :
              ( ~ ( aElement0 @ SY169 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY169 @ SV186 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1512]) ).

thf(1532,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( ( sdtasdt0 @ SV169 @ SV189 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV189 ) )
        = $true )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1513]) ).

thf(1533,plain,
    ! [SV170: $i] :
      ( ( ( aDivisorOf0 @ SV170 @ xb )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1514]) ).

thf(1534,plain,
    ! [SV177: $i] :
      ( ( ( ~ ( aElement0 @ SV177 ) )
        = $true )
      | ( ( ! [SY160: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY160 )
               != xa )
              | ~ ( aElement0 @ SY160 ) ) )
        = $true )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1515]) ).

thf(1535,plain,
    ! [SV178: $i] :
      ( ( ( ~ ( aElement0 @ SV178 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV178 @ xa ) )
        = $true )
      | ( ( ! [SY162: $i] :
              ( ( ( sdtasdt0 @ SV178 @ SY162 )
               != xb )
              | ~ ( aElement0 @ SY162 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1516]) ).

thf(1536,plain,
    ! [SV179: $i] :
      ( ( ( ~ ( aElement0 @ SV179 ) )
        = $true )
      | ( ( ! [SY163: $i] :
              ( ( ( sdtasdt0 @ SV179 @ SY163 )
               != xa )
              | ~ ( aElement0 @ SY163 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1517]) ).

thf(1537,plain,
    ! [SV180: $i] :
      ( ( ( ~ ( aElement0 @ SV180 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV180 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV180 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1518]) ).

thf(1538,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV187 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1519]) ).

thf(1539,plain,
    ! [SV172: $i] :
      ( ( ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( doDivides0 @ SV172 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1520]) ).

thf(1540,plain,
    ! [SV172: $i] :
      ( ( ( ~ ( aElement0 @ ( sK13_W1 @ SV172 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( doDivides0 @ SV172 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1520]) ).

thf(1541,plain,
    ! [SV190: $i,SV173: $i] :
      ( ( ( ( ( sdtasdt0 @ SV173 @ SV190 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV190 ) )
        = $true )
      | ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1521]) ).

thf(1542,plain,
    ! [SV174: $i] :
      ( ( ( aDivisorOf0 @ SV174 @ xb )
        = $false )
      | ( ( aElement0 @ SV174 )
        = $false )
      | ( ( doDivides0 @ SV174 @ xa )
        = $false )
      | ( ( doDivides0 @ SV174 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1522]) ).

thf(1543,plain,
    ! [SV181: $i] :
      ( ( ( ~ ( aElement0 @ SV181 ) )
        = $true )
      | ( ( ! [SY164: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY164 )
               != xa )
              | ~ ( aElement0 @ SY164 ) ) )
        = $true )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1523]) ).

thf(1544,plain,
    ! [SV182: $i] :
      ( ( ( ~ ( aElement0 @ SV182 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV182 @ xa ) )
        = $true )
      | ( ( ! [SY166: $i] :
              ( ( ( sdtasdt0 @ SV182 @ SY166 )
               != xb )
              | ~ ( aElement0 @ SY166 ) ) )
        = $true )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1524]) ).

thf(1545,plain,
    ! [SV183: $i] :
      ( ( ( ~ ( aElement0 @ SV183 ) )
        = $true )
      | ( ( ! [SY167: $i] :
              ( ( ( sdtasdt0 @ SV183 @ SY167 )
               != xa )
              | ~ ( aElement0 @ SY167 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1525]) ).

thf(1546,plain,
    ! [SV184: $i] :
      ( ( ( ~ ( aElement0 @ SV184 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV184 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV184 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1526]) ).

thf(1547,plain,
    ! [SV188: $i,SV175: $i] :
      ( ( ( ( sdtasdt0 @ SV175 @ SV188 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV188 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV175 @ xa )
        = $false )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1527]) ).

thf(1548,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1528]) ).

thf(1549,plain,
    ! [SV185: $i,SV191: $i] :
      ( ( ( ~ ( aElementOf0 @ SV191 @ xI )
          | ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SV191 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV185 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1530]) ).

thf(1550,plain,
    ! [SV186: $i,SV192: $i] :
      ( ( ( ~ ( aElement0 @ SV192 )
          | ( aElementOf0 @ ( sdtasdt0 @ SV192 @ SV186 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV186 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1531]) ).

thf(1551,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV189 ) )
        = $true )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1532]) ).

thf(1552,plain,
    ! [SV170: $i] :
      ( ( ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
           != xc )
          | ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) )
        = $false )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( aDivisorOf0 @ SV170 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1533]) ).

thf(1553,plain,
    ! [SV177: $i] :
      ( ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ! [SY160: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY160 )
               != xa )
              | ~ ( aElement0 @ SY160 ) ) )
        = $true )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1534]) ).

thf(1554,plain,
    ! [SV178: $i] :
      ( ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV178 @ xa ) )
        = $true )
      | ( ( ! [SY162: $i] :
              ( ( ( sdtasdt0 @ SV178 @ SY162 )
               != xb )
              | ~ ( aElement0 @ SY162 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1535]) ).

thf(1555,plain,
    ! [SV179: $i] :
      ( ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ! [SY163: $i] :
              ( ( ( sdtasdt0 @ SV179 @ SY163 )
               != xa )
              | ~ ( aElement0 @ SY163 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1536]) ).

thf(1556,plain,
    ! [SV180: $i] :
      ( ( ( aElement0 @ SV180 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV180 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV180 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1537]) ).

thf(1557,plain,
    ! [SV171: $i,SV187: $i] :
      ( ( ( aElement0 @ SV187 )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1538]) ).

thf(1558,plain,
    ! [SV172: $i] :
      ( ( ( ( sdtasdt0 @ SV172 @ ( sK13_W1 @ SV172 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( doDivides0 @ SV172 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1539]) ).

thf(1559,plain,
    ! [SV172: $i] :
      ( ( ( aElement0 @ ( sK13_W1 @ SV172 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV172 @ xa )
        = $false )
      | ( ( doDivides0 @ SV172 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1540]) ).

thf(1560,plain,
    ! [SV190: $i,SV173: $i] :
      ( ( ( ( sdtasdt0 @ SV173 @ SV190 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV190 ) )
        = $true )
      | ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1541]) ).

thf(1561,plain,
    ! [SV181: $i] :
      ( ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ! [SY164: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY164 )
               != xa )
              | ~ ( aElement0 @ SY164 ) ) )
        = $true )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1543]) ).

thf(1562,plain,
    ! [SV182: $i] :
      ( ( ( aElement0 @ SV182 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV182 @ xa ) )
        = $true )
      | ( ( ! [SY166: $i] :
              ( ( ( sdtasdt0 @ SV182 @ SY166 )
               != xb )
              | ~ ( aElement0 @ SY166 ) ) )
        = $true )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1544]) ).

thf(1563,plain,
    ! [SV183: $i] :
      ( ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ! [SY167: $i] :
              ( ( ( sdtasdt0 @ SV183 @ SY167 )
               != xa )
              | ~ ( aElement0 @ SY167 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1545]) ).

thf(1564,plain,
    ! [SV184: $i] :
      ( ( ( aElement0 @ SV184 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV184 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV184 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1546]) ).

thf(1565,plain,
    ! [SV175: $i,SV188: $i] :
      ( ( ( aElement0 @ SV188 )
        = $false )
      | ( ( ( sdtasdt0 @ SV175 @ SV188 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV175 @ xa )
        = $false )
      | ( ( doDivides0 @ SV175 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1547]) ).

thf(1566,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1548]) ).

thf(1567,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1548]) ).

thf(1568,plain,
    ! [SV185: $i,SV191: $i] :
      ( ( ( ~ ( aElementOf0 @ SV191 @ xI ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SV191 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV185 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1549]) ).

thf(1569,plain,
    ! [SV186: $i,SV192: $i] :
      ( ( ( ~ ( aElement0 @ SV192 ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV192 @ SV186 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV186 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1550]) ).

thf(1570,plain,
    ! [SV169: $i,SV189: $i] :
      ( ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV169 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1551]) ).

thf(1571,plain,
    ! [SV170: $i] :
      ( ( ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( aDivisorOf0 @ SV170 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1552]) ).

thf(1572,plain,
    ! [SV170: $i] :
      ( ( ( ~ ( aElement0 @ ( sK20_W1 @ SV170 ) ) )
        = $false )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( aDivisorOf0 @ SV170 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1552]) ).

thf(1573,plain,
    ! [SV193: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ SV193 )
           != xa )
          | ~ ( aElement0 @ SV193 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1553]) ).

thf(1574,plain,
    ! [SV178: $i] :
      ( ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ! [SY162: $i] :
              ( ( ( sdtasdt0 @ SV178 @ SY162 )
               != xb )
              | ~ ( aElement0 @ SY162 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1554]) ).

thf(1575,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( ( sdtasdt0 @ SV179 @ SV194 )
           != xa )
          | ~ ( aElement0 @ SV194 ) )
        = $true )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1555]) ).

thf(1576,plain,
    ! [SV180: $i] :
      ( ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV180 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1556]) ).

thf(1577,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
           != xc )
          | ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV187 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1557]) ).

thf(1578,plain,
    ! [SV173: $i,SV190: $i] :
      ( ( ( aElement0 @ SV190 )
        = $false )
      | ( ( ( sdtasdt0 @ SV173 @ SV190 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV173 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1560]) ).

thf(1579,plain,
    ! [SV195: $i,SV181: $i] :
      ( ( ( ( ( sdtasdt0 @ SV181 @ SV195 )
           != xa )
          | ~ ( aElement0 @ SV195 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1561]) ).

thf(1580,plain,
    ! [SV182: $i] :
      ( ( ( doDivides0 @ SV182 @ xa )
        = $false )
      | ( ( aElement0 @ SV182 )
        = $false )
      | ( ( ! [SY166: $i] :
              ( ( ( sdtasdt0 @ SV182 @ SY166 )
               != xb )
              | ~ ( aElement0 @ SY166 ) ) )
        = $true )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1562]) ).

thf(1581,plain,
    ! [SV196: $i,SV183: $i] :
      ( ( ( ( ( sdtasdt0 @ SV183 @ SV196 )
           != xa )
          | ~ ( aElement0 @ SV196 ) )
        = $true )
      | ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1563]) ).

thf(1582,plain,
    ! [SV184: $i] :
      ( ( ( doDivides0 @ SV184 @ xa )
        = $false )
      | ( ( aElement0 @ SV184 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV184 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1564]) ).

thf(1583,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
           != xa )
          | ~ ( aElement0 @ sK12_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1566]) ).

thf(1584,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1567]) ).

thf(1585,plain,
    ! [SV185: $i,SV191: $i] :
      ( ( ( aElementOf0 @ SV191 @ xI )
        = $false )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV185 @ SV191 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV185 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1568]) ).

thf(1586,plain,
    ! [SV186: $i,SV192: $i] :
      ( ( ( aElement0 @ SV192 )
        = $false )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV192 @ SV186 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV186 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1569]) ).

thf(1587,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( aDivisorOf0 @ SV169 @ xb )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1570]) ).

thf(1588,plain,
    ! [SV170: $i] :
      ( ( ( ( sdtasdt0 @ SV170 @ ( sK20_W1 @ SV170 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( aDivisorOf0 @ SV170 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1571]) ).

thf(1589,plain,
    ! [SV170: $i] :
      ( ( ( aElement0 @ ( sK20_W1 @ SV170 ) )
        = $true )
      | ( ( doDivides0 @ SV170 @ xa )
        = $false )
      | ( ( aElement0 @ SV170 )
        = $false )
      | ( ( aDivisorOf0 @ SV170 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1572]) ).

thf(1590,plain,
    ! [SV193: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ SV193 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV193 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1573]) ).

thf(1591,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( ( sdtasdt0 @ SV178 @ SV197 )
           != xb )
          | ~ ( aElement0 @ SV197 ) )
        = $true )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1574]) ).

thf(1592,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( ( sdtasdt0 @ SV179 @ SV194 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV194 ) )
        = $true )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1575]) ).

thf(1593,plain,
    ! [SV180: $i] :
      ( ( ( doDivides0 @ SV180 @ xb )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1576]) ).

thf(1594,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV187 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1577]) ).

thf(1595,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ~ ( aElement0 @ ( sK14_W1 @ SV171 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV187 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1577]) ).

thf(1596,plain,
    ! [SV190: $i,SV173: $i] :
      ( ( ( aDivisorOf0 @ SV173 @ xb )
        = $false )
      | ( ( aElement0 @ SV173 )
        = $false )
      | ( ( ( sdtasdt0 @ SV173 @ SV190 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV190 )
        = $false )
      | ( ( doDivides0 @ SV173 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1578]) ).

thf(1597,plain,
    ! [SV195: $i,SV181: $i] :
      ( ( ( ( ( sdtasdt0 @ SV181 @ SV195 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV195 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1579]) ).

thf(1598,plain,
    ! [SV198: $i,SV182: $i] :
      ( ( ( ( ( sdtasdt0 @ SV182 @ SV198 )
           != xb )
          | ~ ( aElement0 @ SV198 ) )
        = $true )
      | ( ( aElement0 @ SV182 )
        = $false )
      | ( ( doDivides0 @ SV182 @ xa )
        = $false )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1580]) ).

thf(1599,plain,
    ! [SV196: $i,SV183: $i] :
      ( ( ( ( ( sdtasdt0 @ SV183 @ SV196 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV196 ) )
        = $true )
      | ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1581]) ).

thf(1600,plain,
    ! [SV184: $i] :
      ( ( ( doDivides0 @ SV184 @ xb )
        = $false )
      | ( ( aElement0 @ SV184 )
        = $false )
      | ( ( doDivides0 @ SV184 @ xa )
        = $false )
      | ( ( doDivides0 @ SV184 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1582]) ).

thf(1601,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa )
      | ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1583]) ).

thf(1602,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
           != xc )
          | ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) )
        = $false )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( aDivisorOf0 @ SV169 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1587]) ).

thf(1603,plain,
    ! [SV193: $i,SV177: $i] :
      ( ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV193 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1590]) ).

thf(1604,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( ( sdtasdt0 @ SV178 @ SV197 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV197 ) )
        = $true )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1591]) ).

thf(1605,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV194 ) )
        = $true )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1592]) ).

thf(1606,plain,
    ! [SV180: $i] :
      ( ( ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
           != xc )
          | ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) )
        = $false )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1593]) ).

thf(1607,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( ( sdtasdt0 @ SV171 @ ( sK14_W1 @ SV171 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV187 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1594]) ).

thf(1608,plain,
    ! [SV187: $i,SV171: $i] :
      ( ( ( aElement0 @ ( sK14_W1 @ SV171 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV171 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV171 @ SV187 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV187 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1595]) ).

thf(1609,plain,
    ! [SV195: $i,SV181: $i] :
      ( ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV195 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1597]) ).

thf(1610,plain,
    ! [SV198: $i,SV182: $i] :
      ( ( ( ( ( sdtasdt0 @ SV182 @ SV198 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV198 ) )
        = $true )
      | ( ( aElement0 @ SV182 )
        = $false )
      | ( ( doDivides0 @ SV182 @ xa )
        = $false )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1598]) ).

thf(1611,plain,
    ! [SV196: $i,SV183: $i] :
      ( ( ( ( sdtasdt0 @ SV183 @ SV196 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV196 ) )
        = $true )
      | ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1599]) ).

thf(1612,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1601]) ).

thf(1613,plain,
    ( ( ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1601]) ).

thf(1614,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( aDivisorOf0 @ SV169 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1602]) ).

thf(1615,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ~ ( aElement0 @ ( sK21_W1 @ SV169 ) ) )
        = $false )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( aDivisorOf0 @ SV169 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1602]) ).

thf(1616,plain,
    ! [SV177: $i,SV193: $i] :
      ( ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ! [SY161: $i] :
              ( ( ( sdtasdt0 @ SV177 @ SY161 )
               != xb )
              | ~ ( aElement0 @ SY161 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1603]) ).

thf(1617,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV197 ) )
        = $true )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1604]) ).

thf(1618,plain,
    ! [SV179: $i,SV194: $i] :
      ( ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV179 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1605]) ).

thf(1619,plain,
    ! [SV180: $i] :
      ( ( ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1606]) ).

thf(1620,plain,
    ! [SV180: $i] :
      ( ( ( ~ ( aElement0 @ ( sK16_W1 @ SV180 ) ) )
        = $false )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1606]) ).

thf(1621,plain,
    ! [SV181: $i,SV195: $i] :
      ( ( ( aElement0 @ SV195 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ! [SY165: $i] :
              ( ( ( sdtasdt0 @ SV181 @ SY165 )
               != xb )
              | ~ ( aElement0 @ SY165 ) ) )
        = $true )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1609]) ).

thf(1622,plain,
    ! [SV198: $i,SV182: $i] :
      ( ( ( ( sdtasdt0 @ SV182 @ SV198 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV198 ) )
        = $true )
      | ( ( aElement0 @ SV182 )
        = $false )
      | ( ( doDivides0 @ SV182 @ xa )
        = $false )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1610]) ).

thf(1623,plain,
    ! [SV183: $i,SV196: $i] :
      ( ( ( aElement0 @ SV196 )
        = $false )
      | ( ( ( sdtasdt0 @ SV183 @ SV196 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV183 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1611]) ).

thf(1624,plain,
    ( ( ( sdtasdt0 @ xc @ sK12_W0 )
      = xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1612]) ).

thf(1625,plain,
    ( ( aElement0 @ sK12_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1613]) ).

thf(1626,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( ( sdtasdt0 @ SV169 @ ( sK21_W1 @ SV169 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( aDivisorOf0 @ SV169 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1614]) ).

thf(1627,plain,
    ! [SV189: $i,SV169: $i] :
      ( ( ( aElement0 @ ( sK21_W1 @ SV169 ) )
        = $true )
      | ( ( aElement0 @ SV189 )
        = $false )
      | ( ( ( sdtasdt0 @ SV169 @ SV189 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV169 )
        = $false )
      | ( ( aDivisorOf0 @ SV169 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1615]) ).

thf(1628,plain,
    ! [SV193: $i,SV199: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ SV199 )
           != xb )
          | ~ ( aElement0 @ SV199 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1616]) ).

thf(1629,plain,
    ! [SV178: $i,SV197: $i] :
      ( ( ( aElement0 @ SV197 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1617]) ).

thf(1630,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( doDivides0 @ SV179 @ xb )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1618]) ).

thf(1631,plain,
    ! [SV180: $i] :
      ( ( ( ( sdtasdt0 @ SV180 @ ( sK16_W1 @ SV180 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1619]) ).

thf(1632,plain,
    ! [SV180: $i] :
      ( ( ( aElement0 @ ( sK16_W1 @ SV180 ) )
        = $true )
      | ( ( doDivides0 @ SV180 @ xa )
        = $false )
      | ( ( aElement0 @ SV180 )
        = $false )
      | ( ( doDivides0 @ SV180 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1620]) ).

thf(1633,plain,
    ! [SV195: $i,SV200: $i,SV181: $i] :
      ( ( ( ( ( sdtasdt0 @ SV181 @ SV200 )
           != xb )
          | ~ ( aElement0 @ SV200 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV195 )
        = $false )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1621]) ).

thf(1634,plain,
    ! [SV182: $i,SV198: $i] :
      ( ( ( aElement0 @ SV198 )
        = $false )
      | ( ( ( sdtasdt0 @ SV182 @ SV198 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV182 )
        = $false )
      | ( ( doDivides0 @ SV182 @ xa )
        = $false )
      | ( ( doDivides0 @ SV182 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1622]) ).

thf(1635,plain,
    ! [SV196: $i,SV183: $i] :
      ( ( ( doDivides0 @ SV183 @ xb )
        = $false )
      | ( ( aElement0 @ SV183 )
        = $false )
      | ( ( ( sdtasdt0 @ SV183 @ SV196 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV196 )
        = $false )
      | ( ( doDivides0 @ SV183 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1623]) ).

thf(1636,plain,
    ! [SV193: $i,SV199: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ SV199 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV199 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1628]) ).

thf(1637,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
           != xc )
          | ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV197 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1629]) ).

thf(1638,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
           != xc )
          | ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) )
        = $false )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( doDivides0 @ SV179 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1630]) ).

thf(1639,plain,
    ! [SV195: $i,SV200: $i,SV181: $i] :
      ( ( ( ( ( sdtasdt0 @ SV181 @ SV200 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV200 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV195 )
        = $false )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1633]) ).

thf(1640,plain,
    ! [SV193: $i,SV199: $i,SV177: $i] :
      ( ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV199 ) )
        = $true )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1636]) ).

thf(1641,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV197 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1637]) ).

thf(1642,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ~ ( aElement0 @ ( sK18_W1 @ SV178 ) ) )
        = $false )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV197 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1637]) ).

thf(1643,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( doDivides0 @ SV179 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1638]) ).

thf(1644,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ~ ( aElement0 @ ( sK17_W1 @ SV179 ) ) )
        = $false )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( doDivides0 @ SV179 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1638]) ).

thf(1645,plain,
    ! [SV195: $i,SV200: $i,SV181: $i] :
      ( ( ( ( sdtasdt0 @ SV181 @ SV200 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV200 ) )
        = $true )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV195 )
        = $false )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1639]) ).

thf(1646,plain,
    ! [SV193: $i,SV177: $i,SV199: $i] :
      ( ( ( aElement0 @ SV199 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1640]) ).

thf(1647,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( ( sdtasdt0 @ SV178 @ ( sK18_W1 @ SV178 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV197 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1641]) ).

thf(1648,plain,
    ! [SV197: $i,SV178: $i] :
      ( ( ( aElement0 @ ( sK18_W1 @ SV178 ) )
        = $true )
      | ( ( doDivides0 @ SV178 @ xa )
        = $false )
      | ( ( aElement0 @ SV178 )
        = $false )
      | ( ( ( sdtasdt0 @ SV178 @ SV197 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV197 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1642]) ).

thf(1649,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( ( sdtasdt0 @ SV179 @ ( sK17_W1 @ SV179 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( doDivides0 @ SV179 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1643]) ).

thf(1650,plain,
    ! [SV194: $i,SV179: $i] :
      ( ( ( aElement0 @ ( sK17_W1 @ SV179 ) )
        = $true )
      | ( ( aElement0 @ SV194 )
        = $false )
      | ( ( ( sdtasdt0 @ SV179 @ SV194 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV179 )
        = $false )
      | ( ( doDivides0 @ SV179 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1644]) ).

thf(1651,plain,
    ! [SV195: $i,SV181: $i,SV200: $i] :
      ( ( ( aElement0 @ SV200 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV200 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV181 )
        = $false )
      | ( ( ( sdtasdt0 @ SV181 @ SV195 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV195 )
        = $false )
      | ( ( doDivides0 @ SV181 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1645]) ).

thf(1652,plain,
    ! [SV199: $i,SV193: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
           != xc )
          | ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV199 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1646]) ).

thf(1653,plain,
    ! [SV199: $i,SV193: $i,SV177: $i] :
      ( ( ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV199 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1652]) ).

thf(1654,plain,
    ! [SV199: $i,SV193: $i,SV177: $i] :
      ( ( ( ~ ( aElement0 @ ( sK19_W1 @ SV177 ) ) )
        = $false )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV199 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1652]) ).

thf(1655,plain,
    ! [SV199: $i,SV193: $i,SV177: $i] :
      ( ( ( ( sdtasdt0 @ SV177 @ ( sK19_W1 @ SV177 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV199 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1653]) ).

thf(1656,plain,
    ! [SV199: $i,SV193: $i,SV177: $i] :
      ( ( ( aElement0 @ ( sK19_W1 @ SV177 ) )
        = $true )
      | ( ( aElement0 @ SV193 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV193 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV177 )
        = $false )
      | ( ( ( sdtasdt0 @ SV177 @ SV199 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV199 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1654]) ).

thf(1657,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[890,1656,1655,1651,1650,1649,1648,1647,1635,1634,1632,1631,1627,1626,1625,1624,1608,1607,1600,1596,1589,1588,1586,1585,1584,1565,1559,1558,1542,1529,1508,1498,1497,1490,1489,1465,1464,1461,1460,1459,1458,1427,1411,1388,1386,1382,1381,1380,1379,1378,1377,1376,1375,1374,1325,1324,1316,1301,1295,1291,1290,1264,1251,1231,1230,1221,1213,1169,1163,1162,1161,1138,1131,1130,1126,1125,1120,1119,1116,1115,1113,1112,1111,1110,1109,1108,1105,1103,1102,1101,1060,1049,1031,1026,1025,1022,1015,1002,1001,947,943,942,933,891]) ).

thf(1658,plain,
    ( ( ( aElement0 @ xa )
      & ( aElement0 @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(1659,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(1660,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK21_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK21_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK20_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK20_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK19_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK19_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK18_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK18_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK17_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK17_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK16_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK16_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK15_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK15_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK14_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK14_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK13_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK13_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ( ( sdtasdt0 @ xc @ sK12_W0 )
        = xa )
      & ( aElement0 @ sK12_W0 )
      & ( aElement0 @ xc )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ( ( sdtasdt0 @ xc @ sK11_W0 )
        = xb )
      & ( aElement0 @ sK11_W0 )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(1661,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ W1 @ W2 )
               != W0 ) )
          | ( aElementOf0 @ W0 @ xI ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ( ( aElementOf0 @ ( sK9_W1 @ W0 ) @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ ( sK10_SY73 @ W0 ) @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ ( sK9_W1 @ W0 ) @ ( sK10_SY73 @ W0 ) )
              = W0 ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xb @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
          | ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK8_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xa @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
          | ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK7_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElement0 @ W1 )
              | ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
      & ( aSet0 @ xI )
      & ( aIdeal0 @ xI )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(1662,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(1663,plain,
    ( ( aElement0 @ sz00 )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(1664,plain,
    ( ( aElement0 @ sz10 )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(1665,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(1666,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(1667,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(1668,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(1669,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(1670,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtpldt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(1671,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(1672,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(1673,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(1674,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz10 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtasdt0 @ sz10 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(1675,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(1676,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
            = ( smndt0 @ W0 ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( smndt0 @ W0 )
            = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(1677,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz00 )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(1678,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
           != sz00 )
          | ( W0 = sz00 )
          | ( W1 = sz00 ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(1679,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(1680,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(1681,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aSet0 @ W0 )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ W0 )
              | ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(1682,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aSet0 @ W0 )
          | ~ ( aSet0 @ W1 )
          | ( ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W0 )
            & ~ ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W1 ) )
          | ( ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W1 )
            & ~ ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W0 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(1683,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(1684,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(1685,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( ( aElement0 @ ( sK4_W2 @ W1 @ W0 ) )
            & ~ ( aElementOf0 @ ( sK4_W2 @ W1 @ W0 ) @ ( sdtpldt1 @ W0 @ W1 ) ) )
          | ! [W2: $i,W3: $i] :
              ( ~ ( aElement0 @ W2 )
              | ~ ( aElement0 @ W3 )
              | ( ( aElement0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W3 @ W1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(1686,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(1687,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(1688,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(1689,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( W1 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( aElement0 @ ( sK1_W2 @ W1 @ W0 ) )
            & ( aElement0 @ ( sK2_SY72 @ W1 @ W0 ) )
            & ( W0
              = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 ) @ ( sK2_SY72 @ W1 @ W0 ) ) )
            & ( ( ( sK2_SY72 @ W1 @ W0 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ W1 @ W0 ) ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(1690,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(1691,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xb @ W0 )
           != sz00 )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(1692,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aIdeal0 @ SX0 )
          | ~ ( aIdeal0 @ SX1 )
          | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SX1 @ SX0 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SX1 @ SX0 ) @ ( sdtpldt1 @ SX0 @ SX1 ) ) )
          | ! [SX2: $i,SX3: $i] :
              ( ~ ( aElement0 @ SX2 )
              | ~ ( aElement0 @ SX3 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1685]) ).

thf(1693,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( sdtasdt0 @ xb @ SX0 )
                 != sz00 )
                | ~ ( aElement0 @ SX0 ) )
          | ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1691]) ).

thf(1694,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1675]) ).

thf(1695,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i,SX2: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                                | ( ( sdtpldt0 @ SX1 @ SX2 )
                                 != SX0 ) )
                            | ( aElementOf0 @ SX0 @ xI ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                                 != SX0 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xb @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ xa @ SX1 )
                                             != SX0 )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                             != SX0 )
                                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElement0 @ SX1 )
                                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                        | ~ ( aSet0 @ xI ) )
                                  | ~ ( aIdeal0 @ xI ) ) ) ) )
          | ( xI
           != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1661]) ).

thf(1696,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
                  = ( smndt0 @ SX0 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( smndt0 @ SX0 )
                  = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1676]) ).

thf(1697,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aSet0 @ SX0 )
          | ~ ( aSet0 @ SX1 )
          | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1682]) ).

thf(1698,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz10 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1674]) ).

thf(1699,plain,
    ( ( ~ ( ~ ( aElement0 @ xa )
          | ~ ( aElement0 @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1658]) ).

thf(1700,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz00 )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1677]) ).

thf(1701,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 = sz00 )
          | ~ ( aElement0 @ SX0 )
          | ~ ( aElement0 @ SX1 )
          | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SX1 @ SX0 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) )
                    | ( SX0
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 ) @ ( sK2_SY72 @ SX1 @ SX0 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SX1 @ SX0 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1689]) ).

thf(1702,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1671]) ).

thf(1703,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ sz00 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1670]) ).

thf(1704,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                                 != xa )
                                                                | ~ ( aElement0 @ sK12_W0 ) )
                                                          | ~ ( aElement0 @ xc ) )
                                                    | ~ ( doDivides0 @ xc @ xa ) )
                                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                         != xb )
                                        | ~ ( aElement0 @ sK11_W0 ) ) )
                            | ~ ( doDivides0 @ xc @ xb ) )
                      | ~ ( aDivisorOf0 @ xc @ xb ) ) )
          | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1660]) ).

thf(1705,plain,
    ( ( ( ( xa != sz00 ) )
      = $true )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1659]) ).

thf(1706,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[1662]) ).

thf(1707,plain,
    ! [SV202: $i] :
      ( ( ~ ( aElement0 @ SV202 )
        | ( aElement0 @ ( smndt0 @ SV202 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1665]) ).

thf(1708,plain,
    ! [SV203: $i] :
      ( ( ! [SY170: $i] :
            ( ~ ( aElement0 @ SV203 )
            | ~ ( aElement0 @ SY170 )
            | ( aElement0 @ ( sdtpldt0 @ SV203 @ SY170 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1666]) ).

thf(1709,plain,
    ! [SV204: $i] :
      ( ( ! [SY171: $i] :
            ( ~ ( aElement0 @ SV204 )
            | ~ ( aElement0 @ SY171 )
            | ( aElement0 @ ( sdtasdt0 @ SV204 @ SY171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1667]) ).

thf(1710,plain,
    ! [SV205: $i] :
      ( ( ! [SY172: $i] :
            ( ~ ( aElement0 @ SV205 )
            | ~ ( aElement0 @ SY172 )
            | ( ( sdtpldt0 @ SV205 @ SY172 )
              = ( sdtpldt0 @ SY172 @ SV205 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1668]) ).

thf(1711,plain,
    ! [SV206: $i] :
      ( ( ! [SY173: $i,SY174: $i] :
            ( ~ ( aElement0 @ SV206 )
            | ~ ( aElement0 @ SY173 )
            | ~ ( aElement0 @ SY174 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SY173 ) @ SY174 )
              = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SY173 @ SY174 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1669]) ).

thf(1712,plain,
    ! [SV207: $i] :
      ( ( ! [SY175: $i] :
            ( ~ ( aElement0 @ SV207 )
            | ~ ( aElement0 @ SY175 )
            | ( ( sdtasdt0 @ SV207 @ SY175 )
              = ( sdtasdt0 @ SY175 @ SV207 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1672]) ).

thf(1713,plain,
    ! [SV208: $i] :
      ( ( ! [SY176: $i,SY177: $i] :
            ( ~ ( aElement0 @ SV208 )
            | ~ ( aElement0 @ SY176 )
            | ~ ( aElement0 @ SY177 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SY176 ) @ SY177 )
              = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SY176 @ SY177 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1673]) ).

thf(1714,plain,
    ! [SV209: $i] :
      ( ( ! [SY178: $i] :
            ( ~ ( aElement0 @ SV209 )
            | ~ ( aElement0 @ SY178 )
            | ( ( sdtasdt0 @ SV209 @ SY178 )
             != sz00 )
            | ( SV209 = sz00 )
            | ( SY178 = sz00 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1678]) ).

thf(1715,plain,
    ( ( sz10 = sz00 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1679]) ).

thf(1716,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[1680]) ).

thf(1717,plain,
    ! [SV211: $i] :
      ( ( ~ ( aSet0 @ SV211 )
        | ! [SY179: $i] :
            ( ~ ( aElementOf0 @ SY179 @ SV211 )
            | ( aElement0 @ SY179 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1681]) ).

thf(1718,plain,
    ! [SV212: $i] :
      ( ( ! [SY180: $i] :
            ( ~ ( aIdeal0 @ SV212 )
            | ~ ( aIdeal0 @ SY180 )
            | ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SY180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1683]) ).

thf(1719,plain,
    ! [SV213: $i] :
      ( ( ! [SY181: $i] :
            ( ~ ( aIdeal0 @ SV213 )
            | ~ ( aIdeal0 @ SY181 )
            | ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SY181 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1684]) ).

thf(1720,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[1686]) ).

thf(1721,plain,
    ! [SV215: $i] :
      ( ( ( SV215 = sz00 )
        | ~ ( aElement0 @ SV215 )
        | ( aNaturalNumber0 @ ( sbrdtbr0 @ SV215 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1687]) ).

thf(1722,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 )
        | ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1688]) ).

thf(1723,plain,
    ! [SV216: $i] :
      ( ( ~ ( aElement0 @ SV216 )
        | ( aIdeal0 @ ( slsdtgt0 @ SV216 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1690]) ).

thf(1724,plain,
    ! [SV217: $i] :
      ( ( ! [SY182: $i] :
            ( ~ ( aIdeal0 @ SV217 )
            | ~ ( aIdeal0 @ SY182 )
            | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SY182 @ SV217 ) )
                | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SY182 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SY182 ) ) )
            | ! [SY183: $i,SY184: $i] :
                ( ~ ( aElement0 @ SY183 )
                | ~ ( aElement0 @ SY184 )
                | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY184 @ SY183 @ SY182 @ SV217 ) )
                          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY184 @ SY183 @ SY182 @ SV217 ) @ SY183 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY184 @ SY183 @ SY182 @ SV217 ) @ SY184 @ SY182 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1692]) ).

thf(1725,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xb @ SX0 )
             != sz00 )
            | ~ ( aElement0 @ SX0 ) )
      | ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1693]) ).

thf(1726,plain,
    ! [SV218: $i] :
      ( ( ~ ( ~ ! [SY185: $i,SY186: $i] :
                  ( ~ ( aElement0 @ SV218 )
                  | ~ ( aElement0 @ SY185 )
                  | ~ ( aElement0 @ SY186 )
                  | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SY185 @ SY186 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SY185 ) @ ( sdtasdt0 @ SV218 @ SY186 ) ) ) )
            | ~ ! [SY187: $i,SY188: $i] :
                  ( ~ ( aElement0 @ SV218 )
                  | ~ ( aElement0 @ SY187 )
                  | ~ ( aElement0 @ SY188 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SY187 @ SY188 ) @ SV218 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SY187 @ SV218 ) @ ( sdtasdt0 @ SY188 @ SV218 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1694]) ).

thf(1727,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) )
      | ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1695]) ).

thf(1728,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1696]) ).

thf(1729,plain,
    ! [SV219: $i] :
      ( ( ! [SY189: $i] :
            ( ~ ( aSet0 @ SV219 )
            | ~ ( aSet0 @ SY189 )
            | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SY189 @ SV219 ) @ SV219 )
                | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SY189 @ SV219 ) @ SY189 ) )
            | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SY189 @ SV219 ) @ SY189 )
                | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SY189 @ SV219 ) @ SV219 ) )
            | ( SV219 = SY189 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1697]) ).

thf(1730,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1698]) ).

thf(1731,plain,
    ( ( ~ ( aElement0 @ xa )
      | ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1699]) ).

thf(1732,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1700]) ).

thf(1733,plain,
    ! [SV220: $i] :
      ( ( ! [SY190: $i] :
            ( ( SY190 = sz00 )
            | ~ ( aElement0 @ SV220 )
            | ~ ( aElement0 @ SY190 )
            | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SY190 @ SV220 ) )
                            | ~ ( aElement0 @ ( sK2_SY72 @ SY190 @ SV220 ) ) )
                      | ( SV220
                       != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SY190 @ SV220 ) @ SY190 ) @ ( sK2_SY72 @ SY190 @ SV220 ) ) ) )
                | ~ ( ( ( sK2_SY72 @ SY190 @ SV220 )
                      = sz00 )
                    | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SY190 @ SV220 ) ) @ ( sbrdtbr0 @ SY190 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1701]) ).

thf(1734,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1702]) ).

thf(1735,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1703]) ).

thf(1736,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) )
      | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1704]) ).

thf(1737,plain,
    ( ( ( xa = sz00 )
      = $false )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1705]) ).

thf(1738,plain,
    ! [SV202: $i] :
      ( ( ( ~ ( aElement0 @ SV202 ) )
        = $true )
      | ( ( aElement0 @ ( smndt0 @ SV202 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1707]) ).

thf(1739,plain,
    ! [SV221: $i,SV203: $i] :
      ( ( ~ ( aElement0 @ SV203 )
        | ~ ( aElement0 @ SV221 )
        | ( aElement0 @ ( sdtpldt0 @ SV203 @ SV221 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1708]) ).

thf(1740,plain,
    ! [SV222: $i,SV204: $i] :
      ( ( ~ ( aElement0 @ SV204 )
        | ~ ( aElement0 @ SV222 )
        | ( aElement0 @ ( sdtasdt0 @ SV204 @ SV222 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1709]) ).

thf(1741,plain,
    ! [SV223: $i,SV205: $i] :
      ( ( ~ ( aElement0 @ SV205 )
        | ~ ( aElement0 @ SV223 )
        | ( ( sdtpldt0 @ SV205 @ SV223 )
          = ( sdtpldt0 @ SV223 @ SV205 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1710]) ).

thf(1742,plain,
    ! [SV224: $i,SV206: $i] :
      ( ( ! [SY191: $i] :
            ( ~ ( aElement0 @ SV206 )
            | ~ ( aElement0 @ SV224 )
            | ~ ( aElement0 @ SY191 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SY191 )
              = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SY191 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1711]) ).

thf(1743,plain,
    ! [SV225: $i,SV207: $i] :
      ( ( ~ ( aElement0 @ SV207 )
        | ~ ( aElement0 @ SV225 )
        | ( ( sdtasdt0 @ SV207 @ SV225 )
          = ( sdtasdt0 @ SV225 @ SV207 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1712]) ).

thf(1744,plain,
    ! [SV226: $i,SV208: $i] :
      ( ( ! [SY192: $i] :
            ( ~ ( aElement0 @ SV208 )
            | ~ ( aElement0 @ SV226 )
            | ~ ( aElement0 @ SY192 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SY192 )
              = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SY192 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1713]) ).

thf(1745,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ~ ( aElement0 @ SV209 )
        | ~ ( aElement0 @ SV227 )
        | ( ( sdtasdt0 @ SV209 @ SV227 )
         != sz00 )
        | ( SV209 = sz00 )
        | ( SV227 = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1714]) ).

thf(1746,plain,
    ! [SV211: $i] :
      ( ( ( ~ ( aSet0 @ SV211 ) )
        = $true )
      | ( ( ! [SY179: $i] :
              ( ~ ( aElementOf0 @ SY179 @ SV211 )
              | ( aElement0 @ SY179 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1717]) ).

thf(1747,plain,
    ! [SV228: $i,SV212: $i] :
      ( ( ~ ( aIdeal0 @ SV212 )
        | ~ ( aIdeal0 @ SV228 )
        | ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SV228 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1718]) ).

thf(1748,plain,
    ! [SV229: $i,SV213: $i] :
      ( ( ~ ( aIdeal0 @ SV213 )
        | ~ ( aIdeal0 @ SV229 )
        | ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SV229 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1719]) ).

thf(1749,plain,
    ! [SV215: $i] :
      ( ( ( ( SV215 = sz00 )
          | ~ ( aElement0 @ SV215 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV215 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1721]) ).

thf(1750,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1722]) ).

thf(1751,plain,
    ! [SV216: $i] :
      ( ( ( ~ ( aElement0 @ SV216 ) )
        = $true )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV216 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1723]) ).

thf(1752,plain,
    ! [SV230: $i,SV217: $i] :
      ( ( ~ ( aIdeal0 @ SV217 )
        | ~ ( aIdeal0 @ SV230 )
        | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
            | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
        | ! [SY193: $i,SY194: $i] :
            ( ~ ( aElement0 @ SY193 )
            | ~ ( aElement0 @ SY194 )
            | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                      | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1724]) ).

thf(1753,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xb @ SX0 )
             != sz00 )
            | ~ ( aElement0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1725]) ).

thf(1754,plain,
    ( ( ~ ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1725]) ).

thf(1755,plain,
    ! [SV218: $i] :
      ( ( ~ ! [SY185: $i,SY186: $i] :
              ( ~ ( aElement0 @ SV218 )
              | ~ ( aElement0 @ SY185 )
              | ~ ( aElement0 @ SY186 )
              | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SY185 @ SY186 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SY185 ) @ ( sdtasdt0 @ SV218 @ SY186 ) ) ) )
        | ~ ! [SY187: $i,SY188: $i] :
              ( ~ ( aElement0 @ SV218 )
              | ~ ( aElement0 @ SY187 )
              | ~ ( aElement0 @ SY188 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY187 @ SY188 ) @ SV218 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY187 @ SV218 ) @ ( sdtasdt0 @ SY188 @ SV218 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1726]) ).

thf(1756,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1727]) ).

thf(1757,plain,
    ( ( ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1727]) ).

thf(1758,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1728]) ).

thf(1759,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1728]) ).

thf(1760,plain,
    ! [SV231: $i,SV219: $i] :
      ( ( ~ ( aSet0 @ SV219 )
        | ~ ( aSet0 @ SV231 )
        | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
            | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
        | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
            | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        | ( SV219 = SV231 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1729]) ).

thf(1761,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1730]) ).

thf(1762,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1730]) ).

thf(1763,plain,
    ( ( ~ ( aElement0 @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1731]) ).

thf(1764,plain,
    ( ( ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1731]) ).

thf(1765,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1732]) ).

thf(1766,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1732]) ).

thf(1767,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( SV232 = sz00 )
        | ~ ( aElement0 @ SV220 )
        | ~ ( aElement0 @ SV232 )
        | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                        | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                  | ( SV220
                   != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
            | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                  = sz00 )
                | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1733]) ).

thf(1768,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1734]) ).

thf(1769,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1734]) ).

thf(1770,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1735]) ).

thf(1771,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1735]) ).

thf(1772,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1736]) ).

thf(1773,plain,
    ( ( ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1736]) ).

thf(1774,plain,
    ( ( ( xb = sz00 )
      = $false )
    | ( ( xa = sz00 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1737]) ).

thf(1775,plain,
    ! [SV202: $i] :
      ( ( ( aElement0 @ SV202 )
        = $false )
      | ( ( aElement0 @ ( smndt0 @ SV202 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1738]) ).

thf(1776,plain,
    ! [SV221: $i,SV203: $i] :
      ( ( ( ~ ( aElement0 @ SV203 )
          | ~ ( aElement0 @ SV221 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV203 @ SV221 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1739]) ).

thf(1777,plain,
    ! [SV222: $i,SV204: $i] :
      ( ( ( ~ ( aElement0 @ SV204 )
          | ~ ( aElement0 @ SV222 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV204 @ SV222 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1740]) ).

thf(1778,plain,
    ! [SV223: $i,SV205: $i] :
      ( ( ( ~ ( aElement0 @ SV205 )
          | ~ ( aElement0 @ SV223 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV205 @ SV223 )
          = ( sdtpldt0 @ SV223 @ SV205 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1741]) ).

thf(1779,plain,
    ! [SV233: $i,SV224: $i,SV206: $i] :
      ( ( ~ ( aElement0 @ SV206 )
        | ~ ( aElement0 @ SV224 )
        | ~ ( aElement0 @ SV233 )
        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1742]) ).

thf(1780,plain,
    ! [SV225: $i,SV207: $i] :
      ( ( ( ~ ( aElement0 @ SV207 )
          | ~ ( aElement0 @ SV225 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV207 @ SV225 )
          = ( sdtasdt0 @ SV225 @ SV207 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1743]) ).

thf(1781,plain,
    ! [SV234: $i,SV226: $i,SV208: $i] :
      ( ( ~ ( aElement0 @ SV208 )
        | ~ ( aElement0 @ SV226 )
        | ~ ( aElement0 @ SV234 )
        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1744]) ).

thf(1782,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( ~ ( aElement0 @ SV209 )
          | ~ ( aElement0 @ SV227 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
           != sz00 )
          | ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1745]) ).

thf(1783,plain,
    ! [SV211: $i] :
      ( ( ( aSet0 @ SV211 )
        = $false )
      | ( ( ! [SY179: $i] :
              ( ~ ( aElementOf0 @ SY179 @ SV211 )
              | ( aElement0 @ SY179 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1746]) ).

thf(1784,plain,
    ! [SV228: $i,SV212: $i] :
      ( ( ( ~ ( aIdeal0 @ SV212 )
          | ~ ( aIdeal0 @ SV228 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SV228 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1747]) ).

thf(1785,plain,
    ! [SV229: $i,SV213: $i] :
      ( ( ( ~ ( aIdeal0 @ SV213 )
          | ~ ( aIdeal0 @ SV229 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1748]) ).

thf(1786,plain,
    ! [SV215: $i] :
      ( ( ( SV215 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV215 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV215 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1749]) ).

thf(1787,plain,
    ! [SV235: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV235 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1750]) ).

thf(1788,plain,
    ! [SV216: $i] :
      ( ( ( aElement0 @ SV216 )
        = $false )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV216 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1751]) ).

thf(1789,plain,
    ! [SV230: $i,SV217: $i] :
      ( ( ( ~ ( aIdeal0 @ SV217 )
          | ~ ( aIdeal0 @ SV230 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
          | ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1752]) ).

thf(1790,plain,
    ( ( ! [SX0: $i] :
          ( ( ( sdtasdt0 @ xb @ SX0 )
           != sz00 )
          | ~ ( aElement0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1753]) ).

thf(1791,plain,
    ( ( ~ ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1754]) ).

thf(1792,plain,
    ! [SV218: $i] :
      ( ( ~ ! [SY185: $i,SY186: $i] :
              ( ~ ( aElement0 @ SV218 )
              | ~ ( aElement0 @ SY185 )
              | ~ ( aElement0 @ SY186 )
              | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SY185 @ SY186 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SY185 ) @ ( sdtasdt0 @ SV218 @ SY186 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1755]) ).

thf(1793,plain,
    ! [SV218: $i] :
      ( ( ~ ! [SY187: $i,SY188: $i] :
              ( ~ ( aElement0 @ SV218 )
              | ~ ( aElement0 @ SY187 )
              | ~ ( aElement0 @ SY188 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY187 @ SY188 ) @ SV218 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY187 @ SV218 ) @ ( sdtasdt0 @ SY188 @ SV218 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1755]) ).

thf(1794,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i,SX2: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                          | ( ( sdtpldt0 @ SX1 @ SX2 )
                           != SX0 ) )
                      | ( aElementOf0 @ SX0 @ xI ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                          | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                           != SX0 ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xb @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xa @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElement0 @ SX1 )
                                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                  | ~ ( aSet0 @ xI ) )
                            | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1756]) ).

thf(1795,plain,
    ( ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1757]) ).

thf(1796,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
            = ( smndt0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1758]) ).

thf(1797,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( smndt0 @ SX0 )
            = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1759]) ).

thf(1798,plain,
    ! [SV231: $i,SV219: $i] :
      ( ( ( ~ ( aSet0 @ SV219 )
          | ~ ( aSet0 @ SV231 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
          | ( SV219 = SV231 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1760]) ).

thf(1799,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz10 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1761]) ).

thf(1800,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1762]) ).

thf(1801,plain,
    ( ( aElement0 @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1763]) ).

thf(1802,plain,
    ( ( aElement0 @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1764]) ).

thf(1803,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz00 )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1765]) ).

thf(1804,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1766]) ).

thf(1805,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ( SV232 = sz00 )
          | ~ ( aElement0 @ SV220 )
          | ~ ( aElement0 @ SV232 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                    | ( SV220
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1767]) ).

thf(1806,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1768]) ).

thf(1807,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1769]) ).

thf(1808,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ sz00 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1770]) ).

thf(1809,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1771]) ).

thf(1810,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                           != xa )
                                                          | ~ ( aElement0 @ sK12_W0 ) )
                                                    | ~ ( aElement0 @ xc ) )
                                              | ~ ( doDivides0 @ xc @ xa ) )
                                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                   != xb )
                                  | ~ ( aElement0 @ sK11_W0 ) ) )
                      | ~ ( doDivides0 @ xc @ xb ) )
                | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1772]) ).

thf(1811,plain,
    ( ( aGcdOfAnd0 @ xc @ xa @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1773]) ).

thf(1812,plain,
    ! [SV221: $i,SV203: $i] :
      ( ( ( ~ ( aElement0 @ SV203 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV221 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV203 @ SV221 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1776]) ).

thf(1813,plain,
    ! [SV222: $i,SV204: $i] :
      ( ( ( ~ ( aElement0 @ SV204 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV222 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV204 @ SV222 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1777]) ).

thf(1814,plain,
    ! [SV223: $i,SV205: $i] :
      ( ( ( ~ ( aElement0 @ SV205 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV223 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV205 @ SV223 )
          = ( sdtpldt0 @ SV223 @ SV205 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1778]) ).

thf(1815,plain,
    ! [SV233: $i,SV224: $i,SV206: $i] :
      ( ( ( ~ ( aElement0 @ SV206 )
          | ~ ( aElement0 @ SV224 )
          | ~ ( aElement0 @ SV233 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1779]) ).

thf(1816,plain,
    ! [SV225: $i,SV207: $i] :
      ( ( ( ~ ( aElement0 @ SV207 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV225 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV207 @ SV225 )
          = ( sdtasdt0 @ SV225 @ SV207 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1780]) ).

thf(1817,plain,
    ! [SV234: $i,SV226: $i,SV208: $i] :
      ( ( ( ~ ( aElement0 @ SV208 )
          | ~ ( aElement0 @ SV226 )
          | ~ ( aElement0 @ SV234 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1781]) ).

thf(1818,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( ~ ( aElement0 @ SV209 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV227 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
           != sz00 )
          | ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1782]) ).

thf(1819,plain,
    ! [SV211: $i,SV236: $i] :
      ( ( ( ~ ( aElementOf0 @ SV236 @ SV211 )
          | ( aElement0 @ SV236 ) )
        = $true )
      | ( ( aSet0 @ SV211 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1783]) ).

thf(1820,plain,
    ! [SV228: $i,SV212: $i] :
      ( ( ( ~ ( aIdeal0 @ SV212 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV228 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SV228 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1784]) ).

thf(1821,plain,
    ! [SV229: $i,SV213: $i] :
      ( ( ( ~ ( aIdeal0 @ SV213 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV229 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1785]) ).

thf(1822,plain,
    ! [SV215: $i] :
      ( ( ( aElement0 @ SV215 )
        = $false )
      | ( ( SV215 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV215 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1786]) ).

thf(1823,plain,
    ! [SV235: $i] :
      ( ( ( aNaturalNumber0 @ SV235 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1787]) ).

thf(1824,plain,
    ! [SV230: $i,SV217: $i] :
      ( ( ( ~ ( aIdeal0 @ SV217 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV230 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
          | ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1789]) ).

thf(1825,plain,
    ! [SV237: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV237 )
         != sz00 )
        | ~ ( aElement0 @ SV237 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1790]) ).

thf(1826,plain,
    ( ( aElementOf0 @ sz00 @ ( slsdtgt0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1791]) ).

thf(1827,plain,
    ! [SV218: $i] :
      ( ( ! [SY185: $i,SY186: $i] :
            ( ~ ( aElement0 @ SV218 )
            | ~ ( aElement0 @ SY185 )
            | ~ ( aElement0 @ SY186 )
            | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SY185 @ SY186 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SY185 ) @ ( sdtasdt0 @ SV218 @ SY186 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1792]) ).

thf(1828,plain,
    ! [SV218: $i] :
      ( ( ! [SY187: $i,SY188: $i] :
            ( ~ ( aElement0 @ SV218 )
            | ~ ( aElement0 @ SY187 )
            | ~ ( aElement0 @ SY188 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SY187 @ SY188 ) @ SV218 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SY187 @ SV218 ) @ ( sdtasdt0 @ SY188 @ SV218 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1793]) ).

thf(1829,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1794]) ).

thf(1830,plain,
    ! [SV238: $i] :
      ( ( ~ ( aElement0 @ SV238 )
        | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV238 )
          = ( smndt0 @ SV238 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1796]) ).

thf(1831,plain,
    ! [SV239: $i] :
      ( ( ~ ( aElement0 @ SV239 )
        | ( ( smndt0 @ SV239 )
          = ( sdtasdt0 @ SV239 @ ( smndt0 @ sz10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1797]) ).

thf(1832,plain,
    ! [SV231: $i,SV219: $i] :
      ( ( ( ~ ( aSet0 @ SV219 ) )
        = $true )
      | ( ( ~ ( aSet0 @ SV231 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
          | ( SV219 = SV231 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1798]) ).

thf(1833,plain,
    ! [SV240: $i] :
      ( ( ~ ( aElement0 @ SV240 )
        | ( ( sdtasdt0 @ SV240 @ sz10 )
          = SV240 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1799]) ).

thf(1834,plain,
    ! [SV241: $i] :
      ( ( ~ ( aElement0 @ SV241 )
        | ( SV241
          = ( sdtasdt0 @ sz10 @ SV241 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1800]) ).

thf(1835,plain,
    ! [SV242: $i] :
      ( ( ~ ( aElement0 @ SV242 )
        | ( ( sdtasdt0 @ SV242 @ sz00 )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1803]) ).

thf(1836,plain,
    ! [SV243: $i] :
      ( ( ~ ( aElement0 @ SV243 )
        | ( sz00
          = ( sdtasdt0 @ sz00 @ SV243 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1804]) ).

thf(1837,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( SV232 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV220 )
          | ~ ( aElement0 @ SV232 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                    | ( SV220
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1805]) ).

thf(1838,plain,
    ! [SV244: $i] :
      ( ( ~ ( aElement0 @ SV244 )
        | ( ( sdtpldt0 @ SV244 @ ( smndt0 @ SV244 ) )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1806]) ).

thf(1839,plain,
    ! [SV245: $i] :
      ( ( ~ ( aElement0 @ SV245 )
        | ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV245 ) @ SV245 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1807]) ).

thf(1840,plain,
    ! [SV246: $i] :
      ( ( ~ ( aElement0 @ SV246 )
        | ( ( sdtpldt0 @ SV246 @ sz00 )
          = SV246 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1808]) ).

thf(1841,plain,
    ! [SV247: $i] :
      ( ( ~ ( aElement0 @ SV247 )
        | ( SV247
          = ( sdtpldt0 @ sz00 @ SV247 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1809]) ).

thf(1842,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1810]) ).

thf(1843,plain,
    ! [SV221: $i,SV203: $i] :
      ( ( ( aElement0 @ SV203 )
        = $false )
      | ( ( ~ ( aElement0 @ SV221 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV203 @ SV221 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1812]) ).

thf(1844,plain,
    ! [SV222: $i,SV204: $i] :
      ( ( ( aElement0 @ SV204 )
        = $false )
      | ( ( ~ ( aElement0 @ SV222 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV204 @ SV222 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1813]) ).

thf(1845,plain,
    ! [SV223: $i,SV205: $i] :
      ( ( ( aElement0 @ SV205 )
        = $false )
      | ( ( ~ ( aElement0 @ SV223 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV205 @ SV223 )
          = ( sdtpldt0 @ SV223 @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1814]) ).

thf(1846,plain,
    ! [SV233: $i,SV224: $i,SV206: $i] :
      ( ( ( ~ ( aElement0 @ SV206 )
          | ~ ( aElement0 @ SV224 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV233 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1815]) ).

thf(1847,plain,
    ! [SV225: $i,SV207: $i] :
      ( ( ( aElement0 @ SV207 )
        = $false )
      | ( ( ~ ( aElement0 @ SV225 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV207 @ SV225 )
          = ( sdtasdt0 @ SV225 @ SV207 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1816]) ).

thf(1848,plain,
    ! [SV234: $i,SV226: $i,SV208: $i] :
      ( ( ( ~ ( aElement0 @ SV208 )
          | ~ ( aElement0 @ SV226 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV234 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1817]) ).

thf(1849,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( aElement0 @ SV209 )
        = $false )
      | ( ( ~ ( aElement0 @ SV227 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
           != sz00 )
          | ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1818]) ).

thf(1850,plain,
    ! [SV211: $i,SV236: $i] :
      ( ( ( ~ ( aElementOf0 @ SV236 @ SV211 ) )
        = $true )
      | ( ( aElement0 @ SV236 )
        = $true )
      | ( ( aSet0 @ SV211 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1819]) ).

thf(1851,plain,
    ! [SV228: $i,SV212: $i] :
      ( ( ( aIdeal0 @ SV212 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV228 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SV228 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1820]) ).

thf(1852,plain,
    ! [SV229: $i,SV213: $i] :
      ( ( ( aIdeal0 @ SV213 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV229 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1821]) ).

thf(1853,plain,
    ! [SV235: $i,SV248: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV248 ) )
        = $true )
      | ( ( aNaturalNumber0 @ SV235 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1823]) ).

thf(1854,plain,
    ! [SV230: $i,SV217: $i] :
      ( ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV230 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
          | ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1824]) ).

thf(1855,plain,
    ! [SV237: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV237 )
           != sz00 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV237 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1825]) ).

thf(1856,plain,
    ! [SV249: $i,SV218: $i] :
      ( ( ! [SY195: $i] :
            ( ~ ( aElement0 @ SV218 )
            | ~ ( aElement0 @ SV249 )
            | ~ ( aElement0 @ SY195 )
            | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SY195 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SY195 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1827]) ).

thf(1857,plain,
    ! [SV250: $i,SV218: $i] :
      ( ( ! [SY196: $i] :
            ( ~ ( aElement0 @ SV218 )
            | ~ ( aElement0 @ SV250 )
            | ~ ( aElement0 @ SY196 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SY196 ) @ SV218 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SY196 @ SV218 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1828]) ).

thf(1858,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1829]) ).

thf(1859,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1829]) ).

thf(1860,plain,
    ! [SV238: $i] :
      ( ( ( ~ ( aElement0 @ SV238 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV238 )
          = ( smndt0 @ SV238 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1830]) ).

thf(1861,plain,
    ! [SV239: $i] :
      ( ( ( ~ ( aElement0 @ SV239 ) )
        = $true )
      | ( ( ( smndt0 @ SV239 )
          = ( sdtasdt0 @ SV239 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1831]) ).

thf(1862,plain,
    ! [SV231: $i,SV219: $i] :
      ( ( ( aSet0 @ SV219 )
        = $false )
      | ( ( ~ ( aSet0 @ SV231 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
          | ( SV219 = SV231 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1832]) ).

thf(1863,plain,
    ! [SV240: $i] :
      ( ( ( ~ ( aElement0 @ SV240 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV240 @ sz10 )
          = SV240 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1833]) ).

thf(1864,plain,
    ! [SV241: $i] :
      ( ( ( ~ ( aElement0 @ SV241 ) )
        = $true )
      | ( ( SV241
          = ( sdtasdt0 @ sz10 @ SV241 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1834]) ).

thf(1865,plain,
    ! [SV242: $i] :
      ( ( ( ~ ( aElement0 @ SV242 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV242 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1835]) ).

thf(1866,plain,
    ! [SV243: $i] :
      ( ( ( ~ ( aElement0 @ SV243 ) )
        = $true )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV243 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1836]) ).

thf(1867,plain,
    ! [SV232: $i,SV220: $i] :
      ( ( ( ~ ( aElement0 @ SV220 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV232 ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                    | ( SV220
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1837]) ).

thf(1868,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( aElement0 @ SV244 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV244 @ ( smndt0 @ SV244 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1838]) ).

thf(1869,plain,
    ! [SV245: $i] :
      ( ( ( ~ ( aElement0 @ SV245 ) )
        = $true )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV245 ) @ SV245 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1839]) ).

thf(1870,plain,
    ! [SV246: $i] :
      ( ( ( ~ ( aElement0 @ SV246 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV246 @ sz00 )
          = SV246 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1840]) ).

thf(1871,plain,
    ! [SV247: $i] :
      ( ( ( ~ ( aElement0 @ SV247 ) )
        = $true )
      | ( ( SV247
          = ( sdtpldt0 @ sz00 @ SV247 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1841]) ).

thf(1872,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1842]) ).

thf(1873,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1842]) ).

thf(1874,plain,
    ! [SV203: $i,SV221: $i] :
      ( ( ( aElement0 @ SV221 )
        = $false )
      | ( ( aElement0 @ SV203 )
        = $false )
      | ( ( aElement0 @ ( sdtpldt0 @ SV203 @ SV221 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1843]) ).

thf(1875,plain,
    ! [SV204: $i,SV222: $i] :
      ( ( ( aElement0 @ SV222 )
        = $false )
      | ( ( aElement0 @ SV204 )
        = $false )
      | ( ( aElement0 @ ( sdtasdt0 @ SV204 @ SV222 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1844]) ).

thf(1876,plain,
    ! [SV205: $i,SV223: $i] :
      ( ( ( aElement0 @ SV223 )
        = $false )
      | ( ( aElement0 @ SV205 )
        = $false )
      | ( ( ( sdtpldt0 @ SV205 @ SV223 )
          = ( sdtpldt0 @ SV223 @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1845]) ).

thf(1877,plain,
    ! [SV233: $i,SV224: $i,SV206: $i] :
      ( ( ( ~ ( aElement0 @ SV206 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV224 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV233 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1846]) ).

thf(1878,plain,
    ! [SV207: $i,SV225: $i] :
      ( ( ( aElement0 @ SV225 )
        = $false )
      | ( ( aElement0 @ SV207 )
        = $false )
      | ( ( ( sdtasdt0 @ SV207 @ SV225 )
          = ( sdtasdt0 @ SV225 @ SV207 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1847]) ).

thf(1879,plain,
    ! [SV234: $i,SV226: $i,SV208: $i] :
      ( ( ( ~ ( aElement0 @ SV208 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV226 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV234 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1848]) ).

thf(1880,plain,
    ! [SV209: $i,SV227: $i] :
      ( ( ( aElement0 @ SV227 )
        = $false )
      | ( ( aElement0 @ SV209 )
        = $false )
      | ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
           != sz00 )
          | ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1849]) ).

thf(1881,plain,
    ! [SV211: $i,SV236: $i] :
      ( ( ( aElementOf0 @ SV236 @ SV211 )
        = $false )
      | ( ( aElement0 @ SV236 )
        = $true )
      | ( ( aSet0 @ SV211 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1850]) ).

thf(1882,plain,
    ! [SV212: $i,SV228: $i] :
      ( ( ( aIdeal0 @ SV228 )
        = $false )
      | ( ( aIdeal0 @ SV212 )
        = $false )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV212 @ SV228 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1851]) ).

thf(1883,plain,
    ! [SV213: $i,SV229: $i] :
      ( ( ( aIdeal0 @ SV229 )
        = $false )
      | ( ( aIdeal0 @ SV213 )
        = $false )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV213 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1852]) ).

thf(1884,plain,
    ! [SV235: $i,SV248: $i] :
      ( ( ( aNaturalNumber0 @ SV248 )
        = $false )
      | ( ( aNaturalNumber0 @ SV235 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1853]) ).

thf(1885,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( aIdeal0 @ SV230 )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
          | ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1854]) ).

thf(1886,plain,
    ! [SV237: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV237 )
          = sz00 )
        = $false )
      | ( ( ~ ( aElement0 @ SV237 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1855]) ).

thf(1887,plain,
    ! [SV251: $i,SV249: $i,SV218: $i] :
      ( ( ~ ( aElement0 @ SV218 )
        | ~ ( aElement0 @ SV249 )
        | ~ ( aElement0 @ SV251 )
        | ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1856]) ).

thf(1888,plain,
    ! [SV252: $i,SV250: $i,SV218: $i] :
      ( ( ~ ( aElement0 @ SV218 )
        | ~ ( aElement0 @ SV250 )
        | ~ ( aElement0 @ SV252 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1857]) ).

thf(1889,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i,SX2: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                    | ( ( sdtpldt0 @ SX1 @ SX2 )
                     != SX0 ) )
                | ( aElementOf0 @ SX0 @ xI ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                    | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                     != SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1858]) ).

thf(1890,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xb @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                      | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xa @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElementOf0 @ SX1 @ xI )
                                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElement0 @ SX1 )
                                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                            | ~ ( aSet0 @ xI ) )
                      | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1859]) ).

thf(1891,plain,
    ! [SV238: $i] :
      ( ( ( aElement0 @ SV238 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV238 )
          = ( smndt0 @ SV238 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1860]) ).

thf(1892,plain,
    ! [SV239: $i] :
      ( ( ( aElement0 @ SV239 )
        = $false )
      | ( ( ( smndt0 @ SV239 )
          = ( sdtasdt0 @ SV239 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1861]) ).

thf(1893,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aSet0 @ SV231 )
        = $false )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
          | ( SV219 = SV231 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1862]) ).

thf(1894,plain,
    ! [SV240: $i] :
      ( ( ( aElement0 @ SV240 )
        = $false )
      | ( ( ( sdtasdt0 @ SV240 @ sz10 )
          = SV240 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1863]) ).

thf(1895,plain,
    ! [SV241: $i] :
      ( ( ( aElement0 @ SV241 )
        = $false )
      | ( ( SV241
          = ( sdtasdt0 @ sz10 @ SV241 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1864]) ).

thf(1896,plain,
    ! [SV242: $i] :
      ( ( ( aElement0 @ SV242 )
        = $false )
      | ( ( ( sdtasdt0 @ SV242 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1865]) ).

thf(1897,plain,
    ! [SV243: $i] :
      ( ( ( aElement0 @ SV243 )
        = $false )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV243 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1866]) ).

thf(1898,plain,
    ! [SV232: $i,SV220: $i] :
      ( ( ( aElement0 @ SV220 )
        = $false )
      | ( ( ~ ( aElement0 @ SV232 ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                    | ( SV220
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1867]) ).

thf(1899,plain,
    ! [SV244: $i] :
      ( ( ( aElement0 @ SV244 )
        = $false )
      | ( ( ( sdtpldt0 @ SV244 @ ( smndt0 @ SV244 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1868]) ).

thf(1900,plain,
    ! [SV245: $i] :
      ( ( ( aElement0 @ SV245 )
        = $false )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV245 ) @ SV245 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1869]) ).

thf(1901,plain,
    ! [SV246: $i] :
      ( ( ( aElement0 @ SV246 )
        = $false )
      | ( ( ( sdtpldt0 @ SV246 @ sz00 )
          = SV246 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1870]) ).

thf(1902,plain,
    ! [SV247: $i] :
      ( ( ( aElement0 @ SV247 )
        = $false )
      | ( ( SV247
          = ( sdtpldt0 @ sz00 @ SV247 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1871]) ).

thf(1903,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1872]) ).

thf(1904,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                     != xa )
                                                    | ~ ( aElement0 @ sK12_W0 ) )
                                              | ~ ( aElement0 @ xc ) )
                                        | ~ ( doDivides0 @ xc @ xa ) )
                                  | ~ ( aDivisorOf0 @ xc @ xa ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                             != xb )
                            | ~ ( aElement0 @ sK11_W0 ) ) )
                | ~ ( doDivides0 @ xc @ xb ) )
          | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1873]) ).

thf(1905,plain,
    ! [SV233: $i,SV224: $i,SV206: $i] :
      ( ( ( aElement0 @ SV206 )
        = $false )
      | ( ( ~ ( aElement0 @ SV224 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV233 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1877]) ).

thf(1906,plain,
    ! [SV234: $i,SV226: $i,SV208: $i] :
      ( ( ( aElement0 @ SV208 )
        = $false )
      | ( ( ~ ( aElement0 @ SV226 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV234 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1879]) ).

thf(1907,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
           != sz00 ) )
        = $true )
      | ( ( ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV209 )
        = $false )
      | ( ( aElement0 @ SV227 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1880]) ).

thf(1908,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) ) )
        = $true )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1885]) ).

thf(1909,plain,
    ! [SV237: $i] :
      ( ( ( aElement0 @ SV237 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV237 )
          = sz00 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1886]) ).

thf(1910,plain,
    ! [SV251: $i,SV249: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 )
          | ~ ( aElement0 @ SV249 )
          | ~ ( aElement0 @ SV251 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1887]) ).

thf(1911,plain,
    ! [SV252: $i,SV250: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 )
          | ~ ( aElement0 @ SV250 )
          | ~ ( aElement0 @ SV252 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1888]) ).

thf(1912,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1889]) ).

thf(1913,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1890]) ).

thf(1914,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1893]) ).

thf(1915,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( aElement0 @ SV232 )
        = $false )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                    | ( SV220
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1898]) ).

thf(1916,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1903]) ).

thf(1917,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) )
      | ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1904]) ).

thf(1918,plain,
    ! [SV233: $i,SV206: $i,SV224: $i] :
      ( ( ( aElement0 @ SV224 )
        = $false )
      | ( ( aElement0 @ SV206 )
        = $false )
      | ( ( ~ ( aElement0 @ SV233 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1905]) ).

thf(1919,plain,
    ! [SV234: $i,SV208: $i,SV226: $i] :
      ( ( ( aElement0 @ SV226 )
        = $false )
      | ( ( aElement0 @ SV208 )
        = $false )
      | ( ( ~ ( aElement0 @ SV234 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1906]) ).

thf(1920,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( ( sdtasdt0 @ SV209 @ SV227 )
          = sz00 )
        = $false )
      | ( ( ( SV209 = sz00 )
          | ( SV227 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV209 )
        = $false )
      | ( ( aElement0 @ SV227 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1907]) ).

thf(1921,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
          | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
        = $false )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1908]) ).

thf(1922,plain,
    ! [SV251: $i,SV249: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 )
          | ~ ( aElement0 @ SV249 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV251 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1910]) ).

thf(1923,plain,
    ! [SV252: $i,SV250: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 )
          | ~ ( aElement0 @ SV250 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV252 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1911]) ).

thf(1924,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1912]) ).

thf(1925,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1912]) ).

thf(1926,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1913]) ).

thf(1927,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1913]) ).

thf(1928,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1914]) ).

thf(1929,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                | ( SV220
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
          | ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1915]) ).

thf(1930,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1916]) ).

thf(1931,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1916]) ).

thf(1932,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1917]) ).

thf(1933,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1917]) ).

thf(1934,plain,
    ! [SV224: $i,SV206: $i,SV233: $i] :
      ( ( ( aElement0 @ SV233 )
        = $false )
      | ( ( aElement0 @ SV206 )
        = $false )
      | ( ( aElement0 @ SV224 )
        = $false )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV206 @ SV224 ) @ SV233 )
          = ( sdtpldt0 @ SV206 @ ( sdtpldt0 @ SV224 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1918]) ).

thf(1935,plain,
    ! [SV226: $i,SV208: $i,SV234: $i] :
      ( ( ( aElement0 @ SV234 )
        = $false )
      | ( ( aElement0 @ SV208 )
        = $false )
      | ( ( aElement0 @ SV226 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV208 @ SV226 ) @ SV234 )
          = ( sdtasdt0 @ SV208 @ ( sdtasdt0 @ SV226 @ SV234 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1919]) ).

thf(1936,plain,
    ! [SV227: $i,SV209: $i] :
      ( ( ( SV209 = sz00 )
        = $true )
      | ( ( SV227 = sz00 )
        = $true )
      | ( ( ( sdtasdt0 @ SV209 @ SV227 )
          = sz00 )
        = $false )
      | ( ( aElement0 @ SV209 )
        = $false )
      | ( ( aElement0 @ SV227 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1920]) ).

thf(1937,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) ) )
        = $false )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1921]) ).

thf(1938,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
        = $false )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1921]) ).

thf(1939,plain,
    ! [SV251: $i,SV249: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV249 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV251 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1922]) ).

thf(1940,plain,
    ! [SV252: $i,SV250: $i,SV218: $i] :
      ( ( ( ~ ( aElement0 @ SV218 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV250 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV252 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1923]) ).

thf(1941,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i,SX2: $i] :
              ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SX1 @ SX2 )
               != SX0 ) )
          | ( aElementOf0 @ SX0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1924]) ).

thf(1942,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
               != SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1925]) ).

thf(1943,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xb @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1926]) ).

thf(1944,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xa @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                      | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElementOf0 @ SX1 @ xI )
                                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElement0 @ SX1 )
                                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                      | ~ ( aSet0 @ xI ) )
                | ~ ( aIdeal0 @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1927]) ).

thf(1945,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
          | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1928]) ).

thf(1946,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
                | ( SV220
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1929]) ).

thf(1947,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( ( ( sK2_SY72 @ SV232 @ SV220 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1929]) ).

thf(1948,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1930]) ).

thf(1949,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1931]) ).

thf(1950,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                               != xa )
                                              | ~ ( aElement0 @ sK12_W0 ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ( doDivides0 @ xc @ xa ) )
                            | ~ ( aDivisorOf0 @ xc @ xa ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                       != xb )
                      | ~ ( aElement0 @ sK11_W0 ) ) )
          | ~ ( doDivides0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1932]) ).

thf(1951,plain,
    ( ( aDivisorOf0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1933]) ).

thf(1952,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1937]) ).

thf(1953,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) ) )
        = $true )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1938]) ).

thf(1954,plain,
    ! [SV251: $i,SV249: $i,SV218: $i] :
      ( ( ( aElement0 @ SV218 )
        = $false )
      | ( ( ~ ( aElement0 @ SV249 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV251 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1939]) ).

thf(1955,plain,
    ! [SV252: $i,SV250: $i,SV218: $i] :
      ( ( ( aElement0 @ SV218 )
        = $false )
      | ( ( ~ ( aElement0 @ SV250 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV252 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1940]) ).

thf(1956,plain,
    ! [SV253: $i] :
      ( ( ! [SY197: $i,SY198: $i] :
            ( ~ ( aElementOf0 @ SY197 @ ( slsdtgt0 @ xa ) )
            | ~ ( aElementOf0 @ SY198 @ ( slsdtgt0 @ xb ) )
            | ( ( sdtpldt0 @ SY197 @ SY198 )
             != SV253 ) )
        | ( aElementOf0 @ SV253 @ xI ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1941]) ).

thf(1957,plain,
    ! [SV254: $i] :
      ( ( ~ ( aElementOf0 @ SV254 @ xI )
        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
            | ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
             != SV254 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1942]) ).

thf(1958,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1943]) ).

thf(1959,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1944]) ).

thf(1960,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1945]) ).

thf(1961,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1945]) ).

thf(1962,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                    | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
              | ( SV220
               != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1946]) ).

thf(1963,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ( ( sK2_SY72 @ SV232 @ SV220 )
            = sz00 )
          | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1947]) ).

thf(1964,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1948]) ).

thf(1965,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1949]) ).

thf(1966,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) )
      | ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1950]) ).

thf(1967,plain,
    ! [SV217: $i,SV230: $i,SV255: $i] :
      ( ( ( ! [SY199: $i] :
              ( ~ ( aElement0 @ SV255 )
              | ~ ( aElement0 @ SY199 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY199 @ SV255 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY199 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY199 @ SV255 @ SV230 @ SV217 ) @ SY199 @ SV230 ) ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1952]) ).

thf(1968,plain,
    ! [SV217: $i,SV230: $i] :
      ( ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( ! [SY193: $i,SY194: $i] :
              ( ~ ( aElement0 @ SY193 )
              | ~ ( aElement0 @ SY194 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY193 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY194 @ SY193 @ SV230 @ SV217 ) @ SY194 @ SV230 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1953]) ).

thf(1969,plain,
    ! [SV251: $i,SV218: $i,SV249: $i] :
      ( ( ( aElement0 @ SV249 )
        = $false )
      | ( ( aElement0 @ SV218 )
        = $false )
      | ( ( ~ ( aElement0 @ SV251 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1954]) ).

thf(1970,plain,
    ! [SV252: $i,SV218: $i,SV250: $i] :
      ( ( ( aElement0 @ SV250 )
        = $false )
      | ( ( aElement0 @ SV218 )
        = $false )
      | ( ( ~ ( aElement0 @ SV252 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1955]) ).

thf(1971,plain,
    ! [SV253: $i] :
      ( ( ( ! [SY197: $i,SY198: $i] :
              ( ~ ( aElementOf0 @ SY197 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY198 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SY197 @ SY198 )
               != SV253 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1956]) ).

thf(1972,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( aElementOf0 @ SV254 @ xI ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
               != SV254 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1957]) ).

thf(1973,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1958]) ).

thf(1974,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1958]) ).

thf(1975,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1959]) ).

thf(1976,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1959]) ).

thf(1977,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1960]) ).

thf(1978,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1961]) ).

thf(1979,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
          | ( SV220
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1962]) ).

thf(1980,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ( sK2_SY72 @ SV232 @ SV220 )
          = sz00 )
        = $true )
      | ( ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) @ ( sbrdtbr0 @ SV232 ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1963]) ).

thf(1981,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1964]) ).

thf(1982,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1964]) ).

thf(1983,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1965]) ).

thf(1984,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1965]) ).

thf(1985,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1966]) ).

thf(1986,plain,
    ( ( ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1966]) ).

thf(1987,plain,
    ! [SV217: $i,SV230: $i,SV256: $i,SV255: $i] :
      ( ( ( ~ ( aElement0 @ SV255 )
          | ~ ( aElement0 @ SV256 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1967]) ).

thf(1988,plain,
    ! [SV217: $i,SV230: $i,SV257: $i] :
      ( ( ( ! [SY200: $i] :
              ( ~ ( aElement0 @ SV257 )
              | ~ ( aElement0 @ SY200 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY200 @ SV257 @ SV230 @ SV217 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY200 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY200 @ SV257 @ SV230 @ SV217 ) @ SY200 @ SV230 ) ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1968]) ).

thf(1989,plain,
    ! [SV249: $i,SV218: $i,SV251: $i] :
      ( ( ( aElement0 @ SV251 )
        = $false )
      | ( ( aElement0 @ SV218 )
        = $false )
      | ( ( aElement0 @ SV249 )
        = $false )
      | ( ( ( sdtasdt0 @ SV218 @ ( sdtpldt0 @ SV249 @ SV251 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV218 @ SV249 ) @ ( sdtasdt0 @ SV218 @ SV251 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1969]) ).

thf(1990,plain,
    ! [SV250: $i,SV218: $i,SV252: $i] :
      ( ( ( aElement0 @ SV252 )
        = $false )
      | ( ( aElement0 @ SV218 )
        = $false )
      | ( ( aElement0 @ SV250 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV250 @ SV252 ) @ SV218 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV250 @ SV218 ) @ ( sdtasdt0 @ SV252 @ SV218 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1970]) ).

thf(1991,plain,
    ! [SV253: $i,SV258: $i] :
      ( ( ( ! [SY201: $i] :
              ( ~ ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY201 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SV258 @ SY201 )
               != SV253 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1971]) ).

thf(1992,plain,
    ! [SV254: $i] :
      ( ( ( aElementOf0 @ SV254 @ xI )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
               != SV254 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1972]) ).

thf(1993,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xb @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1973]) ).

thf(1994,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
          | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1974]) ).

thf(1995,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xa @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1975]) ).

thf(1996,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ xI )
                                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElement0 @ SX1 )
                                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                | ~ ( aSet0 @ xI ) )
          | ~ ( aIdeal0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1976]) ).

thf(1997,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1977]) ).

thf(1998,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) ) )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1978]) ).

thf(1999,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1979]) ).

thf(2000,plain,
    ! [SV232: $i,SV220: $i] :
      ( ( ( ( SV220
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1979]) ).

thf(2001,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1981]) ).

thf(2002,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1982]) ).

thf(2003,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1983]) ).

thf(2004,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1984]) ).

thf(2005,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                         != xa )
                                        | ~ ( aElement0 @ sK12_W0 ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ( doDivides0 @ xc @ xa ) )
                      | ~ ( aDivisorOf0 @ xc @ xa ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                 != xb )
                | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1985]) ).

thf(2006,plain,
    ( ( doDivides0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1986]) ).

thf(2007,plain,
    ! [SV217: $i,SV230: $i,SV256: $i,SV255: $i] :
      ( ( ( ~ ( aElement0 @ SV255 )
          | ~ ( aElement0 @ SV256 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1987]) ).

thf(2008,plain,
    ! [SV217: $i,SV230: $i,SV259: $i,SV257: $i] :
      ( ( ( ~ ( aElement0 @ SV257 )
          | ~ ( aElement0 @ SV259 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1988]) ).

thf(2009,plain,
    ! [SV253: $i,SV260: $i,SV258: $i] :
      ( ( ( ~ ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) )
          | ( ( sdtpldt0 @ SV258 @ SV260 )
           != SV253 ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1991]) ).

thf(2010,plain,
    ! [SV254: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
          | ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
           != SV254 ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1992]) ).

thf(2011,plain,
    ! [SV261: $i] :
      ( ( ! [SY202: $i] :
            ( ( ( sdtasdt0 @ xb @ SY202 )
             != SV261 )
            | ~ ( aElement0 @ SY202 ) )
        | ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1993]) ).

thf(2012,plain,
    ! [SV262: $i] :
      ( ( ~ ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
             != SV262 )
            | ~ ( aElement0 @ ( sK8_W1 @ SV262 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1994]) ).

thf(2013,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1995]) ).

thf(2014,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) )
      | ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1996]) ).

thf(2015,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1997]) ).

thf(2016,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1997]) ).

thf(2017,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1998]) ).

thf(2018,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
              | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[1999]) ).

thf(2019,plain,
    ! [SV232: $i,SV220: $i] :
      ( ( ( SV220
          = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV232 @ SV220 ) @ SV232 ) @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2000]) ).

thf(2020,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2001]) ).

thf(2021,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2002]) ).

thf(2022,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2003]) ).

thf(2023,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2004]) ).

thf(2024,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2005]) ).

thf(2025,plain,
    ! [SV217: $i,SV230: $i,SV256: $i,SV255: $i] :
      ( ( ( ~ ( aElement0 @ SV255 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV256 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2007]) ).

thf(2026,plain,
    ! [SV217: $i,SV230: $i,SV259: $i,SV257: $i] :
      ( ( ( ~ ( aElement0 @ SV257 )
          | ~ ( aElement0 @ SV259 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2008]) ).

thf(2027,plain,
    ! [SV253: $i,SV260: $i,SV258: $i] :
      ( ( ( ~ ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV258 @ SV260 )
           != SV253 ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2009]) ).

thf(2028,plain,
    ! [SV254: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2010]) ).

thf(2029,plain,
    ! [SV254: $i] :
      ( ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
           != SV254 ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2010]) ).

thf(2030,plain,
    ! [SV261: $i] :
      ( ( ( ! [SY202: $i] :
              ( ( ( sdtasdt0 @ xb @ SY202 )
               != SV261 )
              | ~ ( aElement0 @ SY202 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2011]) ).

thf(2031,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
               != SV262 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV262 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2012]) ).

thf(2032,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2013]) ).

thf(2033,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2013]) ).

thf(2034,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2014]) ).

thf(2035,plain,
    ( ( ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2014]) ).

thf(2036,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2015]) ).

thf(2037,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2016]) ).

thf(2038,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2017]) ).

thf(2039,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2017]) ).

thf(2040,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
          | ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2018]) ).

thf(2041,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2020]) ).

thf(2042,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2020]) ).

thf(2043,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2021]) ).

thf(2044,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2021]) ).

thf(2045,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2022]) ).

thf(2046,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2022]) ).

thf(2047,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2023]) ).

thf(2048,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2023]) ).

thf(2049,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2024]) ).

thf(2050,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2024]) ).

thf(2051,plain,
    ! [SV217: $i,SV230: $i,SV256: $i,SV255: $i] :
      ( ( ( aElement0 @ SV255 )
        = $false )
      | ( ( ~ ( aElement0 @ SV256 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2025]) ).

thf(2052,plain,
    ! [SV217: $i,SV230: $i,SV259: $i,SV257: $i] :
      ( ( ( ~ ( aElement0 @ SV257 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV259 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2026]) ).

thf(2053,plain,
    ! [SV253: $i,SV260: $i,SV258: $i] :
      ( ( ( ~ ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV258 @ SV260 )
           != SV253 ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2027]) ).

thf(2054,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $true )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2028]) ).

thf(2055,plain,
    ! [SV254: $i] :
      ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV254 ) @ ( sK10_SY73 @ SV254 ) )
          = SV254 )
        = $true )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2029]) ).

thf(2056,plain,
    ! [SV261: $i,SV263: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV263 )
           != SV261 )
          | ~ ( aElement0 @ SV263 ) )
        = $true )
      | ( ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2030]) ).

thf(2057,plain,
    ! [SV262: $i] :
      ( ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
               != SV262 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV262 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2031]) ).

thf(2058,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xa @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2032]) ).

thf(2059,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
          | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2033]) ).

thf(2060,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ xI )
                          | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElement0 @ SX1 )
                          | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
          | ~ ( aSet0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2034]) ).

thf(2061,plain,
    ( ( aIdeal0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2035]) ).

thf(2062,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2037]) ).

thf(2063,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV231 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2038]) ).

thf(2064,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2039]) ).

thf(2065,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2040]) ).

thf(2066,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( ~ ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) ) )
        = $false )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2040]) ).

thf(2067,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2041]) ).

thf(2068,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2042]) ).

thf(2069,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2043]) ).

thf(2070,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2044]) ).

thf(2071,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2045]) ).

thf(2072,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2046]) ).

thf(2073,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2047]) ).

thf(2074,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2048]) ).

thf(2075,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                   != xa )
                                  | ~ ( aElement0 @ sK12_W0 ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ( doDivides0 @ xc @ xa ) )
                | ~ ( aDivisorOf0 @ xc @ xa ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2049]) ).

thf(2076,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
           != xb )
          | ~ ( aElement0 @ sK11_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2050]) ).

thf(2077,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2051]) ).

thf(2078,plain,
    ! [SV217: $i,SV230: $i,SV259: $i,SV257: $i] :
      ( ( ( aElement0 @ SV257 )
        = $false )
      | ( ( ~ ( aElement0 @ SV259 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2052]) ).

thf(2079,plain,
    ! [SV253: $i,SV260: $i,SV258: $i] :
      ( ( ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV258 @ SV260 )
           != SV253 ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2053]) ).

thf(2080,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2054]) ).

thf(2081,plain,
    ! [SV261: $i,SV263: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV263 )
           != SV261 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV263 ) )
        = $true )
      | ( ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2056]) ).

thf(2082,plain,
    ! [SV262: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
           != SV262 )
          | ~ ( aElement0 @ ( sK8_W1 @ SV262 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2057]) ).

thf(2083,plain,
    ! [SV264: $i] :
      ( ( ! [SY203: $i] :
            ( ( ( sdtasdt0 @ xa @ SY203 )
             != SV264 )
            | ~ ( aElement0 @ SY203 ) )
        | ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2058]) ).

thf(2084,plain,
    ! [SV265: $i] :
      ( ( ~ ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
             != SV265 )
            | ~ ( aElement0 @ ( sK7_W1 @ SV265 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2059]) ).

thf(2085,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
      | ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2060]) ).

thf(2086,plain,
    ! [SV219: $i,SV231: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV231 @ SV219 ) @ SV219 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV231 @ SV219 ) @ SV231 )
        = $false )
      | ( ( SV219 = SV231 )
        = $true )
      | ( ( aSet0 @ SV219 )
        = $false )
      | ( ( aSet0 @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2064]) ).

thf(2087,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( aElement0 @ ( sK1_W2 @ SV232 @ SV220 ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2065]) ).

thf(2088,plain,
    ! [SV220: $i,SV232: $i] :
      ( ( ( aElement0 @ ( sK2_SY72 @ SV232 @ SV220 ) )
        = $true )
      | ( ( SV232 = sz00 )
        = $true )
      | ( ( aElement0 @ SV220 )
        = $false )
      | ( ( aElement0 @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2066]) ).

thf(2089,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2067]) ).

thf(2090,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2068]) ).

thf(2091,plain,
    ! [SV266: $i] :
      ( ( ~ ( aDivisorOf0 @ SV266 @ xa )
        | ~ ( aDivisorOf0 @ SV266 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
             != xc )
            | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2069]) ).

thf(2092,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2070]) ).

thf(2093,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2071]) ).

thf(2094,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2072]) ).

thf(2095,plain,
    ! [SV267: $i] :
      ( ( ~ ( aDivisorOf0 @ SV267 @ xa )
        | ~ ( aDivisorOf0 @ SV267 @ xb )
        | ( doDivides0 @ SV267 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2073]) ).

thf(2096,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2074]) ).

thf(2097,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2075]) ).

thf(2098,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb )
      | ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2076]) ).

thf(2099,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2077]) ).

thf(2100,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2078]) ).

thf(2101,plain,
    ! [SV253: $i,SV258: $i,SV260: $i] :
      ( ( ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ( ( sdtpldt0 @ SV258 @ SV260 )
           != SV253 ) )
        = $true )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2079]) ).

thf(2102,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2080]) ).

thf(2103,plain,
    ! [SV254: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2080]) ).

thf(2104,plain,
    ! [SV261: $i,SV263: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV263 )
          = SV261 )
        = $false )
      | ( ( ~ ( aElement0 @ SV263 ) )
        = $true )
      | ( ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2081]) ).

thf(2105,plain,
    ! [SV262: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
           != SV262 ) )
        = $false )
      | ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2082]) ).

thf(2106,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( aElement0 @ ( sK8_W1 @ SV262 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2082]) ).

thf(2107,plain,
    ! [SV264: $i] :
      ( ( ( ! [SY203: $i] :
              ( ( ( sdtasdt0 @ xa @ SY203 )
               != SV264 )
              | ~ ( aElement0 @ SY203 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2083]) ).

thf(2108,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
               != SV265 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV265 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2084]) ).

thf(2109,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2085]) ).

thf(2110,plain,
    ( ( ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2085]) ).

thf(2111,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2089]) ).

thf(2112,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2089]) ).

thf(2113,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2090]) ).

thf(2114,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2090]) ).

thf(2115,plain,
    ! [SV266: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV266 @ xa )
          | ~ ( aDivisorOf0 @ SV266 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2091]) ).

thf(2116,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2092]) ).

thf(2117,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2092]) ).

thf(2118,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2093]) ).

thf(2119,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2093]) ).

thf(2120,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2094]) ).

thf(2121,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2094]) ).

thf(2122,plain,
    ! [SV267: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV267 @ xa )
          | ~ ( aDivisorOf0 @ SV267 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV267 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2095]) ).

thf(2123,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2096]) ).

thf(2124,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2096]) ).

thf(2125,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2097]) ).

thf(2126,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2097]) ).

thf(2127,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2098]) ).

thf(2128,plain,
    ( ( ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2098]) ).

thf(2129,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2099]) ).

thf(2130,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2099]) ).

thf(2131,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2100]) ).

thf(2132,plain,
    ! [SV253: $i,SV260: $i,SV258: $i] :
      ( ( ( ( sdtpldt0 @ SV258 @ SV260 )
          = SV253 )
        = $false )
      | ( ( aElementOf0 @ SV258 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( aElementOf0 @ SV260 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV253 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2101]) ).

thf(2133,plain,
    ! [SV254: $i] :
      ( ( ( aElementOf0 @ ( sK9_W1 @ SV254 ) @ ( slsdtgt0 @ xa ) )
        = $true )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2102]) ).

thf(2134,plain,
    ! [SV254: $i] :
      ( ( ( aElementOf0 @ ( sK10_SY73 @ SV254 ) @ ( slsdtgt0 @ xb ) )
        = $true )
      | ( ( aElementOf0 @ SV254 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2103]) ).

thf(2135,plain,
    ! [SV261: $i,SV263: $i] :
      ( ( ( aElement0 @ SV263 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV263 )
          = SV261 )
        = $false )
      | ( ( aElementOf0 @ SV261 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2104]) ).

thf(2136,plain,
    ! [SV262: $i] :
      ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV262 ) )
          = SV262 )
        = $true )
      | ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2105]) ).

thf(2137,plain,
    ! [SV262: $i] :
      ( ( ( aElement0 @ ( sK8_W1 @ SV262 ) )
        = $true )
      | ( ( aElementOf0 @ SV262 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2106]) ).

thf(2138,plain,
    ! [SV264: $i,SV268: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV268 )
           != SV264 )
          | ~ ( aElement0 @ SV268 ) )
        = $true )
      | ( ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2107]) ).

thf(2139,plain,
    ! [SV265: $i] :
      ( ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
               != SV265 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV265 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2108]) ).

thf(2140,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ xI )
                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElement0 @ SX1 )
                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2109]) ).

thf(2141,plain,
    ( ( aSet0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2110]) ).

thf(2142,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2111]) ).

thf(2143,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2112]) ).

thf(2144,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2113]) ).

thf(2145,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2114]) ).

thf(2146,plain,
    ! [SV266: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV266 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV266 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2115]) ).

thf(2147,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2116]) ).

thf(2148,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2117]) ).

thf(2149,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2118]) ).

thf(2150,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2119]) ).

thf(2151,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2120]) ).

thf(2152,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2121]) ).

thf(2153,plain,
    ! [SV267: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV267 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV267 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV267 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2122]) ).

thf(2154,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2123]) ).

thf(2155,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2124]) ).

thf(2156,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                             != xa )
                            | ~ ( aElement0 @ sK12_W0 ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ( doDivides0 @ xc @ xa ) )
          | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2125]) ).

thf(2157,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2126]) ).

thf(2158,plain,
    ( ( ( sdtasdt0 @ xc @ sK11_W0 )
      = xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2127]) ).

thf(2159,plain,
    ( ( aElement0 @ sK11_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2128]) ).

thf(2160,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) ) )
        = $true )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2129]) ).

thf(2161,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV256 @ SV230 )
        = $true )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2130]) ).

thf(2162,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2131]) ).

thf(2163,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2131]) ).

thf(2164,plain,
    ! [SV264: $i,SV268: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV268 )
           != SV264 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV268 ) )
        = $true )
      | ( ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2138]) ).

thf(2165,plain,
    ! [SV265: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
           != SV265 )
          | ~ ( aElement0 @ ( sK7_W1 @ SV265 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2139]) ).

thf(2166,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2140]) ).

thf(2167,plain,
    ! [SV269: $i] :
      ( ( ~ ( aElement0 @ SV269 )
        | ! [SY204: $i] :
            ( ( ( sdtasdt0 @ SV269 @ SY204 )
             != xa )
            | ~ ( aElement0 @ SY204 ) )
        | ~ ( aDivisorOf0 @ SV269 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
             != xc )
            | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2142]) ).

thf(2168,plain,
    ! [SV270: $i] :
      ( ( ~ ( aElement0 @ SV270 )
        | ~ ( doDivides0 @ SV270 @ xa )
        | ~ ( aDivisorOf0 @ SV270 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
             != xc )
            | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2143]) ).

thf(2169,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2144]) ).

thf(2170,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2145]) ).

thf(2171,plain,
    ! [SV266: $i] :
      ( ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV266 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2146]) ).

thf(2172,plain,
    ! [SV271: $i] :
      ( ( ~ ( aDivisorOf0 @ SV271 @ xa )
        | ! [SY205: $i] :
            ( ( ( sdtasdt0 @ SV271 @ SY205 )
             != xb )
            | ~ ( aElement0 @ SY205 ) )
        | ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
             != xc )
            | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2147]) ).

thf(2173,plain,
    ! [SV272: $i] :
      ( ( ~ ( aDivisorOf0 @ SV272 @ xa )
        | ~ ( doDivides0 @ SV272 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
             != xc )
            | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2148]) ).

thf(2174,plain,
    ! [SV273: $i] :
      ( ( ~ ( aElement0 @ SV273 )
        | ! [SY206: $i] :
            ( ( ( sdtasdt0 @ SV273 @ SY206 )
             != xa )
            | ~ ( aElement0 @ SY206 ) )
        | ~ ( aDivisorOf0 @ SV273 @ xb )
        | ( doDivides0 @ SV273 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2149]) ).

thf(2175,plain,
    ! [SV274: $i] :
      ( ( ~ ( aElement0 @ SV274 )
        | ~ ( doDivides0 @ SV274 @ xa )
        | ~ ( aDivisorOf0 @ SV274 @ xb )
        | ( doDivides0 @ SV274 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2150]) ).

thf(2176,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2151]) ).

thf(2177,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2152]) ).

thf(2178,plain,
    ! [SV267: $i] :
      ( ( ( aDivisorOf0 @ SV267 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV267 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV267 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2153]) ).

thf(2179,plain,
    ! [SV275: $i] :
      ( ( ~ ( aDivisorOf0 @ SV275 @ xa )
        | ! [SY207: $i] :
            ( ( ( sdtasdt0 @ SV275 @ SY207 )
             != xb )
            | ~ ( aElement0 @ SY207 ) )
        | ( doDivides0 @ SV275 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2154]) ).

thf(2180,plain,
    ! [SV276: $i] :
      ( ( ~ ( aDivisorOf0 @ SV276 @ xa )
        | ~ ( doDivides0 @ SV276 @ xb )
        | ( doDivides0 @ SV276 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2155]) ).

thf(2181,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) )
      | ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2156]) ).

thf(2182,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2160]) ).

thf(2183,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) ) )
        = $true )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2162]) ).

thf(2184,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV259 @ SV230 )
        = $true )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2163]) ).

thf(2185,plain,
    ! [SV264: $i,SV268: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV268 )
          = SV264 )
        = $false )
      | ( ( ~ ( aElement0 @ SV268 ) )
        = $true )
      | ( ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2164]) ).

thf(2186,plain,
    ! [SV265: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
           != SV265 ) )
        = $false )
      | ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2165]) ).

thf(2187,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( aElement0 @ ( sK7_W1 @ SV265 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2165]) ).

thf(2188,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2166]) ).

thf(2189,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2166]) ).

thf(2190,plain,
    ! [SV269: $i] :
      ( ( ( ~ ( aElement0 @ SV269 )
          | ! [SY204: $i] :
              ( ( ( sdtasdt0 @ SV269 @ SY204 )
               != xa )
              | ~ ( aElement0 @ SY204 ) )
          | ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2167]) ).

thf(2191,plain,
    ! [SV270: $i] :
      ( ( ( ~ ( aElement0 @ SV270 )
          | ~ ( doDivides0 @ SV270 @ xa )
          | ~ ( aDivisorOf0 @ SV270 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2168]) ).

thf(2192,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2169]) ).

thf(2193,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2169]) ).

thf(2194,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2170]) ).

thf(2195,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2170]) ).

thf(2196,plain,
    ! [SV266: $i] :
      ( ( ( aDivisorOf0 @ SV266 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2171]) ).

thf(2197,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV271 @ xa )
          | ! [SY205: $i] :
              ( ( ( sdtasdt0 @ SV271 @ SY205 )
               != xb )
              | ~ ( aElement0 @ SY205 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2172]) ).

thf(2198,plain,
    ! [SV272: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV272 @ xa )
          | ~ ( doDivides0 @ SV272 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2173]) ).

thf(2199,plain,
    ! [SV273: $i] :
      ( ( ( ~ ( aElement0 @ SV273 )
          | ! [SY206: $i] :
              ( ( ( sdtasdt0 @ SV273 @ SY206 )
               != xa )
              | ~ ( aElement0 @ SY206 ) )
          | ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2174]) ).

thf(2200,plain,
    ! [SV274: $i] :
      ( ( ( ~ ( aElement0 @ SV274 )
          | ~ ( doDivides0 @ SV274 @ xa )
          | ~ ( aDivisorOf0 @ SV274 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2175]) ).

thf(2201,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2176]) ).

thf(2202,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2176]) ).

thf(2203,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2177]) ).

thf(2204,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2177]) ).

thf(2205,plain,
    ! [SV267: $i] :
      ( ( ( aDivisorOf0 @ SV267 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV267 @ xa )
        = $false )
      | ( ( doDivides0 @ SV267 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2178]) ).

thf(2206,plain,
    ! [SV275: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV275 @ xa )
          | ! [SY207: $i] :
              ( ( ( sdtasdt0 @ SV275 @ SY207 )
               != xb )
              | ~ ( aElement0 @ SY207 ) ) )
        = $true )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2179]) ).

thf(2207,plain,
    ! [SV276: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV276 @ xa )
          | ~ ( doDivides0 @ SV276 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV276 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2180]) ).

thf(2208,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2181]) ).

thf(2209,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2181]) ).

thf(2210,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2182]) ).

thf(2211,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 ) )
        = $false )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2182]) ).

thf(2212,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2183]) ).

thf(2213,plain,
    ! [SV264: $i,SV268: $i] :
      ( ( ( aElement0 @ SV268 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV268 )
          = SV264 )
        = $false )
      | ( ( aElementOf0 @ SV264 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2185]) ).

thf(2214,plain,
    ! [SV265: $i] :
      ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV265 ) )
          = SV265 )
        = $true )
      | ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2186]) ).

thf(2215,plain,
    ! [SV265: $i] :
      ( ( ( aElement0 @ ( sK7_W1 @ SV265 ) )
        = $true )
      | ( ( aElementOf0 @ SV265 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2187]) ).

thf(2216,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElementOf0 @ SX1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2188]) ).

thf(2217,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElement0 @ SX1 )
              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2189]) ).

thf(2218,plain,
    ! [SV269: $i] :
      ( ( ( ~ ( aElement0 @ SV269 )
          | ! [SY204: $i] :
              ( ( ( sdtasdt0 @ SV269 @ SY204 )
               != xa )
              | ~ ( aElement0 @ SY204 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2190]) ).

thf(2219,plain,
    ! [SV270: $i] :
      ( ( ( ~ ( aElement0 @ SV270 )
          | ~ ( doDivides0 @ SV270 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV270 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2191]) ).

thf(2220,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2192]) ).

thf(2221,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2193]) ).

thf(2222,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2194]) ).

thf(2223,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2195]) ).

thf(2224,plain,
    ! [SV266: $i] :
      ( ( ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
           != xc )
          | ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2196]) ).

thf(2225,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV271 @ xa ) )
        = $true )
      | ( ( ! [SY205: $i] :
              ( ( ( sdtasdt0 @ SV271 @ SY205 )
               != xb )
              | ~ ( aElement0 @ SY205 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2197]) ).

thf(2226,plain,
    ! [SV272: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV272 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV272 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2198]) ).

thf(2227,plain,
    ! [SV273: $i] :
      ( ( ( ~ ( aElement0 @ SV273 )
          | ! [SY206: $i] :
              ( ( ( sdtasdt0 @ SV273 @ SY206 )
               != xa )
              | ~ ( aElement0 @ SY206 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2199]) ).

thf(2228,plain,
    ! [SV274: $i] :
      ( ( ( ~ ( aElement0 @ SV274 )
          | ~ ( doDivides0 @ SV274 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV274 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2200]) ).

thf(2229,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2201]) ).

thf(2230,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2202]) ).

thf(2231,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2203]) ).

thf(2232,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2204]) ).

thf(2233,plain,
    ! [SV275: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV275 @ xa ) )
        = $true )
      | ( ( ! [SY207: $i] :
              ( ( ( sdtasdt0 @ SV275 @ SY207 )
               != xb )
              | ~ ( aElement0 @ SY207 ) ) )
        = $true )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2206]) ).

thf(2234,plain,
    ! [SV276: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV276 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV276 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV276 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2207]) ).

thf(2235,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                       != xa )
                      | ~ ( aElement0 @ sK12_W0 ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ( doDivides0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2208]) ).

thf(2236,plain,
    ( ( aDivisorOf0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2209]) ).

thf(2237,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2210]) ).

thf(2238,plain,
    ! [SV217: $i,SV230: $i,SV255: $i,SV256: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV256 @ SV255 @ SV230 @ SV217 ) @ SV255 @ SV217 )
        = $true )
      | ( ( aElement0 @ SV255 )
        = $false )
      | ( ( aElement0 @ SV256 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2211]) ).

thf(2239,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2212]) ).

thf(2240,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 ) )
        = $false )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2212]) ).

thf(2241,plain,
    ! [SV277: $i] :
      ( ( ~ ( aElementOf0 @ SV277 @ xI )
        | ! [SY208: $i] :
            ( ~ ( aElementOf0 @ SY208 @ xI )
            | ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SY208 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2216]) ).

thf(2242,plain,
    ! [SV278: $i] :
      ( ( ~ ( aElementOf0 @ SV278 @ xI )
        | ! [SY209: $i] :
            ( ~ ( aElement0 @ SY209 )
            | ( aElementOf0 @ ( sdtasdt0 @ SY209 @ SV278 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2217]) ).

thf(2243,plain,
    ! [SV269: $i] :
      ( ( ( ~ ( aElement0 @ SV269 ) )
        = $true )
      | ( ( ! [SY204: $i] :
              ( ( ( sdtasdt0 @ SV269 @ SY204 )
               != xa )
              | ~ ( aElement0 @ SY204 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2218]) ).

thf(2244,plain,
    ! [SV270: $i] :
      ( ( ( ~ ( aElement0 @ SV270 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV270 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV270 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2219]) ).

thf(2245,plain,
    ! [SV279: $i] :
      ( ( ~ ( aElement0 @ SV279 )
        | ! [SY210: $i] :
            ( ( ( sdtasdt0 @ SV279 @ SY210 )
             != xa )
            | ~ ( aElement0 @ SY210 ) )
        | ! [SY211: $i] :
            ( ( ( sdtasdt0 @ SV279 @ SY211 )
             != xb )
            | ~ ( aElement0 @ SY211 ) )
        | ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
             != xc )
            | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2220]) ).

thf(2246,plain,
    ! [SV280: $i] :
      ( ( ~ ( aElement0 @ SV280 )
        | ~ ( doDivides0 @ SV280 @ xa )
        | ! [SY212: $i] :
            ( ( ( sdtasdt0 @ SV280 @ SY212 )
             != xb )
            | ~ ( aElement0 @ SY212 ) )
        | ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
             != xc )
            | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2221]) ).

thf(2247,plain,
    ! [SV281: $i] :
      ( ( ~ ( aElement0 @ SV281 )
        | ! [SY213: $i] :
            ( ( ( sdtasdt0 @ SV281 @ SY213 )
             != xa )
            | ~ ( aElement0 @ SY213 ) )
        | ~ ( doDivides0 @ SV281 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
             != xc )
            | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2222]) ).

thf(2248,plain,
    ! [SV282: $i] :
      ( ( ~ ( aElement0 @ SV282 )
        | ~ ( doDivides0 @ SV282 @ xa )
        | ~ ( doDivides0 @ SV282 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
             != xc )
            | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2223]) ).

thf(2249,plain,
    ! [SV266: $i] :
      ( ( ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2224]) ).

thf(2250,plain,
    ! [SV266: $i] :
      ( ( ( ~ ( aElement0 @ ( sK15_W1 @ SV266 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2224]) ).

thf(2251,plain,
    ! [SV271: $i] :
      ( ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ! [SY205: $i] :
              ( ( ( sdtasdt0 @ SV271 @ SY205 )
               != xb )
              | ~ ( aElement0 @ SY205 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2225]) ).

thf(2252,plain,
    ! [SV272: $i] :
      ( ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV272 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2226]) ).

thf(2253,plain,
    ! [SV273: $i] :
      ( ( ( ~ ( aElement0 @ SV273 ) )
        = $true )
      | ( ( ! [SY206: $i] :
              ( ( ( sdtasdt0 @ SV273 @ SY206 )
               != xa )
              | ~ ( aElement0 @ SY206 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2227]) ).

thf(2254,plain,
    ! [SV274: $i] :
      ( ( ( ~ ( aElement0 @ SV274 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV274 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV274 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2228]) ).

thf(2255,plain,
    ! [SV283: $i] :
      ( ( ~ ( aElement0 @ SV283 )
        | ! [SY214: $i] :
            ( ( ( sdtasdt0 @ SV283 @ SY214 )
             != xa )
            | ~ ( aElement0 @ SY214 ) )
        | ! [SY215: $i] :
            ( ( ( sdtasdt0 @ SV283 @ SY215 )
             != xb )
            | ~ ( aElement0 @ SY215 ) )
        | ( doDivides0 @ SV283 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2229]) ).

thf(2256,plain,
    ! [SV284: $i] :
      ( ( ~ ( aElement0 @ SV284 )
        | ~ ( doDivides0 @ SV284 @ xa )
        | ! [SY216: $i] :
            ( ( ( sdtasdt0 @ SV284 @ SY216 )
             != xb )
            | ~ ( aElement0 @ SY216 ) )
        | ( doDivides0 @ SV284 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2230]) ).

thf(2257,plain,
    ! [SV285: $i] :
      ( ( ~ ( aElement0 @ SV285 )
        | ! [SY217: $i] :
            ( ( ( sdtasdt0 @ SV285 @ SY217 )
             != xa )
            | ~ ( aElement0 @ SY217 ) )
        | ~ ( doDivides0 @ SV285 @ xb )
        | ( doDivides0 @ SV285 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2231]) ).

thf(2258,plain,
    ! [SV286: $i] :
      ( ( ~ ( aElement0 @ SV286 )
        | ~ ( doDivides0 @ SV286 @ xa )
        | ~ ( doDivides0 @ SV286 @ xb )
        | ( doDivides0 @ SV286 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2232]) ).

thf(2259,plain,
    ! [SV275: $i] :
      ( ( ( aDivisorOf0 @ SV275 @ xa )
        = $false )
      | ( ( ! [SY207: $i] :
              ( ( ( sdtasdt0 @ SV275 @ SY207 )
               != xb )
              | ~ ( aElement0 @ SY207 ) ) )
        = $true )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2233]) ).

thf(2260,plain,
    ! [SV276: $i] :
      ( ( ( aDivisorOf0 @ SV276 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV276 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV276 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2234]) ).

thf(2261,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2235]) ).

thf(2262,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) )
        = $true )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2239]) ).

thf(2263,plain,
    ! [SV217: $i,SV230: $i,SV257: $i,SV259: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV259 @ SV257 @ SV230 @ SV217 ) @ SV257 @ SV217 )
        = $true )
      | ( ( aElement0 @ SV257 )
        = $false )
      | ( ( aElement0 @ SV259 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV230 @ SV217 ) @ ( sdtpldt1 @ SV217 @ SV230 ) )
        = $false )
      | ( ( aIdeal0 @ SV217 )
        = $false )
      | ( ( aIdeal0 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2240]) ).

thf(2264,plain,
    ! [SV277: $i] :
      ( ( ( ~ ( aElementOf0 @ SV277 @ xI ) )
        = $true )
      | ( ( ! [SY208: $i] :
              ( ~ ( aElementOf0 @ SY208 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SY208 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2241]) ).

thf(2265,plain,
    ! [SV278: $i] :
      ( ( ( ~ ( aElementOf0 @ SV278 @ xI ) )
        = $true )
      | ( ( ! [SY209: $i] :
              ( ~ ( aElement0 @ SY209 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY209 @ SV278 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2242]) ).

thf(2266,plain,
    ! [SV269: $i] :
      ( ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ! [SY204: $i] :
              ( ( ( sdtasdt0 @ SV269 @ SY204 )
               != xa )
              | ~ ( aElement0 @ SY204 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2243]) ).

thf(2267,plain,
    ! [SV270: $i] :
      ( ( ( aElement0 @ SV270 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV270 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV270 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2244]) ).

thf(2268,plain,
    ! [SV279: $i] :
      ( ( ( ~ ( aElement0 @ SV279 )
          | ! [SY210: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY210 )
               != xa )
              | ~ ( aElement0 @ SY210 ) )
          | ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2245]) ).

thf(2269,plain,
    ! [SV280: $i] :
      ( ( ( ~ ( aElement0 @ SV280 )
          | ~ ( doDivides0 @ SV280 @ xa )
          | ! [SY212: $i] :
              ( ( ( sdtasdt0 @ SV280 @ SY212 )
               != xb )
              | ~ ( aElement0 @ SY212 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2246]) ).

thf(2270,plain,
    ! [SV281: $i] :
      ( ( ( ~ ( aElement0 @ SV281 )
          | ! [SY213: $i] :
              ( ( ( sdtasdt0 @ SV281 @ SY213 )
               != xa )
              | ~ ( aElement0 @ SY213 ) )
          | ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2247]) ).

thf(2271,plain,
    ! [SV282: $i] :
      ( ( ( ~ ( aElement0 @ SV282 )
          | ~ ( doDivides0 @ SV282 @ xa )
          | ~ ( doDivides0 @ SV282 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2248]) ).

thf(2272,plain,
    ! [SV266: $i] :
      ( ( ( ( sdtasdt0 @ SV266 @ ( sK15_W1 @ SV266 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2249]) ).

thf(2273,plain,
    ! [SV266: $i] :
      ( ( ( aElement0 @ ( sK15_W1 @ SV266 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV266 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV266 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2250]) ).

thf(2274,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( ( sdtasdt0 @ SV271 @ SV287 )
           != xb )
          | ~ ( aElement0 @ SV287 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2251]) ).

thf(2275,plain,
    ! [SV272: $i] :
      ( ( ( doDivides0 @ SV272 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2252]) ).

thf(2276,plain,
    ! [SV273: $i] :
      ( ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ! [SY206: $i] :
              ( ( ( sdtasdt0 @ SV273 @ SY206 )
               != xa )
              | ~ ( aElement0 @ SY206 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2253]) ).

thf(2277,plain,
    ! [SV274: $i] :
      ( ( ( aElement0 @ SV274 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV274 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV274 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2254]) ).

thf(2278,plain,
    ! [SV283: $i] :
      ( ( ( ~ ( aElement0 @ SV283 )
          | ! [SY214: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY214 )
               != xa )
              | ~ ( aElement0 @ SY214 ) )
          | ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2255]) ).

thf(2279,plain,
    ! [SV284: $i] :
      ( ( ( ~ ( aElement0 @ SV284 )
          | ~ ( doDivides0 @ SV284 @ xa )
          | ! [SY216: $i] :
              ( ( ( sdtasdt0 @ SV284 @ SY216 )
               != xb )
              | ~ ( aElement0 @ SY216 ) ) )
        = $true )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2256]) ).

thf(2280,plain,
    ! [SV285: $i] :
      ( ( ( ~ ( aElement0 @ SV285 )
          | ! [SY217: $i] :
              ( ( ( sdtasdt0 @ SV285 @ SY217 )
               != xa )
              | ~ ( aElement0 @ SY217 ) )
          | ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2257]) ).

thf(2281,plain,
    ! [SV286: $i] :
      ( ( ( ~ ( aElement0 @ SV286 )
          | ~ ( doDivides0 @ SV286 @ xa )
          | ~ ( doDivides0 @ SV286 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2258]) ).

thf(2282,plain,
    ! [SV288: $i,SV275: $i] :
      ( ( ( ( ( sdtasdt0 @ SV275 @ SV288 )
           != xb )
          | ~ ( aElement0 @ SV288 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV275 @ xa )
        = $false )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2259]) ).

thf(2283,plain,
    ! [SV276: $i] :
      ( ( ( doDivides0 @ SV276 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV276 @ xa )
        = $false )
      | ( ( doDivides0 @ SV276 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2260]) ).

thf(2284,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2261]) ).

thf(2285,plain,
    ( ( ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2261]) ).

thf(2286,plain,
    ! [SV277: $i] :
      ( ( ( aElementOf0 @ SV277 @ xI )
        = $false )
      | ( ( ! [SY208: $i] :
              ( ~ ( aElementOf0 @ SY208 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SY208 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2264]) ).

thf(2287,plain,
    ! [SV278: $i] :
      ( ( ( aElementOf0 @ SV278 @ xI )
        = $false )
      | ( ( ! [SY209: $i] :
              ( ~ ( aElement0 @ SY209 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY209 @ SV278 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2265]) ).

thf(2288,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( ( sdtasdt0 @ SV269 @ SV289 )
           != xa )
          | ~ ( aElement0 @ SV289 ) )
        = $true )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2266]) ).

thf(2289,plain,
    ! [SV270: $i] :
      ( ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV270 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2267]) ).

thf(2290,plain,
    ! [SV279: $i] :
      ( ( ( ~ ( aElement0 @ SV279 )
          | ! [SY210: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY210 )
               != xa )
              | ~ ( aElement0 @ SY210 ) ) )
        = $true )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2268]) ).

thf(2291,plain,
    ! [SV280: $i] :
      ( ( ( ~ ( aElement0 @ SV280 )
          | ~ ( doDivides0 @ SV280 @ xa ) )
        = $true )
      | ( ( ! [SY212: $i] :
              ( ( ( sdtasdt0 @ SV280 @ SY212 )
               != xb )
              | ~ ( aElement0 @ SY212 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2269]) ).

thf(2292,plain,
    ! [SV281: $i] :
      ( ( ( ~ ( aElement0 @ SV281 )
          | ! [SY213: $i] :
              ( ( ( sdtasdt0 @ SV281 @ SY213 )
               != xa )
              | ~ ( aElement0 @ SY213 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2270]) ).

thf(2293,plain,
    ! [SV282: $i] :
      ( ( ( ~ ( aElement0 @ SV282 )
          | ~ ( doDivides0 @ SV282 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV282 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2271]) ).

thf(2294,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( ( sdtasdt0 @ SV271 @ SV287 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV287 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2274]) ).

thf(2295,plain,
    ! [SV272: $i] :
      ( ( ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
           != xc )
          | ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( doDivides0 @ SV272 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2275]) ).

thf(2296,plain,
    ! [SV290: $i,SV273: $i] :
      ( ( ( ( ( sdtasdt0 @ SV273 @ SV290 )
           != xa )
          | ~ ( aElement0 @ SV290 ) )
        = $true )
      | ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2276]) ).

thf(2297,plain,
    ! [SV274: $i] :
      ( ( ( doDivides0 @ SV274 @ xa )
        = $false )
      | ( ( aElement0 @ SV274 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV274 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2277]) ).

thf(2298,plain,
    ! [SV283: $i] :
      ( ( ( ~ ( aElement0 @ SV283 )
          | ! [SY214: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY214 )
               != xa )
              | ~ ( aElement0 @ SY214 ) ) )
        = $true )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2278]) ).

thf(2299,plain,
    ! [SV284: $i] :
      ( ( ( ~ ( aElement0 @ SV284 )
          | ~ ( doDivides0 @ SV284 @ xa ) )
        = $true )
      | ( ( ! [SY216: $i] :
              ( ( ( sdtasdt0 @ SV284 @ SY216 )
               != xb )
              | ~ ( aElement0 @ SY216 ) ) )
        = $true )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2279]) ).

thf(2300,plain,
    ! [SV285: $i] :
      ( ( ( ~ ( aElement0 @ SV285 )
          | ! [SY217: $i] :
              ( ( ( sdtasdt0 @ SV285 @ SY217 )
               != xa )
              | ~ ( aElement0 @ SY217 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2280]) ).

thf(2301,plain,
    ! [SV286: $i] :
      ( ( ( ~ ( aElement0 @ SV286 )
          | ~ ( doDivides0 @ SV286 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV286 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2281]) ).

thf(2302,plain,
    ! [SV288: $i,SV275: $i] :
      ( ( ( ( ( sdtasdt0 @ SV275 @ SV288 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV288 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV275 @ xa )
        = $false )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2282]) ).

thf(2303,plain,
    ( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                 != xa )
                | ~ ( aElement0 @ sK12_W0 ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2284]) ).

thf(2304,plain,
    ( ( doDivides0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2285]) ).

thf(2305,plain,
    ! [SV277: $i,SV291: $i] :
      ( ( ( ~ ( aElementOf0 @ SV291 @ xI )
          | ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SV291 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV277 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2286]) ).

thf(2306,plain,
    ! [SV278: $i,SV292: $i] :
      ( ( ( ~ ( aElement0 @ SV292 )
          | ( aElementOf0 @ ( sdtasdt0 @ SV292 @ SV278 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV278 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2287]) ).

thf(2307,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( ( sdtasdt0 @ SV269 @ SV289 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV289 ) )
        = $true )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2288]) ).

thf(2308,plain,
    ! [SV270: $i] :
      ( ( ( aDivisorOf0 @ SV270 @ xb )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2289]) ).

thf(2309,plain,
    ! [SV279: $i] :
      ( ( ( ~ ( aElement0 @ SV279 ) )
        = $true )
      | ( ( ! [SY210: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY210 )
               != xa )
              | ~ ( aElement0 @ SY210 ) ) )
        = $true )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2290]) ).

thf(2310,plain,
    ! [SV280: $i] :
      ( ( ( ~ ( aElement0 @ SV280 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV280 @ xa ) )
        = $true )
      | ( ( ! [SY212: $i] :
              ( ( ( sdtasdt0 @ SV280 @ SY212 )
               != xb )
              | ~ ( aElement0 @ SY212 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2291]) ).

thf(2311,plain,
    ! [SV281: $i] :
      ( ( ( ~ ( aElement0 @ SV281 ) )
        = $true )
      | ( ( ! [SY213: $i] :
              ( ( ( sdtasdt0 @ SV281 @ SY213 )
               != xa )
              | ~ ( aElement0 @ SY213 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2292]) ).

thf(2312,plain,
    ! [SV282: $i] :
      ( ( ( ~ ( aElement0 @ SV282 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV282 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV282 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2293]) ).

thf(2313,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV287 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2294]) ).

thf(2314,plain,
    ! [SV272: $i] :
      ( ( ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( doDivides0 @ SV272 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2295]) ).

thf(2315,plain,
    ! [SV272: $i] :
      ( ( ( ~ ( aElement0 @ ( sK13_W1 @ SV272 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( doDivides0 @ SV272 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2295]) ).

thf(2316,plain,
    ! [SV290: $i,SV273: $i] :
      ( ( ( ( ( sdtasdt0 @ SV273 @ SV290 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV290 ) )
        = $true )
      | ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2296]) ).

thf(2317,plain,
    ! [SV274: $i] :
      ( ( ( aDivisorOf0 @ SV274 @ xb )
        = $false )
      | ( ( aElement0 @ SV274 )
        = $false )
      | ( ( doDivides0 @ SV274 @ xa )
        = $false )
      | ( ( doDivides0 @ SV274 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2297]) ).

thf(2318,plain,
    ! [SV283: $i] :
      ( ( ( ~ ( aElement0 @ SV283 ) )
        = $true )
      | ( ( ! [SY214: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY214 )
               != xa )
              | ~ ( aElement0 @ SY214 ) ) )
        = $true )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2298]) ).

thf(2319,plain,
    ! [SV284: $i] :
      ( ( ( ~ ( aElement0 @ SV284 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV284 @ xa ) )
        = $true )
      | ( ( ! [SY216: $i] :
              ( ( ( sdtasdt0 @ SV284 @ SY216 )
               != xb )
              | ~ ( aElement0 @ SY216 ) ) )
        = $true )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2299]) ).

thf(2320,plain,
    ! [SV285: $i] :
      ( ( ( ~ ( aElement0 @ SV285 ) )
        = $true )
      | ( ( ! [SY217: $i] :
              ( ( ( sdtasdt0 @ SV285 @ SY217 )
               != xa )
              | ~ ( aElement0 @ SY217 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2300]) ).

thf(2321,plain,
    ! [SV286: $i] :
      ( ( ( ~ ( aElement0 @ SV286 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV286 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV286 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2301]) ).

thf(2322,plain,
    ! [SV288: $i,SV275: $i] :
      ( ( ( ( sdtasdt0 @ SV275 @ SV288 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV288 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV275 @ xa )
        = $false )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2302]) ).

thf(2323,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2303]) ).

thf(2324,plain,
    ! [SV277: $i,SV291: $i] :
      ( ( ( ~ ( aElementOf0 @ SV291 @ xI ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SV291 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV277 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2305]) ).

thf(2325,plain,
    ! [SV278: $i,SV292: $i] :
      ( ( ( ~ ( aElement0 @ SV292 ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV292 @ SV278 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV278 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2306]) ).

thf(2326,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV289 ) )
        = $true )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2307]) ).

thf(2327,plain,
    ! [SV270: $i] :
      ( ( ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
           != xc )
          | ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) )
        = $false )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( aDivisorOf0 @ SV270 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2308]) ).

thf(2328,plain,
    ! [SV279: $i] :
      ( ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ! [SY210: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY210 )
               != xa )
              | ~ ( aElement0 @ SY210 ) ) )
        = $true )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2309]) ).

thf(2329,plain,
    ! [SV280: $i] :
      ( ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV280 @ xa ) )
        = $true )
      | ( ( ! [SY212: $i] :
              ( ( ( sdtasdt0 @ SV280 @ SY212 )
               != xb )
              | ~ ( aElement0 @ SY212 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2310]) ).

thf(2330,plain,
    ! [SV281: $i] :
      ( ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ! [SY213: $i] :
              ( ( ( sdtasdt0 @ SV281 @ SY213 )
               != xa )
              | ~ ( aElement0 @ SY213 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2311]) ).

thf(2331,plain,
    ! [SV282: $i] :
      ( ( ( aElement0 @ SV282 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV282 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV282 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2312]) ).

thf(2332,plain,
    ! [SV271: $i,SV287: $i] :
      ( ( ( aElement0 @ SV287 )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2313]) ).

thf(2333,plain,
    ! [SV272: $i] :
      ( ( ( ( sdtasdt0 @ SV272 @ ( sK13_W1 @ SV272 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( doDivides0 @ SV272 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2314]) ).

thf(2334,plain,
    ! [SV272: $i] :
      ( ( ( aElement0 @ ( sK13_W1 @ SV272 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV272 @ xa )
        = $false )
      | ( ( doDivides0 @ SV272 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2315]) ).

thf(2335,plain,
    ! [SV290: $i,SV273: $i] :
      ( ( ( ( sdtasdt0 @ SV273 @ SV290 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV290 ) )
        = $true )
      | ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2316]) ).

thf(2336,plain,
    ! [SV283: $i] :
      ( ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ! [SY214: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY214 )
               != xa )
              | ~ ( aElement0 @ SY214 ) ) )
        = $true )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2318]) ).

thf(2337,plain,
    ! [SV284: $i] :
      ( ( ( aElement0 @ SV284 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV284 @ xa ) )
        = $true )
      | ( ( ! [SY216: $i] :
              ( ( ( sdtasdt0 @ SV284 @ SY216 )
               != xb )
              | ~ ( aElement0 @ SY216 ) ) )
        = $true )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2319]) ).

thf(2338,plain,
    ! [SV285: $i] :
      ( ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ! [SY217: $i] :
              ( ( ( sdtasdt0 @ SV285 @ SY217 )
               != xa )
              | ~ ( aElement0 @ SY217 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2320]) ).

thf(2339,plain,
    ! [SV286: $i] :
      ( ( ( aElement0 @ SV286 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV286 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV286 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2321]) ).

thf(2340,plain,
    ! [SV275: $i,SV288: $i] :
      ( ( ( aElement0 @ SV288 )
        = $false )
      | ( ( ( sdtasdt0 @ SV275 @ SV288 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV275 @ xa )
        = $false )
      | ( ( doDivides0 @ SV275 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2322]) ).

thf(2341,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2323]) ).

thf(2342,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2323]) ).

thf(2343,plain,
    ! [SV277: $i,SV291: $i] :
      ( ( ( aElementOf0 @ SV291 @ xI )
        = $false )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV277 @ SV291 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV277 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2324]) ).

thf(2344,plain,
    ! [SV278: $i,SV292: $i] :
      ( ( ( aElement0 @ SV292 )
        = $false )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV292 @ SV278 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV278 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2325]) ).

thf(2345,plain,
    ! [SV269: $i,SV289: $i] :
      ( ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV269 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2326]) ).

thf(2346,plain,
    ! [SV270: $i] :
      ( ( ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( aDivisorOf0 @ SV270 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2327]) ).

thf(2347,plain,
    ! [SV270: $i] :
      ( ( ( ~ ( aElement0 @ ( sK20_W1 @ SV270 ) ) )
        = $false )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( aDivisorOf0 @ SV270 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2327]) ).

thf(2348,plain,
    ! [SV293: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ SV293 )
           != xa )
          | ~ ( aElement0 @ SV293 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2328]) ).

thf(2349,plain,
    ! [SV280: $i] :
      ( ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ! [SY212: $i] :
              ( ( ( sdtasdt0 @ SV280 @ SY212 )
               != xb )
              | ~ ( aElement0 @ SY212 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2329]) ).

thf(2350,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( ( sdtasdt0 @ SV281 @ SV294 )
           != xa )
          | ~ ( aElement0 @ SV294 ) )
        = $true )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2330]) ).

thf(2351,plain,
    ! [SV282: $i] :
      ( ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV282 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2331]) ).

thf(2352,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
           != xc )
          | ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV287 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2332]) ).

thf(2353,plain,
    ! [SV273: $i,SV290: $i] :
      ( ( ( aElement0 @ SV290 )
        = $false )
      | ( ( ( sdtasdt0 @ SV273 @ SV290 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV273 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2335]) ).

thf(2354,plain,
    ! [SV295: $i,SV283: $i] :
      ( ( ( ( ( sdtasdt0 @ SV283 @ SV295 )
           != xa )
          | ~ ( aElement0 @ SV295 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2336]) ).

thf(2355,plain,
    ! [SV284: $i] :
      ( ( ( doDivides0 @ SV284 @ xa )
        = $false )
      | ( ( aElement0 @ SV284 )
        = $false )
      | ( ( ! [SY216: $i] :
              ( ( ( sdtasdt0 @ SV284 @ SY216 )
               != xb )
              | ~ ( aElement0 @ SY216 ) ) )
        = $true )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2337]) ).

thf(2356,plain,
    ! [SV296: $i,SV285: $i] :
      ( ( ( ( ( sdtasdt0 @ SV285 @ SV296 )
           != xa )
          | ~ ( aElement0 @ SV296 ) )
        = $true )
      | ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2338]) ).

thf(2357,plain,
    ! [SV286: $i] :
      ( ( ( doDivides0 @ SV286 @ xa )
        = $false )
      | ( ( aElement0 @ SV286 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV286 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2339]) ).

thf(2358,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
           != xa )
          | ~ ( aElement0 @ sK12_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2341]) ).

thf(2359,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2342]) ).

thf(2360,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( aDivisorOf0 @ SV269 @ xb )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2345]) ).

thf(2361,plain,
    ! [SV270: $i] :
      ( ( ( ( sdtasdt0 @ SV270 @ ( sK20_W1 @ SV270 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( aDivisorOf0 @ SV270 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2346]) ).

thf(2362,plain,
    ! [SV270: $i] :
      ( ( ( aElement0 @ ( sK20_W1 @ SV270 ) )
        = $true )
      | ( ( doDivides0 @ SV270 @ xa )
        = $false )
      | ( ( aElement0 @ SV270 )
        = $false )
      | ( ( aDivisorOf0 @ SV270 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2347]) ).

thf(2363,plain,
    ! [SV293: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ SV293 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV293 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2348]) ).

thf(2364,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( ( sdtasdt0 @ SV280 @ SV297 )
           != xb )
          | ~ ( aElement0 @ SV297 ) )
        = $true )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2349]) ).

thf(2365,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( ( sdtasdt0 @ SV281 @ SV294 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV294 ) )
        = $true )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2350]) ).

thf(2366,plain,
    ! [SV282: $i] :
      ( ( ( doDivides0 @ SV282 @ xb )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2351]) ).

thf(2367,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV287 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2352]) ).

thf(2368,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ~ ( aElement0 @ ( sK14_W1 @ SV271 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV287 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2352]) ).

thf(2369,plain,
    ! [SV290: $i,SV273: $i] :
      ( ( ( aDivisorOf0 @ SV273 @ xb )
        = $false )
      | ( ( aElement0 @ SV273 )
        = $false )
      | ( ( ( sdtasdt0 @ SV273 @ SV290 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV290 )
        = $false )
      | ( ( doDivides0 @ SV273 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2353]) ).

thf(2370,plain,
    ! [SV295: $i,SV283: $i] :
      ( ( ( ( ( sdtasdt0 @ SV283 @ SV295 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV295 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2354]) ).

thf(2371,plain,
    ! [SV298: $i,SV284: $i] :
      ( ( ( ( ( sdtasdt0 @ SV284 @ SV298 )
           != xb )
          | ~ ( aElement0 @ SV298 ) )
        = $true )
      | ( ( aElement0 @ SV284 )
        = $false )
      | ( ( doDivides0 @ SV284 @ xa )
        = $false )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2355]) ).

thf(2372,plain,
    ! [SV296: $i,SV285: $i] :
      ( ( ( ( ( sdtasdt0 @ SV285 @ SV296 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV296 ) )
        = $true )
      | ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2356]) ).

thf(2373,plain,
    ! [SV286: $i] :
      ( ( ( doDivides0 @ SV286 @ xb )
        = $false )
      | ( ( aElement0 @ SV286 )
        = $false )
      | ( ( doDivides0 @ SV286 @ xa )
        = $false )
      | ( ( doDivides0 @ SV286 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2357]) ).

thf(2374,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa )
      | ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2358]) ).

thf(2375,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
           != xc )
          | ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) )
        = $false )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( aDivisorOf0 @ SV269 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2360]) ).

thf(2376,plain,
    ! [SV293: $i,SV279: $i] :
      ( ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV293 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2363]) ).

thf(2377,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( ( sdtasdt0 @ SV280 @ SV297 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV297 ) )
        = $true )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2364]) ).

thf(2378,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV294 ) )
        = $true )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2365]) ).

thf(2379,plain,
    ! [SV282: $i] :
      ( ( ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
           != xc )
          | ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) )
        = $false )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2366]) ).

thf(2380,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( ( sdtasdt0 @ SV271 @ ( sK14_W1 @ SV271 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV287 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2367]) ).

thf(2381,plain,
    ! [SV287: $i,SV271: $i] :
      ( ( ( aElement0 @ ( sK14_W1 @ SV271 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV271 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV271 @ SV287 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV287 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2368]) ).

thf(2382,plain,
    ! [SV295: $i,SV283: $i] :
      ( ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV295 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2370]) ).

thf(2383,plain,
    ! [SV298: $i,SV284: $i] :
      ( ( ( ( ( sdtasdt0 @ SV284 @ SV298 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV298 ) )
        = $true )
      | ( ( aElement0 @ SV284 )
        = $false )
      | ( ( doDivides0 @ SV284 @ xa )
        = $false )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2371]) ).

thf(2384,plain,
    ! [SV296: $i,SV285: $i] :
      ( ( ( ( sdtasdt0 @ SV285 @ SV296 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV296 ) )
        = $true )
      | ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2372]) ).

thf(2385,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2374]) ).

thf(2386,plain,
    ( ( ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2374]) ).

thf(2387,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( aDivisorOf0 @ SV269 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2375]) ).

thf(2388,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ~ ( aElement0 @ ( sK21_W1 @ SV269 ) ) )
        = $false )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( aDivisorOf0 @ SV269 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2375]) ).

thf(2389,plain,
    ! [SV279: $i,SV293: $i] :
      ( ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ! [SY211: $i] :
              ( ( ( sdtasdt0 @ SV279 @ SY211 )
               != xb )
              | ~ ( aElement0 @ SY211 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2376]) ).

thf(2390,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV297 ) )
        = $true )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2377]) ).

thf(2391,plain,
    ! [SV281: $i,SV294: $i] :
      ( ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV281 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2378]) ).

thf(2392,plain,
    ! [SV282: $i] :
      ( ( ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2379]) ).

thf(2393,plain,
    ! [SV282: $i] :
      ( ( ( ~ ( aElement0 @ ( sK16_W1 @ SV282 ) ) )
        = $false )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2379]) ).

thf(2394,plain,
    ! [SV283: $i,SV295: $i] :
      ( ( ( aElement0 @ SV295 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ! [SY215: $i] :
              ( ( ( sdtasdt0 @ SV283 @ SY215 )
               != xb )
              | ~ ( aElement0 @ SY215 ) ) )
        = $true )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2382]) ).

thf(2395,plain,
    ! [SV298: $i,SV284: $i] :
      ( ( ( ( sdtasdt0 @ SV284 @ SV298 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV298 ) )
        = $true )
      | ( ( aElement0 @ SV284 )
        = $false )
      | ( ( doDivides0 @ SV284 @ xa )
        = $false )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2383]) ).

thf(2396,plain,
    ! [SV285: $i,SV296: $i] :
      ( ( ( aElement0 @ SV296 )
        = $false )
      | ( ( ( sdtasdt0 @ SV285 @ SV296 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV285 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2384]) ).

thf(2397,plain,
    ( ( ( sdtasdt0 @ xc @ sK12_W0 )
      = xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2385]) ).

thf(2398,plain,
    ( ( aElement0 @ sK12_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2386]) ).

thf(2399,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( ( sdtasdt0 @ SV269 @ ( sK21_W1 @ SV269 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( aDivisorOf0 @ SV269 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2387]) ).

thf(2400,plain,
    ! [SV289: $i,SV269: $i] :
      ( ( ( aElement0 @ ( sK21_W1 @ SV269 ) )
        = $true )
      | ( ( aElement0 @ SV289 )
        = $false )
      | ( ( ( sdtasdt0 @ SV269 @ SV289 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV269 )
        = $false )
      | ( ( aDivisorOf0 @ SV269 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2388]) ).

thf(2401,plain,
    ! [SV293: $i,SV299: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ SV299 )
           != xb )
          | ~ ( aElement0 @ SV299 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2389]) ).

thf(2402,plain,
    ! [SV280: $i,SV297: $i] :
      ( ( ( aElement0 @ SV297 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2390]) ).

thf(2403,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( doDivides0 @ SV281 @ xb )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2391]) ).

thf(2404,plain,
    ! [SV282: $i] :
      ( ( ( ( sdtasdt0 @ SV282 @ ( sK16_W1 @ SV282 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2392]) ).

thf(2405,plain,
    ! [SV282: $i] :
      ( ( ( aElement0 @ ( sK16_W1 @ SV282 ) )
        = $true )
      | ( ( doDivides0 @ SV282 @ xa )
        = $false )
      | ( ( aElement0 @ SV282 )
        = $false )
      | ( ( doDivides0 @ SV282 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2393]) ).

thf(2406,plain,
    ! [SV295: $i,SV300: $i,SV283: $i] :
      ( ( ( ( ( sdtasdt0 @ SV283 @ SV300 )
           != xb )
          | ~ ( aElement0 @ SV300 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV295 )
        = $false )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2394]) ).

thf(2407,plain,
    ! [SV284: $i,SV298: $i] :
      ( ( ( aElement0 @ SV298 )
        = $false )
      | ( ( ( sdtasdt0 @ SV284 @ SV298 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV284 )
        = $false )
      | ( ( doDivides0 @ SV284 @ xa )
        = $false )
      | ( ( doDivides0 @ SV284 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2395]) ).

thf(2408,plain,
    ! [SV296: $i,SV285: $i] :
      ( ( ( doDivides0 @ SV285 @ xb )
        = $false )
      | ( ( aElement0 @ SV285 )
        = $false )
      | ( ( ( sdtasdt0 @ SV285 @ SV296 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV296 )
        = $false )
      | ( ( doDivides0 @ SV285 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2396]) ).

thf(2409,plain,
    ! [SV293: $i,SV299: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ SV299 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV299 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2401]) ).

thf(2410,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
           != xc )
          | ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV297 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2402]) ).

thf(2411,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
           != xc )
          | ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) )
        = $false )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( doDivides0 @ SV281 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2403]) ).

thf(2412,plain,
    ! [SV295: $i,SV300: $i,SV283: $i] :
      ( ( ( ( ( sdtasdt0 @ SV283 @ SV300 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV300 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV295 )
        = $false )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2406]) ).

thf(2413,plain,
    ! [SV293: $i,SV299: $i,SV279: $i] :
      ( ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV299 ) )
        = $true )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2409]) ).

thf(2414,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV297 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2410]) ).

thf(2415,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ~ ( aElement0 @ ( sK18_W1 @ SV280 ) ) )
        = $false )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV297 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2410]) ).

thf(2416,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( doDivides0 @ SV281 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2411]) ).

thf(2417,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ~ ( aElement0 @ ( sK17_W1 @ SV281 ) ) )
        = $false )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( doDivides0 @ SV281 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2411]) ).

thf(2418,plain,
    ! [SV295: $i,SV300: $i,SV283: $i] :
      ( ( ( ( sdtasdt0 @ SV283 @ SV300 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV300 ) )
        = $true )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV295 )
        = $false )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2412]) ).

thf(2419,plain,
    ! [SV293: $i,SV279: $i,SV299: $i] :
      ( ( ( aElement0 @ SV299 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2413]) ).

thf(2420,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( ( sdtasdt0 @ SV280 @ ( sK18_W1 @ SV280 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV297 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2414]) ).

thf(2421,plain,
    ! [SV297: $i,SV280: $i] :
      ( ( ( aElement0 @ ( sK18_W1 @ SV280 ) )
        = $true )
      | ( ( doDivides0 @ SV280 @ xa )
        = $false )
      | ( ( aElement0 @ SV280 )
        = $false )
      | ( ( ( sdtasdt0 @ SV280 @ SV297 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV297 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2415]) ).

thf(2422,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( ( sdtasdt0 @ SV281 @ ( sK17_W1 @ SV281 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( doDivides0 @ SV281 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2416]) ).

thf(2423,plain,
    ! [SV294: $i,SV281: $i] :
      ( ( ( aElement0 @ ( sK17_W1 @ SV281 ) )
        = $true )
      | ( ( aElement0 @ SV294 )
        = $false )
      | ( ( ( sdtasdt0 @ SV281 @ SV294 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV281 )
        = $false )
      | ( ( doDivides0 @ SV281 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2417]) ).

thf(2424,plain,
    ! [SV295: $i,SV283: $i,SV300: $i] :
      ( ( ( aElement0 @ SV300 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV300 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV283 )
        = $false )
      | ( ( ( sdtasdt0 @ SV283 @ SV295 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV295 )
        = $false )
      | ( ( doDivides0 @ SV283 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2418]) ).

thf(2425,plain,
    ! [SV299: $i,SV293: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
           != xc )
          | ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV299 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2419]) ).

thf(2426,plain,
    ! [SV299: $i,SV293: $i,SV279: $i] :
      ( ( ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV299 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2425]) ).

thf(2427,plain,
    ! [SV299: $i,SV293: $i,SV279: $i] :
      ( ( ( ~ ( aElement0 @ ( sK19_W1 @ SV279 ) ) )
        = $false )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV299 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2425]) ).

thf(2428,plain,
    ! [SV299: $i,SV293: $i,SV279: $i] :
      ( ( ( ( sdtasdt0 @ SV279 @ ( sK19_W1 @ SV279 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV299 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2426]) ).

thf(2429,plain,
    ! [SV299: $i,SV293: $i,SV279: $i] :
      ( ( ( aElement0 @ ( sK19_W1 @ SV279 ) )
        = $true )
      | ( ( aElement0 @ SV293 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV293 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV279 )
        = $false )
      | ( ( ( sdtasdt0 @ SV279 @ SV299 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV299 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2427]) ).

thf(2430,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[1663,2429,2428,2424,2423,2422,2421,2420,2408,2407,2405,2404,2400,2399,2398,2397,2381,2380,2373,2369,2362,2361,2359,2344,2343,2340,2334,2333,2317,2304,2283,2273,2272,2263,2262,2238,2237,2236,2215,2214,2213,2205,2184,2161,2159,2158,2157,2141,2137,2136,2135,2134,2133,2132,2088,2087,2086,2063,2062,2061,2055,2036,2019,2006,1990,1989,1980,1951,1936,1935,1934,1909,1902,1901,1900,1899,1897,1896,1895,1894,1892,1891,1884,1883,1882,1881,1878,1876,1875,1874,1826,1822,1811,1802,1801,1795,1788,1775,1774,1720,1716,1715,1706,1664]) ).

thf(2431,plain,
    ( ( ( aElement0 @ xa )
      & ( aElement0 @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(2432,plain,
    ( ( ( xa != sz00 )
      | ( xb != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(2433,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK21_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK21_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK20_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK20_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK19_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK19_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK18_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK18_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK17_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK17_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK16_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK16_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK15_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK15_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( ( ( sdtasdt0 @ W0 @ ( sK14_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK14_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( ( ( sdtasdt0 @ W0 @ ( sK13_W1 @ W0 ) )
              = xc )
            & ( aElement0 @ ( sK13_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xa )
              | ~ ( aElement0 @ W1 ) )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( doDivides0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( aDivisorOf0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ! [W1: $i] :
              ( ( ( sdtasdt0 @ W0 @ W1 )
               != xb )
              | ~ ( aElement0 @ W1 ) )
          | ( doDivides0 @ W0 @ xc ) )
      & ! [W0: $i] :
          ( ~ ( aDivisorOf0 @ W0 @ xa )
          | ~ ( doDivides0 @ W0 @ xb )
          | ( doDivides0 @ W0 @ xc ) )
      & ( ( sdtasdt0 @ xc @ sK12_W0 )
        = xa )
      & ( aElement0 @ sK12_W0 )
      & ( aElement0 @ xc )
      & ( doDivides0 @ xc @ xa )
      & ( aDivisorOf0 @ xc @ xa )
      & ( aElement0 @ xc )
      & ( ( sdtasdt0 @ xc @ sK11_W0 )
        = xb )
      & ( aElement0 @ sK11_W0 )
      & ( doDivides0 @ xc @ xb )
      & ( aDivisorOf0 @ xc @ xb )
      & ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(2434,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElementOf0 @ W1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ W2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ W1 @ W2 )
               != W0 ) )
          | ( aElementOf0 @ W0 @ xI ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ( ( aElementOf0 @ ( sK9_W1 @ W0 ) @ ( slsdtgt0 @ xa ) )
            & ( aElementOf0 @ ( sK10_SY73 @ W0 ) @ ( slsdtgt0 @ xb ) )
            & ( ( sdtpldt0 @ ( sK9_W1 @ W0 ) @ ( sK10_SY73 @ W0 ) )
              = W0 ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xb @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xb ) )
          | ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK8_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ! [W1: $i] :
              ( ( ( sdtasdt0 @ xa @ W1 )
               != W0 )
              | ~ ( aElement0 @ W1 ) )
          | ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ ( slsdtgt0 @ xa ) )
          | ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ W0 ) )
              = W0 )
            & ( aElement0 @ ( sK7_W1 @ W0 ) ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ W0 @ W1 ) @ xI ) ) )
      & ! [W0: $i] :
          ( ~ ( aElementOf0 @ W0 @ xI )
          | ! [W1: $i] :
              ( ~ ( aElement0 @ W1 )
              | ( aElementOf0 @ ( sdtasdt0 @ W1 @ W0 ) @ xI ) ) )
      & ( aSet0 @ xI )
      & ( aIdeal0 @ xI )
      & ( xI
        = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(2435,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(2436,plain,
    ( ( aElement0 @ sz00 )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(2437,plain,
    ( ( aElement0 @ sz10 )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(2438,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aElement0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(2439,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(2440,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( aElement0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(2441,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(2442,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
            = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(2443,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtpldt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(2444,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(2445,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
            = ( sdtasdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(2446,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ~ ( aElement0 @ W2 )
          | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
            = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(2447,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz10 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( W0
            = ( sdtasdt0 @ sz10 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(2448,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aElement0 @ W0 )
              | ~ ( aElement0 @ W1 )
              | ~ ( aElement0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(2449,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
            = ( smndt0 @ W0 ) ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( smndt0 @ W0 )
            = ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(2450,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz00 )
            = sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(2451,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W1 )
           != sz00 )
          | ( W0 = sz00 )
          | ( W1 = sz00 ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(2452,plain,
    ( ( ( sz10 != sz00 ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(2453,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(2454,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aSet0 @ W0 )
          | ! [W1: $i] :
              ( ~ ( aElementOf0 @ W1 @ W0 )
              | ( aElement0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(2455,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aSet0 @ W0 )
          | ~ ( aSet0 @ W1 )
          | ( ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W0 )
            & ~ ( aElementOf0 @ ( sK6_W2 @ W1 @ W0 ) @ W1 ) )
          | ( ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W1 )
            & ~ ( aElementOf0 @ ( sK5_W2 @ W1 @ W0 ) @ W0 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(2456,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtpldt1 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(2457,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( aIdeal0 @ ( sdtasasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(2458,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aIdeal0 @ W0 )
          | ~ ( aIdeal0 @ W1 )
          | ( ( aElement0 @ ( sK4_W2 @ W1 @ W0 ) )
            & ~ ( aElementOf0 @ ( sK4_W2 @ W1 @ W0 ) @ ( sdtpldt1 @ W0 @ W1 ) ) )
          | ! [W2: $i,W3: $i] :
              ( ~ ( aElement0 @ W2 )
              | ~ ( aElement0 @ W3 )
              | ( ( aElement0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W2 @ W0 )
                & ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ W3 @ W2 @ W1 @ W0 ) @ W3 @ W1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(2459,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(2460,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ( aNaturalNumber0 @ ( sbrdtbr0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(2461,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(2462,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( W1 = sz00 )
          | ~ ( aElement0 @ W0 )
          | ~ ( aElement0 @ W1 )
          | ( ( aElement0 @ ( sK1_W2 @ W1 @ W0 ) )
            & ( aElement0 @ ( sK2_SY72 @ W1 @ W0 ) )
            & ( W0
              = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ W1 @ W0 ) @ W1 ) @ ( sK2_SY72 @ W1 @ W0 ) ) )
            & ( ( ( sK2_SY72 @ W1 @ W0 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ W1 @ W0 ) ) @ ( sbrdtbr0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(2463,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aElement0 @ W0 )
          | ( aIdeal0 @ ( slsdtgt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(2464,plain,
    ( ( ! [W0: $i] :
          ( ( ( sdtasdt0 @ xb @ W0 )
           != xb )
          | ~ ( aElement0 @ W0 ) )
      & ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(2465,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
                  = ( smndt0 @ SX0 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( smndt0 @ SX0 )
                  = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2449]) ).

thf(2466,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 = sz00 )
          | ~ ( aElement0 @ SX0 )
          | ~ ( aElement0 @ SX1 )
          | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SX1 @ SX0 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) )
                    | ( SX0
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SX1 @ SX0 ) @ SX1 ) @ ( sK2_SY72 @ SX1 @ SX0 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SX1 @ SX0 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SX1 @ SX0 ) ) @ ( sbrdtbr0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2462]) ).

thf(2467,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i,SX2: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                                | ( ( sdtpldt0 @ SX1 @ SX2 )
                                 != SX0 ) )
                            | ( aElementOf0 @ SX0 @ xI ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                                 != SX0 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xb @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ xa @ SX1 )
                                             != SX0 )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                             != SX0 )
                                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                                    | ! [SX1: $i] :
                                                        ( ~ ( aElement0 @ SX1 )
                                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                        | ~ ( aSet0 @ xI ) )
                                  | ~ ( aIdeal0 @ xI ) ) ) ) )
          | ( xI
           != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2434]) ).

thf(2468,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2444]) ).

thf(2469,plain,
    ( ( ~ ( ~ ( aElement0 @ xa )
          | ~ ( aElement0 @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2431]) ).

thf(2470,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aIdeal0 @ SX0 )
          | ~ ( aIdeal0 @ SX1 )
          | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SX1 @ SX0 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SX1 @ SX0 ) @ ( sdtpldt1 @ SX0 @ SX1 ) ) )
          | ! [SX2: $i,SX3: $i] :
              ( ~ ( aElement0 @ SX2 )
              | ~ ( aElement0 @ SX3 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX0 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2458]) ).

thf(2471,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz10 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtasdt0 @ sz10 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2447]) ).

thf(2472,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz00 )
                  = sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( sz00
                  = ( sdtasdt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2450]) ).

thf(2473,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ sz00 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ( SX0
                  = ( sdtpldt0 @ sz00 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2443]) ).

thf(2474,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( sdtasdt0 @ xb @ SX0 )
                 != xb )
                | ~ ( aElement0 @ SX0 ) )
          | ~ ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2464]) ).

thf(2475,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aSet0 @ SX0 )
          | ~ ( aSet0 @ SX1 )
          | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SX1 @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SX1 @ SX0 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2455]) ).

thf(2476,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                         != xc )
                                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xb )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ( doDivides0 @ SX0 @ xc ) ) )
                                        | ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ! [SX1: $i] :
                                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                         != xa )
                                                        | ~ ( aElement0 @ SX1 ) )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aElement0 @ SX0 )
                                                    | ~ ( doDivides0 @ SX0 @ xa )
                                                    | ~ ( doDivides0 @ SX0 @ xb )
                                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                                 != xa )
                                                                | ~ ( aElement0 @ sK12_W0 ) )
                                                          | ~ ( aElement0 @ xc ) )
                                                    | ~ ( doDivides0 @ xc @ xa ) )
                                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                         != xb )
                                        | ~ ( aElement0 @ sK11_W0 ) ) )
                            | ~ ( doDivides0 @ xc @ xb ) )
                      | ~ ( aDivisorOf0 @ xc @ xb ) ) )
          | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2433]) ).

thf(2477,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( aElement0 @ SX1 )
                  | ~ ( aElement0 @ SX2 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SX1 @ SX2 ) @ SX0 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ ( sdtasdt0 @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2448]) ).

thf(2478,plain,
    ( ( ( ( xa != sz00 ) )
      = $true )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2432]) ).

thf(2479,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[2435]) ).

thf(2480,plain,
    ! [SV302: $i] :
      ( ( ~ ( aElement0 @ SV302 )
        | ( aElement0 @ ( smndt0 @ SV302 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2438]) ).

thf(2481,plain,
    ! [SV303: $i] :
      ( ( ! [SY218: $i] :
            ( ~ ( aElement0 @ SV303 )
            | ~ ( aElement0 @ SY218 )
            | ( aElement0 @ ( sdtpldt0 @ SV303 @ SY218 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2439]) ).

thf(2482,plain,
    ! [SV304: $i] :
      ( ( ! [SY219: $i] :
            ( ~ ( aElement0 @ SV304 )
            | ~ ( aElement0 @ SY219 )
            | ( aElement0 @ ( sdtasdt0 @ SV304 @ SY219 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2440]) ).

thf(2483,plain,
    ! [SV305: $i] :
      ( ( ! [SY220: $i] :
            ( ~ ( aElement0 @ SV305 )
            | ~ ( aElement0 @ SY220 )
            | ( ( sdtpldt0 @ SV305 @ SY220 )
              = ( sdtpldt0 @ SY220 @ SV305 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2441]) ).

thf(2484,plain,
    ! [SV306: $i] :
      ( ( ! [SY221: $i,SY222: $i] :
            ( ~ ( aElement0 @ SV306 )
            | ~ ( aElement0 @ SY221 )
            | ~ ( aElement0 @ SY222 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SY221 ) @ SY222 )
              = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SY221 @ SY222 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2442]) ).

thf(2485,plain,
    ! [SV307: $i] :
      ( ( ! [SY223: $i] :
            ( ~ ( aElement0 @ SV307 )
            | ~ ( aElement0 @ SY223 )
            | ( ( sdtasdt0 @ SV307 @ SY223 )
              = ( sdtasdt0 @ SY223 @ SV307 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2445]) ).

thf(2486,plain,
    ! [SV308: $i] :
      ( ( ! [SY224: $i,SY225: $i] :
            ( ~ ( aElement0 @ SV308 )
            | ~ ( aElement0 @ SY224 )
            | ~ ( aElement0 @ SY225 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SY224 ) @ SY225 )
              = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SY224 @ SY225 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2446]) ).

thf(2487,plain,
    ! [SV309: $i] :
      ( ( ! [SY226: $i] :
            ( ~ ( aElement0 @ SV309 )
            | ~ ( aElement0 @ SY226 )
            | ( ( sdtasdt0 @ SV309 @ SY226 )
             != sz00 )
            | ( SV309 = sz00 )
            | ( SY226 = sz00 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2451]) ).

thf(2488,plain,
    ( ( sz10 = sz00 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2452]) ).

thf(2489,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[2453]) ).

thf(2490,plain,
    ! [SV311: $i] :
      ( ( ~ ( aSet0 @ SV311 )
        | ! [SY227: $i] :
            ( ~ ( aElementOf0 @ SY227 @ SV311 )
            | ( aElement0 @ SY227 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2454]) ).

thf(2491,plain,
    ! [SV312: $i] :
      ( ( ! [SY228: $i] :
            ( ~ ( aIdeal0 @ SV312 )
            | ~ ( aIdeal0 @ SY228 )
            | ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SY228 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2456]) ).

thf(2492,plain,
    ! [SV313: $i] :
      ( ( ! [SY229: $i] :
            ( ~ ( aIdeal0 @ SV313 )
            | ~ ( aIdeal0 @ SY229 )
            | ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SY229 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2457]) ).

thf(2493,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[2459]) ).

thf(2494,plain,
    ! [SV315: $i] :
      ( ( ( SV315 = sz00 )
        | ~ ( aElement0 @ SV315 )
        | ( aNaturalNumber0 @ ( sbrdtbr0 @ SV315 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2460]) ).

thf(2495,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 )
        | ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2461]) ).

thf(2496,plain,
    ! [SV316: $i] :
      ( ( ~ ( aElement0 @ SV316 )
        | ( aIdeal0 @ ( slsdtgt0 @ SV316 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2463]) ).

thf(2497,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2465]) ).

thf(2498,plain,
    ! [SV317: $i] :
      ( ( ! [SY230: $i] :
            ( ( SY230 = sz00 )
            | ~ ( aElement0 @ SV317 )
            | ~ ( aElement0 @ SY230 )
            | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SY230 @ SV317 ) )
                            | ~ ( aElement0 @ ( sK2_SY72 @ SY230 @ SV317 ) ) )
                      | ( SV317
                       != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SY230 @ SV317 ) @ SY230 ) @ ( sK2_SY72 @ SY230 @ SV317 ) ) ) )
                | ~ ( ( ( sK2_SY72 @ SY230 @ SV317 )
                      = sz00 )
                    | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SY230 @ SV317 ) ) @ ( sbrdtbr0 @ SY230 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2466]) ).

thf(2499,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) )
      | ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2467]) ).

thf(2500,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2468]) ).

thf(2501,plain,
    ( ( ~ ( aElement0 @ xa )
      | ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2469]) ).

thf(2502,plain,
    ! [SV318: $i] :
      ( ( ! [SY231: $i] :
            ( ~ ( aIdeal0 @ SV318 )
            | ~ ( aIdeal0 @ SY231 )
            | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SY231 @ SV318 ) )
                | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SY231 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SY231 ) ) )
            | ! [SY232: $i,SY233: $i] :
                ( ~ ( aElement0 @ SY232 )
                | ~ ( aElement0 @ SY233 )
                | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY233 @ SY232 @ SY231 @ SV318 ) )
                          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY233 @ SY232 @ SY231 @ SV318 ) @ SY232 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY233 @ SY232 @ SY231 @ SV318 ) @ SY233 @ SY231 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2470]) ).

thf(2503,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2471]) ).

thf(2504,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2472]) ).

thf(2505,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2473]) ).

thf(2506,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xb @ SX0 )
             != xb )
            | ~ ( aElement0 @ SX0 ) )
      | ~ ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2474]) ).

thf(2507,plain,
    ! [SV319: $i] :
      ( ( ! [SY234: $i] :
            ( ~ ( aSet0 @ SV319 )
            | ~ ( aSet0 @ SY234 )
            | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SY234 @ SV319 ) @ SV319 )
                | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SY234 @ SV319 ) @ SY234 ) )
            | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SY234 @ SV319 ) @ SY234 )
                | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SY234 @ SV319 ) @ SV319 ) )
            | ( SV319 = SY234 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2475]) ).

thf(2508,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) )
      | ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2476]) ).

thf(2509,plain,
    ! [SV320: $i] :
      ( ( ~ ( ~ ! [SY235: $i,SY236: $i] :
                  ( ~ ( aElement0 @ SV320 )
                  | ~ ( aElement0 @ SY235 )
                  | ~ ( aElement0 @ SY236 )
                  | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SY235 @ SY236 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SY235 ) @ ( sdtasdt0 @ SV320 @ SY236 ) ) ) )
            | ~ ! [SY237: $i,SY238: $i] :
                  ( ~ ( aElement0 @ SV320 )
                  | ~ ( aElement0 @ SY237 )
                  | ~ ( aElement0 @ SY238 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SY237 @ SY238 ) @ SV320 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SY237 @ SV320 ) @ ( sdtasdt0 @ SY238 @ SV320 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2477]) ).

thf(2510,plain,
    ( ( ( xa = sz00 )
      = $false )
    | ( ( ( xb != sz00 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2478]) ).

thf(2511,plain,
    ! [SV302: $i] :
      ( ( ( ~ ( aElement0 @ SV302 ) )
        = $true )
      | ( ( aElement0 @ ( smndt0 @ SV302 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2480]) ).

thf(2512,plain,
    ! [SV321: $i,SV303: $i] :
      ( ( ~ ( aElement0 @ SV303 )
        | ~ ( aElement0 @ SV321 )
        | ( aElement0 @ ( sdtpldt0 @ SV303 @ SV321 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2481]) ).

thf(2513,plain,
    ! [SV322: $i,SV304: $i] :
      ( ( ~ ( aElement0 @ SV304 )
        | ~ ( aElement0 @ SV322 )
        | ( aElement0 @ ( sdtasdt0 @ SV304 @ SV322 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2482]) ).

thf(2514,plain,
    ! [SV323: $i,SV305: $i] :
      ( ( ~ ( aElement0 @ SV305 )
        | ~ ( aElement0 @ SV323 )
        | ( ( sdtpldt0 @ SV305 @ SV323 )
          = ( sdtpldt0 @ SV323 @ SV305 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2483]) ).

thf(2515,plain,
    ! [SV324: $i,SV306: $i] :
      ( ( ! [SY239: $i] :
            ( ~ ( aElement0 @ SV306 )
            | ~ ( aElement0 @ SV324 )
            | ~ ( aElement0 @ SY239 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SY239 )
              = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SY239 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2484]) ).

thf(2516,plain,
    ! [SV325: $i,SV307: $i] :
      ( ( ~ ( aElement0 @ SV307 )
        | ~ ( aElement0 @ SV325 )
        | ( ( sdtasdt0 @ SV307 @ SV325 )
          = ( sdtasdt0 @ SV325 @ SV307 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2485]) ).

thf(2517,plain,
    ! [SV326: $i,SV308: $i] :
      ( ( ! [SY240: $i] :
            ( ~ ( aElement0 @ SV308 )
            | ~ ( aElement0 @ SV326 )
            | ~ ( aElement0 @ SY240 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SY240 )
              = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SY240 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2486]) ).

thf(2518,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ~ ( aElement0 @ SV309 )
        | ~ ( aElement0 @ SV327 )
        | ( ( sdtasdt0 @ SV309 @ SV327 )
         != sz00 )
        | ( SV309 = sz00 )
        | ( SV327 = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2487]) ).

thf(2519,plain,
    ! [SV311: $i] :
      ( ( ( ~ ( aSet0 @ SV311 ) )
        = $true )
      | ( ( ! [SY227: $i] :
              ( ~ ( aElementOf0 @ SY227 @ SV311 )
              | ( aElement0 @ SY227 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2490]) ).

thf(2520,plain,
    ! [SV328: $i,SV312: $i] :
      ( ( ~ ( aIdeal0 @ SV312 )
        | ~ ( aIdeal0 @ SV328 )
        | ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SV328 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2491]) ).

thf(2521,plain,
    ! [SV329: $i,SV313: $i] :
      ( ( ~ ( aIdeal0 @ SV313 )
        | ~ ( aIdeal0 @ SV329 )
        | ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SV329 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2492]) ).

thf(2522,plain,
    ! [SV315: $i] :
      ( ( ( ( SV315 = sz00 )
          | ~ ( aElement0 @ SV315 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2494]) ).

thf(2523,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2495]) ).

thf(2524,plain,
    ! [SV316: $i] :
      ( ( ( ~ ( aElement0 @ SV316 ) )
        = $true )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV316 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2496]) ).

thf(2525,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
              = ( smndt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2497]) ).

thf(2526,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( smndt0 @ SX0 )
              = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2497]) ).

thf(2527,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( SV330 = sz00 )
        | ~ ( aElement0 @ SV317 )
        | ~ ( aElement0 @ SV330 )
        | ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                        | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                  | ( SV317
                   != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
            | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                  = sz00 )
                | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2498]) ).

thf(2528,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i,SX2: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                            | ( ( sdtpldt0 @ SX1 @ SX2 )
                             != SX0 ) )
                        | ( aElementOf0 @ SX0 @ xI ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                            | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                             != SX0 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xb @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                              | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ xa @ SX1 )
                                         != SX0 )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                    | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                         != SX0 )
                                        | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElementOf0 @ SX1 @ xI )
                                                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElementOf0 @ SX0 @ xI )
                                                | ! [SX1: $i] :
                                                    ( ~ ( aElement0 @ SX1 )
                                                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                    | ~ ( aSet0 @ xI ) )
                              | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2499]) ).

thf(2529,plain,
    ( ( ( xI
       != ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2499]) ).

thf(2530,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2500]) ).

thf(2531,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2500]) ).

thf(2532,plain,
    ( ( ~ ( aElement0 @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2501]) ).

thf(2533,plain,
    ( ( ~ ( aElement0 @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2501]) ).

thf(2534,plain,
    ! [SV331: $i,SV318: $i] :
      ( ( ~ ( aIdeal0 @ SV318 )
        | ~ ( aIdeal0 @ SV331 )
        | ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
            | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
        | ! [SY241: $i,SY242: $i] :
            ( ~ ( aElement0 @ SY241 )
            | ~ ( aElement0 @ SY242 )
            | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                      | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2502]) ).

thf(2535,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz10 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2503]) ).

thf(2536,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2503]) ).

thf(2537,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz00 )
              = sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2504]) ).

thf(2538,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( sz00
              = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2504]) ).

thf(2539,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz00 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2505]) ).

thf(2540,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ( SX0
              = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2505]) ).

thf(2541,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( sdtasdt0 @ xb @ SX0 )
             != xb )
            | ~ ( aElement0 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2506]) ).

thf(2542,plain,
    ( ( ~ ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2506]) ).

thf(2543,plain,
    ! [SV332: $i,SV319: $i] :
      ( ( ~ ( aSet0 @ SV319 )
        | ~ ( aSet0 @ SV332 )
        | ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
            | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
        | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
            | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        | ( SV319 = SV332 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2507]) ).

thf(2544,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                     != xc )
                                                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( aDivisorOf0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xb )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ( doDivides0 @ SX0 @ xc ) ) )
                                    | ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ! [SX1: $i] :
                                                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                     != xa )
                                                    | ~ ( aElement0 @ SX1 ) )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aElement0 @ SX0 )
                                                | ~ ( doDivides0 @ SX0 @ xa )
                                                | ~ ( doDivides0 @ SX0 @ xb )
                                                | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                             != xa )
                                                            | ~ ( aElement0 @ sK12_W0 ) )
                                                      | ~ ( aElement0 @ xc ) )
                                                | ~ ( doDivides0 @ xc @ xa ) )
                                          | ~ ( aDivisorOf0 @ xc @ xa ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                     != xb )
                                    | ~ ( aElement0 @ sK11_W0 ) ) )
                        | ~ ( doDivides0 @ xc @ xb ) )
                  | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2508]) ).

thf(2545,plain,
    ( ( ~ ( aGcdOfAnd0 @ xc @ xa @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2508]) ).

thf(2546,plain,
    ! [SV320: $i] :
      ( ( ~ ! [SY235: $i,SY236: $i] :
              ( ~ ( aElement0 @ SV320 )
              | ~ ( aElement0 @ SY235 )
              | ~ ( aElement0 @ SY236 )
              | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SY235 @ SY236 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SY235 ) @ ( sdtasdt0 @ SV320 @ SY236 ) ) ) )
        | ~ ! [SY237: $i,SY238: $i] :
              ( ~ ( aElement0 @ SV320 )
              | ~ ( aElement0 @ SY237 )
              | ~ ( aElement0 @ SY238 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY237 @ SY238 ) @ SV320 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY237 @ SV320 ) @ ( sdtasdt0 @ SY238 @ SV320 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2509]) ).

thf(2547,plain,
    ( ( ( xb = sz00 )
      = $false )
    | ( ( xa = sz00 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2510]) ).

thf(2548,plain,
    ! [SV302: $i] :
      ( ( ( aElement0 @ SV302 )
        = $false )
      | ( ( aElement0 @ ( smndt0 @ SV302 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2511]) ).

thf(2549,plain,
    ! [SV321: $i,SV303: $i] :
      ( ( ( ~ ( aElement0 @ SV303 )
          | ~ ( aElement0 @ SV321 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV303 @ SV321 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2512]) ).

thf(2550,plain,
    ! [SV322: $i,SV304: $i] :
      ( ( ( ~ ( aElement0 @ SV304 )
          | ~ ( aElement0 @ SV322 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV304 @ SV322 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2513]) ).

thf(2551,plain,
    ! [SV323: $i,SV305: $i] :
      ( ( ( ~ ( aElement0 @ SV305 )
          | ~ ( aElement0 @ SV323 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV305 @ SV323 )
          = ( sdtpldt0 @ SV323 @ SV305 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2514]) ).

thf(2552,plain,
    ! [SV333: $i,SV324: $i,SV306: $i] :
      ( ( ~ ( aElement0 @ SV306 )
        | ~ ( aElement0 @ SV324 )
        | ~ ( aElement0 @ SV333 )
        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2515]) ).

thf(2553,plain,
    ! [SV325: $i,SV307: $i] :
      ( ( ( ~ ( aElement0 @ SV307 )
          | ~ ( aElement0 @ SV325 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV307 @ SV325 )
          = ( sdtasdt0 @ SV325 @ SV307 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2516]) ).

thf(2554,plain,
    ! [SV334: $i,SV326: $i,SV308: $i] :
      ( ( ~ ( aElement0 @ SV308 )
        | ~ ( aElement0 @ SV326 )
        | ~ ( aElement0 @ SV334 )
        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2517]) ).

thf(2555,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( ~ ( aElement0 @ SV309 )
          | ~ ( aElement0 @ SV327 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
           != sz00 )
          | ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2518]) ).

thf(2556,plain,
    ! [SV311: $i] :
      ( ( ( aSet0 @ SV311 )
        = $false )
      | ( ( ! [SY227: $i] :
              ( ~ ( aElementOf0 @ SY227 @ SV311 )
              | ( aElement0 @ SY227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2519]) ).

thf(2557,plain,
    ! [SV328: $i,SV312: $i] :
      ( ( ( ~ ( aIdeal0 @ SV312 )
          | ~ ( aIdeal0 @ SV328 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SV328 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2520]) ).

thf(2558,plain,
    ! [SV329: $i,SV313: $i] :
      ( ( ( ~ ( aIdeal0 @ SV313 )
          | ~ ( aIdeal0 @ SV329 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SV329 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2521]) ).

thf(2559,plain,
    ! [SV315: $i] :
      ( ( ( SV315 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV315 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2522]) ).

thf(2560,plain,
    ! [SV335: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV335 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2523]) ).

thf(2561,plain,
    ! [SV316: $i] :
      ( ( ( aElement0 @ SV316 )
        = $false )
      | ( ( aIdeal0 @ ( slsdtgt0 @ SV316 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2524]) ).

thf(2562,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SX0 )
            = ( smndt0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2525]) ).

thf(2563,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( smndt0 @ SX0 )
            = ( sdtasdt0 @ SX0 @ ( smndt0 @ sz10 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2526]) ).

thf(2564,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ( SV330 = sz00 )
          | ~ ( aElement0 @ SV317 )
          | ~ ( aElement0 @ SV330 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                    | ( SV317
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2527]) ).

thf(2565,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i,SX2: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                          | ( ( sdtpldt0 @ SX1 @ SX2 )
                           != SX0 ) )
                      | ( aElementOf0 @ SX0 @ xI ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                                | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                          | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                           != SX0 ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xb @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ xa @ SX1 )
                                       != SX0 )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                       != SX0 )
                                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElementOf0 @ SX0 @ xI )
                                              | ! [SX1: $i] :
                                                  ( ~ ( aElement0 @ SX1 )
                                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                                  | ~ ( aSet0 @ xI ) )
                            | ~ ( aIdeal0 @ xI ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2528]) ).

thf(2566,plain,
    ( ( xI
      = ( sdtpldt1 @ ( slsdtgt0 @ xa ) @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2529]) ).

thf(2567,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2530]) ).

thf(2568,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2531]) ).

thf(2569,plain,
    ( ( aElement0 @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2532]) ).

thf(2570,plain,
    ( ( aElement0 @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2533]) ).

thf(2571,plain,
    ! [SV331: $i,SV318: $i] :
      ( ( ( ~ ( aIdeal0 @ SV318 )
          | ~ ( aIdeal0 @ SV331 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
          | ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2534]) ).

thf(2572,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz10 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2535]) ).

thf(2573,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtasdt0 @ sz10 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2536]) ).

thf(2574,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz00 )
            = sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2537]) ).

thf(2575,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( sz00
            = ( sdtasdt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2538]) ).

thf(2576,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ sz00 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2539]) ).

thf(2577,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ( SX0
            = ( sdtpldt0 @ sz00 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2540]) ).

thf(2578,plain,
    ( ( ! [SX0: $i] :
          ( ( ( sdtasdt0 @ xb @ SX0 )
           != xb )
          | ~ ( aElement0 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2541]) ).

thf(2579,plain,
    ( ( ~ ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2542]) ).

thf(2580,plain,
    ! [SV332: $i,SV319: $i] :
      ( ( ( ~ ( aSet0 @ SV319 )
          | ~ ( aSet0 @ SV332 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
          | ( SV319 = SV332 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2543]) ).

thf(2581,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                                   != xc )
                                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xb )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ( doDivides0 @ SX0 @ xc ) ) )
                                  | ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ! [SX1: $i] :
                                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                                   != xa )
                                                  | ~ ( aElement0 @ SX1 ) )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aElement0 @ SX0 )
                                              | ~ ( doDivides0 @ SX0 @ xa )
                                              | ~ ( doDivides0 @ SX0 @ xb )
                                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                           != xa )
                                                          | ~ ( aElement0 @ sK12_W0 ) )
                                                    | ~ ( aElement0 @ xc ) )
                                              | ~ ( doDivides0 @ xc @ xa ) )
                                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                                   != xb )
                                  | ~ ( aElement0 @ sK11_W0 ) ) )
                      | ~ ( doDivides0 @ xc @ xb ) )
                | ~ ( aDivisorOf0 @ xc @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2544]) ).

thf(2582,plain,
    ( ( aGcdOfAnd0 @ xc @ xa @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2545]) ).

thf(2583,plain,
    ! [SV320: $i] :
      ( ( ~ ! [SY235: $i,SY236: $i] :
              ( ~ ( aElement0 @ SV320 )
              | ~ ( aElement0 @ SY235 )
              | ~ ( aElement0 @ SY236 )
              | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SY235 @ SY236 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SY235 ) @ ( sdtasdt0 @ SV320 @ SY236 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2546]) ).

thf(2584,plain,
    ! [SV320: $i] :
      ( ( ~ ! [SY237: $i,SY238: $i] :
              ( ~ ( aElement0 @ SV320 )
              | ~ ( aElement0 @ SY237 )
              | ~ ( aElement0 @ SY238 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SY237 @ SY238 ) @ SV320 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SY237 @ SV320 ) @ ( sdtasdt0 @ SY238 @ SV320 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2546]) ).

thf(2585,plain,
    ! [SV321: $i,SV303: $i] :
      ( ( ( ~ ( aElement0 @ SV303 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV321 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV303 @ SV321 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2549]) ).

thf(2586,plain,
    ! [SV322: $i,SV304: $i] :
      ( ( ( ~ ( aElement0 @ SV304 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV322 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV304 @ SV322 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2550]) ).

thf(2587,plain,
    ! [SV323: $i,SV305: $i] :
      ( ( ( ~ ( aElement0 @ SV305 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV323 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV305 @ SV323 )
          = ( sdtpldt0 @ SV323 @ SV305 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2551]) ).

thf(2588,plain,
    ! [SV333: $i,SV324: $i,SV306: $i] :
      ( ( ( ~ ( aElement0 @ SV306 )
          | ~ ( aElement0 @ SV324 )
          | ~ ( aElement0 @ SV333 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2552]) ).

thf(2589,plain,
    ! [SV325: $i,SV307: $i] :
      ( ( ( ~ ( aElement0 @ SV307 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV325 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV307 @ SV325 )
          = ( sdtasdt0 @ SV325 @ SV307 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2553]) ).

thf(2590,plain,
    ! [SV334: $i,SV326: $i,SV308: $i] :
      ( ( ( ~ ( aElement0 @ SV308 )
          | ~ ( aElement0 @ SV326 )
          | ~ ( aElement0 @ SV334 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2554]) ).

thf(2591,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( ~ ( aElement0 @ SV309 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV327 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
           != sz00 )
          | ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2555]) ).

thf(2592,plain,
    ! [SV311: $i,SV336: $i] :
      ( ( ( ~ ( aElementOf0 @ SV336 @ SV311 )
          | ( aElement0 @ SV336 ) )
        = $true )
      | ( ( aSet0 @ SV311 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2556]) ).

thf(2593,plain,
    ! [SV328: $i,SV312: $i] :
      ( ( ( ~ ( aIdeal0 @ SV312 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV328 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SV328 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2557]) ).

thf(2594,plain,
    ! [SV329: $i,SV313: $i] :
      ( ( ( ~ ( aIdeal0 @ SV313 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV329 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SV329 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2558]) ).

thf(2595,plain,
    ! [SV315: $i] :
      ( ( ( aElement0 @ SV315 )
        = $false )
      | ( ( SV315 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ ( sbrdtbr0 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2559]) ).

thf(2596,plain,
    ! [SV335: $i] :
      ( ( ( aNaturalNumber0 @ SV335 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2560]) ).

thf(2597,plain,
    ! [SV337: $i] :
      ( ( ~ ( aElement0 @ SV337 )
        | ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV337 )
          = ( smndt0 @ SV337 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2562]) ).

thf(2598,plain,
    ! [SV338: $i] :
      ( ( ~ ( aElement0 @ SV338 )
        | ( ( smndt0 @ SV338 )
          = ( sdtasdt0 @ SV338 @ ( smndt0 @ sz10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2563]) ).

thf(2599,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( SV330 = sz00 )
        = $true )
      | ( ( ~ ( aElement0 @ SV317 )
          | ~ ( aElement0 @ SV330 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                    | ( SV317
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2564]) ).

thf(2600,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2565]) ).

thf(2601,plain,
    ! [SV339: $i] :
      ( ( ~ ( aElement0 @ SV339 )
        | ( ( sdtpldt0 @ SV339 @ ( smndt0 @ SV339 ) )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2567]) ).

thf(2602,plain,
    ! [SV340: $i] :
      ( ( ~ ( aElement0 @ SV340 )
        | ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV340 ) @ SV340 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2568]) ).

thf(2603,plain,
    ! [SV331: $i,SV318: $i] :
      ( ( ( ~ ( aIdeal0 @ SV318 ) )
        = $true )
      | ( ( ~ ( aIdeal0 @ SV331 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
          | ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2571]) ).

thf(2604,plain,
    ! [SV341: $i] :
      ( ( ~ ( aElement0 @ SV341 )
        | ( ( sdtasdt0 @ SV341 @ sz10 )
          = SV341 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2572]) ).

thf(2605,plain,
    ! [SV342: $i] :
      ( ( ~ ( aElement0 @ SV342 )
        | ( SV342
          = ( sdtasdt0 @ sz10 @ SV342 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2573]) ).

thf(2606,plain,
    ! [SV343: $i] :
      ( ( ~ ( aElement0 @ SV343 )
        | ( ( sdtasdt0 @ SV343 @ sz00 )
          = sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2574]) ).

thf(2607,plain,
    ! [SV344: $i] :
      ( ( ~ ( aElement0 @ SV344 )
        | ( sz00
          = ( sdtasdt0 @ sz00 @ SV344 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2575]) ).

thf(2608,plain,
    ! [SV345: $i] :
      ( ( ~ ( aElement0 @ SV345 )
        | ( ( sdtpldt0 @ SV345 @ sz00 )
          = SV345 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2576]) ).

thf(2609,plain,
    ! [SV346: $i] :
      ( ( ~ ( aElement0 @ SV346 )
        | ( SV346
          = ( sdtpldt0 @ sz00 @ SV346 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2577]) ).

thf(2610,plain,
    ! [SV347: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV347 )
         != xb )
        | ~ ( aElement0 @ SV347 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2578]) ).

thf(2611,plain,
    ( ( aElementOf0 @ xb @ ( slsdtgt0 @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2579]) ).

thf(2612,plain,
    ! [SV332: $i,SV319: $i] :
      ( ( ( ~ ( aSet0 @ SV319 ) )
        = $true )
      | ( ( ~ ( aSet0 @ SV332 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
          | ( SV319 = SV332 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2580]) ).

thf(2613,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2581]) ).

thf(2614,plain,
    ! [SV320: $i] :
      ( ( ! [SY235: $i,SY236: $i] :
            ( ~ ( aElement0 @ SV320 )
            | ~ ( aElement0 @ SY235 )
            | ~ ( aElement0 @ SY236 )
            | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SY235 @ SY236 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SY235 ) @ ( sdtasdt0 @ SV320 @ SY236 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2583]) ).

thf(2615,plain,
    ! [SV320: $i] :
      ( ( ! [SY237: $i,SY238: $i] :
            ( ~ ( aElement0 @ SV320 )
            | ~ ( aElement0 @ SY237 )
            | ~ ( aElement0 @ SY238 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SY237 @ SY238 ) @ SV320 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SY237 @ SV320 ) @ ( sdtasdt0 @ SY238 @ SV320 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2584]) ).

thf(2616,plain,
    ! [SV321: $i,SV303: $i] :
      ( ( ( aElement0 @ SV303 )
        = $false )
      | ( ( ~ ( aElement0 @ SV321 ) )
        = $true )
      | ( ( aElement0 @ ( sdtpldt0 @ SV303 @ SV321 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2585]) ).

thf(2617,plain,
    ! [SV322: $i,SV304: $i] :
      ( ( ( aElement0 @ SV304 )
        = $false )
      | ( ( ~ ( aElement0 @ SV322 ) )
        = $true )
      | ( ( aElement0 @ ( sdtasdt0 @ SV304 @ SV322 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2586]) ).

thf(2618,plain,
    ! [SV323: $i,SV305: $i] :
      ( ( ( aElement0 @ SV305 )
        = $false )
      | ( ( ~ ( aElement0 @ SV323 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV305 @ SV323 )
          = ( sdtpldt0 @ SV323 @ SV305 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2587]) ).

thf(2619,plain,
    ! [SV333: $i,SV324: $i,SV306: $i] :
      ( ( ( ~ ( aElement0 @ SV306 )
          | ~ ( aElement0 @ SV324 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV333 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2588]) ).

thf(2620,plain,
    ! [SV325: $i,SV307: $i] :
      ( ( ( aElement0 @ SV307 )
        = $false )
      | ( ( ~ ( aElement0 @ SV325 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV307 @ SV325 )
          = ( sdtasdt0 @ SV325 @ SV307 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2589]) ).

thf(2621,plain,
    ! [SV334: $i,SV326: $i,SV308: $i] :
      ( ( ( ~ ( aElement0 @ SV308 )
          | ~ ( aElement0 @ SV326 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV334 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2590]) ).

thf(2622,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( aElement0 @ SV309 )
        = $false )
      | ( ( ~ ( aElement0 @ SV327 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
           != sz00 )
          | ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2591]) ).

thf(2623,plain,
    ! [SV311: $i,SV336: $i] :
      ( ( ( ~ ( aElementOf0 @ SV336 @ SV311 ) )
        = $true )
      | ( ( aElement0 @ SV336 )
        = $true )
      | ( ( aSet0 @ SV311 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2592]) ).

thf(2624,plain,
    ! [SV328: $i,SV312: $i] :
      ( ( ( aIdeal0 @ SV312 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV328 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SV328 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2593]) ).

thf(2625,plain,
    ! [SV329: $i,SV313: $i] :
      ( ( ( aIdeal0 @ SV313 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV329 ) )
        = $true )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SV329 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2594]) ).

thf(2626,plain,
    ! [SV335: $i,SV348: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV348 ) )
        = $true )
      | ( ( aNaturalNumber0 @ SV335 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2596]) ).

thf(2627,plain,
    ! [SV337: $i] :
      ( ( ( ~ ( aElement0 @ SV337 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV337 )
          = ( smndt0 @ SV337 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2597]) ).

thf(2628,plain,
    ! [SV338: $i] :
      ( ( ( ~ ( aElement0 @ SV338 ) )
        = $true )
      | ( ( ( smndt0 @ SV338 )
          = ( sdtasdt0 @ SV338 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2598]) ).

thf(2629,plain,
    ! [SV330: $i,SV317: $i] :
      ( ( ( ~ ( aElement0 @ SV317 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV330 ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                    | ( SV317
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2599]) ).

thf(2630,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i,SX2: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                      | ( ( sdtpldt0 @ SX1 @ SX2 )
                       != SX0 ) )
                  | ( aElementOf0 @ SX0 @ xI ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                            | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                      | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                       != SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2600]) ).

thf(2631,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xb @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ xa @ SX1 )
                                   != SX0 )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                              | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                   != SX0 )
                                  | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElementOf0 @ SX1 @ xI )
                                              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElementOf0 @ SX0 @ xI )
                                          | ! [SX1: $i] :
                                              ( ~ ( aElement0 @ SX1 )
                                              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                              | ~ ( aSet0 @ xI ) )
                        | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2600]) ).

thf(2632,plain,
    ! [SV339: $i] :
      ( ( ( ~ ( aElement0 @ SV339 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV339 @ ( smndt0 @ SV339 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2601]) ).

thf(2633,plain,
    ! [SV340: $i] :
      ( ( ( ~ ( aElement0 @ SV340 ) )
        = $true )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV340 ) @ SV340 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2602]) ).

thf(2634,plain,
    ! [SV331: $i,SV318: $i] :
      ( ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( ~ ( aIdeal0 @ SV331 ) )
        = $true )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
          | ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2603]) ).

thf(2635,plain,
    ! [SV341: $i] :
      ( ( ( ~ ( aElement0 @ SV341 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV341 @ sz10 )
          = SV341 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2604]) ).

thf(2636,plain,
    ! [SV342: $i] :
      ( ( ( ~ ( aElement0 @ SV342 ) )
        = $true )
      | ( ( SV342
          = ( sdtasdt0 @ sz10 @ SV342 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2605]) ).

thf(2637,plain,
    ! [SV343: $i] :
      ( ( ( ~ ( aElement0 @ SV343 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV343 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2606]) ).

thf(2638,plain,
    ! [SV344: $i] :
      ( ( ( ~ ( aElement0 @ SV344 ) )
        = $true )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV344 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2607]) ).

thf(2639,plain,
    ! [SV345: $i] :
      ( ( ( ~ ( aElement0 @ SV345 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV345 @ sz00 )
          = SV345 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2608]) ).

thf(2640,plain,
    ! [SV346: $i] :
      ( ( ( ~ ( aElement0 @ SV346 ) )
        = $true )
      | ( ( SV346
          = ( sdtpldt0 @ sz00 @ SV346 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2609]) ).

thf(2641,plain,
    ! [SV347: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV347 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV347 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2610]) ).

thf(2642,plain,
    ! [SV332: $i,SV319: $i] :
      ( ( ( aSet0 @ SV319 )
        = $false )
      | ( ( ~ ( aSet0 @ SV332 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
          | ( SV319 = SV332 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2612]) ).

thf(2643,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                               != xc )
                                              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( aDivisorOf0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xb )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ( doDivides0 @ SX0 @ xc ) ) )
                              | ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ! [SX1: $i] :
                                              ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                               != xa )
                                              | ~ ( aElement0 @ SX1 ) )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aElement0 @ SX0 )
                                          | ~ ( doDivides0 @ SX0 @ xa )
                                          | ~ ( doDivides0 @ SX0 @ xb )
                                          | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2613]) ).

thf(2644,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                       != xa )
                                                      | ~ ( aElement0 @ sK12_W0 ) )
                                                | ~ ( aElement0 @ xc ) )
                                          | ~ ( doDivides0 @ xc @ xa ) )
                                    | ~ ( aDivisorOf0 @ xc @ xa ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                               != xb )
                              | ~ ( aElement0 @ sK11_W0 ) ) )
                  | ~ ( doDivides0 @ xc @ xb ) )
            | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2613]) ).

thf(2645,plain,
    ! [SV349: $i,SV320: $i] :
      ( ( ! [SY243: $i] :
            ( ~ ( aElement0 @ SV320 )
            | ~ ( aElement0 @ SV349 )
            | ~ ( aElement0 @ SY243 )
            | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SY243 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SY243 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2614]) ).

thf(2646,plain,
    ! [SV350: $i,SV320: $i] :
      ( ( ! [SY244: $i] :
            ( ~ ( aElement0 @ SV320 )
            | ~ ( aElement0 @ SV350 )
            | ~ ( aElement0 @ SY244 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SY244 ) @ SV320 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SY244 @ SV320 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2615]) ).

thf(2647,plain,
    ! [SV303: $i,SV321: $i] :
      ( ( ( aElement0 @ SV321 )
        = $false )
      | ( ( aElement0 @ SV303 )
        = $false )
      | ( ( aElement0 @ ( sdtpldt0 @ SV303 @ SV321 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2616]) ).

thf(2648,plain,
    ! [SV304: $i,SV322: $i] :
      ( ( ( aElement0 @ SV322 )
        = $false )
      | ( ( aElement0 @ SV304 )
        = $false )
      | ( ( aElement0 @ ( sdtasdt0 @ SV304 @ SV322 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2617]) ).

thf(2649,plain,
    ! [SV305: $i,SV323: $i] :
      ( ( ( aElement0 @ SV323 )
        = $false )
      | ( ( aElement0 @ SV305 )
        = $false )
      | ( ( ( sdtpldt0 @ SV305 @ SV323 )
          = ( sdtpldt0 @ SV323 @ SV305 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2618]) ).

thf(2650,plain,
    ! [SV333: $i,SV324: $i,SV306: $i] :
      ( ( ( ~ ( aElement0 @ SV306 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV324 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV333 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2619]) ).

thf(2651,plain,
    ! [SV307: $i,SV325: $i] :
      ( ( ( aElement0 @ SV325 )
        = $false )
      | ( ( aElement0 @ SV307 )
        = $false )
      | ( ( ( sdtasdt0 @ SV307 @ SV325 )
          = ( sdtasdt0 @ SV325 @ SV307 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2620]) ).

thf(2652,plain,
    ! [SV334: $i,SV326: $i,SV308: $i] :
      ( ( ( ~ ( aElement0 @ SV308 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV326 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV334 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2621]) ).

thf(2653,plain,
    ! [SV309: $i,SV327: $i] :
      ( ( ( aElement0 @ SV327 )
        = $false )
      | ( ( aElement0 @ SV309 )
        = $false )
      | ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
           != sz00 )
          | ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2622]) ).

thf(2654,plain,
    ! [SV311: $i,SV336: $i] :
      ( ( ( aElementOf0 @ SV336 @ SV311 )
        = $false )
      | ( ( aElement0 @ SV336 )
        = $true )
      | ( ( aSet0 @ SV311 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2623]) ).

thf(2655,plain,
    ! [SV312: $i,SV328: $i] :
      ( ( ( aIdeal0 @ SV328 )
        = $false )
      | ( ( aIdeal0 @ SV312 )
        = $false )
      | ( ( aIdeal0 @ ( sdtpldt1 @ SV312 @ SV328 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2624]) ).

thf(2656,plain,
    ! [SV313: $i,SV329: $i] :
      ( ( ( aIdeal0 @ SV329 )
        = $false )
      | ( ( aIdeal0 @ SV313 )
        = $false )
      | ( ( aIdeal0 @ ( sdtasasdt0 @ SV313 @ SV329 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2625]) ).

thf(2657,plain,
    ! [SV335: $i,SV348: $i] :
      ( ( ( aNaturalNumber0 @ SV348 )
        = $false )
      | ( ( aNaturalNumber0 @ SV335 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2626]) ).

thf(2658,plain,
    ! [SV337: $i] :
      ( ( ( aElement0 @ SV337 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ SV337 )
          = ( smndt0 @ SV337 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2627]) ).

thf(2659,plain,
    ! [SV338: $i] :
      ( ( ( aElement0 @ SV338 )
        = $false )
      | ( ( ( smndt0 @ SV338 )
          = ( sdtasdt0 @ SV338 @ ( smndt0 @ sz10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2628]) ).

thf(2660,plain,
    ! [SV330: $i,SV317: $i] :
      ( ( ( aElement0 @ SV317 )
        = $false )
      | ( ( ~ ( aElement0 @ SV330 ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                    | ( SV317
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2629]) ).

thf(2661,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i,SX2: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                    | ( ( sdtpldt0 @ SX1 @ SX2 )
                     != SX0 ) )
                | ( aElementOf0 @ SX0 @ xI ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                          | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                    | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                     != SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2630]) ).

thf(2662,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xb @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                      | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ xa @ SX1 )
                                 != SX0 )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                                 != SX0 )
                                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElementOf0 @ SX1 @ xI )
                                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElementOf0 @ SX0 @ xI )
                                        | ! [SX1: $i] :
                                            ( ~ ( aElement0 @ SX1 )
                                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                            | ~ ( aSet0 @ xI ) )
                      | ~ ( aIdeal0 @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2631]) ).

thf(2663,plain,
    ! [SV339: $i] :
      ( ( ( aElement0 @ SV339 )
        = $false )
      | ( ( ( sdtpldt0 @ SV339 @ ( smndt0 @ SV339 ) )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2632]) ).

thf(2664,plain,
    ! [SV340: $i] :
      ( ( ( aElement0 @ SV340 )
        = $false )
      | ( ( sz00
          = ( sdtpldt0 @ ( smndt0 @ SV340 ) @ SV340 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2633]) ).

thf(2665,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( aIdeal0 @ SV331 )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
          | ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2634]) ).

thf(2666,plain,
    ! [SV341: $i] :
      ( ( ( aElement0 @ SV341 )
        = $false )
      | ( ( ( sdtasdt0 @ SV341 @ sz10 )
          = SV341 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2635]) ).

thf(2667,plain,
    ! [SV342: $i] :
      ( ( ( aElement0 @ SV342 )
        = $false )
      | ( ( SV342
          = ( sdtasdt0 @ sz10 @ SV342 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2636]) ).

thf(2668,plain,
    ! [SV343: $i] :
      ( ( ( aElement0 @ SV343 )
        = $false )
      | ( ( ( sdtasdt0 @ SV343 @ sz00 )
          = sz00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2637]) ).

thf(2669,plain,
    ! [SV344: $i] :
      ( ( ( aElement0 @ SV344 )
        = $false )
      | ( ( sz00
          = ( sdtasdt0 @ sz00 @ SV344 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2638]) ).

thf(2670,plain,
    ! [SV345: $i] :
      ( ( ( aElement0 @ SV345 )
        = $false )
      | ( ( ( sdtpldt0 @ SV345 @ sz00 )
          = SV345 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2639]) ).

thf(2671,plain,
    ! [SV346: $i] :
      ( ( ( aElement0 @ SV346 )
        = $false )
      | ( ( SV346
          = ( sdtpldt0 @ sz00 @ SV346 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2640]) ).

thf(2672,plain,
    ! [SV347: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV347 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV347 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2641]) ).

thf(2673,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aSet0 @ SV332 )
        = $false )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
          | ( SV319 = SV332 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2642]) ).

thf(2674,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                             != xc )
                                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xb )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ( doDivides0 @ SX0 @ xc ) ) )
                            | ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ! [SX1: $i] :
                                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                             != xa )
                                            | ~ ( aElement0 @ SX1 ) )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aElement0 @ SX0 )
                                        | ~ ( doDivides0 @ SX0 @ xa )
                                        | ~ ( doDivides0 @ SX0 @ xb )
                                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2643]) ).

thf(2675,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                     != xa )
                                                    | ~ ( aElement0 @ sK12_W0 ) )
                                              | ~ ( aElement0 @ xc ) )
                                        | ~ ( doDivides0 @ xc @ xa ) )
                                  | ~ ( aDivisorOf0 @ xc @ xa ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                             != xb )
                            | ~ ( aElement0 @ sK11_W0 ) ) )
                | ~ ( doDivides0 @ xc @ xb ) )
          | ~ ( aDivisorOf0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2644]) ).

thf(2676,plain,
    ! [SV351: $i,SV349: $i,SV320: $i] :
      ( ( ~ ( aElement0 @ SV320 )
        | ~ ( aElement0 @ SV349 )
        | ~ ( aElement0 @ SV351 )
        | ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2645]) ).

thf(2677,plain,
    ! [SV352: $i,SV350: $i,SV320: $i] :
      ( ( ~ ( aElement0 @ SV320 )
        | ~ ( aElement0 @ SV350 )
        | ~ ( aElement0 @ SV352 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2646]) ).

thf(2678,plain,
    ! [SV333: $i,SV324: $i,SV306: $i] :
      ( ( ( aElement0 @ SV306 )
        = $false )
      | ( ( ~ ( aElement0 @ SV324 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV333 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2650]) ).

thf(2679,plain,
    ! [SV334: $i,SV326: $i,SV308: $i] :
      ( ( ( aElement0 @ SV308 )
        = $false )
      | ( ( ~ ( aElement0 @ SV326 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV334 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2652]) ).

thf(2680,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
           != sz00 ) )
        = $true )
      | ( ( ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV309 )
        = $false )
      | ( ( aElement0 @ SV327 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2653]) ).

thf(2681,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( aElement0 @ SV330 )
        = $false )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                    | ( SV317
                     != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
              | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                    = sz00 )
                  | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2660]) ).

thf(2682,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2661]) ).

thf(2683,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2662]) ).

thf(2684,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
              | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) ) )
        = $true )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2665]) ).

thf(2685,plain,
    ! [SV347: $i] :
      ( ( ( aElement0 @ SV347 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV347 )
          = xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2672]) ).

thf(2686,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
          | ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2673]) ).

thf(2687,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2674]) ).

thf(2688,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) )
      | ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2675]) ).

thf(2689,plain,
    ! [SV351: $i,SV349: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 )
          | ~ ( aElement0 @ SV349 )
          | ~ ( aElement0 @ SV351 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2676]) ).

thf(2690,plain,
    ! [SV352: $i,SV350: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 )
          | ~ ( aElement0 @ SV350 )
          | ~ ( aElement0 @ SV352 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2677]) ).

thf(2691,plain,
    ! [SV333: $i,SV306: $i,SV324: $i] :
      ( ( ( aElement0 @ SV324 )
        = $false )
      | ( ( aElement0 @ SV306 )
        = $false )
      | ( ( ~ ( aElement0 @ SV333 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2678]) ).

thf(2692,plain,
    ! [SV334: $i,SV308: $i,SV326: $i] :
      ( ( ( aElement0 @ SV326 )
        = $false )
      | ( ( aElement0 @ SV308 )
        = $false )
      | ( ( ~ ( aElement0 @ SV334 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2679]) ).

thf(2693,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( ( sdtasdt0 @ SV309 @ SV327 )
          = sz00 )
        = $false )
      | ( ( ( SV309 = sz00 )
          | ( SV327 = sz00 ) )
        = $true )
      | ( ( aElement0 @ SV309 )
        = $false )
      | ( ( aElement0 @ SV327 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2680]) ).

thf(2694,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                | ( SV317
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
          | ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2681]) ).

thf(2695,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i,SX2: $i] :
                ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
                | ( ( sdtpldt0 @ SX1 @ SX2 )
                 != SX0 ) )
            | ( aElementOf0 @ SX0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2682]) ).

thf(2696,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                      | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
                | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
                 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2682]) ).

thf(2697,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xb @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                  | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2683]) ).

thf(2698,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ xa @ SX1 )
                             != SX0 )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                             != SX0 )
                            | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElementOf0 @ SX1 @ xI )
                                        | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElementOf0 @ SX0 @ xI )
                                    | ! [SX1: $i] :
                                        ( ~ ( aElement0 @ SX1 )
                                        | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                        | ~ ( aSet0 @ xI ) )
                  | ~ ( aIdeal0 @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2683]) ).

thf(2699,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
          | ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
        = $false )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2684]) ).

thf(2700,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
              | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2686]) ).

thf(2701,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                         != xc )
                                        | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2687]) ).

thf(2702,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( aDivisorOf0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xb )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ( doDivides0 @ SX0 @ xc ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ! [SX1: $i] :
                                        ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                         != xa )
                                        | ~ ( aElement0 @ SX1 ) )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aElement0 @ SX0 )
                                    | ~ ( doDivides0 @ SX0 @ xa )
                                    | ~ ( doDivides0 @ SX0 @ xb )
                                    | ( doDivides0 @ SX0 @ xc ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aDivisorOf0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2687]) ).

thf(2703,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                                 != xa )
                                                | ~ ( aElement0 @ sK12_W0 ) )
                                          | ~ ( aElement0 @ xc ) )
                                    | ~ ( doDivides0 @ xc @ xa ) )
                              | ~ ( aDivisorOf0 @ xc @ xa ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                         != xb )
                        | ~ ( aElement0 @ sK11_W0 ) ) )
            | ~ ( doDivides0 @ xc @ xb ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2688]) ).

thf(2704,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2688]) ).

thf(2705,plain,
    ! [SV351: $i,SV349: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 )
          | ~ ( aElement0 @ SV349 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV351 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2689]) ).

thf(2706,plain,
    ! [SV352: $i,SV350: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 )
          | ~ ( aElement0 @ SV350 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV352 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2690]) ).

thf(2707,plain,
    ! [SV324: $i,SV306: $i,SV333: $i] :
      ( ( ( aElement0 @ SV333 )
        = $false )
      | ( ( aElement0 @ SV306 )
        = $false )
      | ( ( aElement0 @ SV324 )
        = $false )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV306 @ SV324 ) @ SV333 )
          = ( sdtpldt0 @ SV306 @ ( sdtpldt0 @ SV324 @ SV333 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2691]) ).

thf(2708,plain,
    ! [SV326: $i,SV308: $i,SV334: $i] :
      ( ( ( aElement0 @ SV334 )
        = $false )
      | ( ( aElement0 @ SV308 )
        = $false )
      | ( ( aElement0 @ SV326 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV308 @ SV326 ) @ SV334 )
          = ( sdtasdt0 @ SV308 @ ( sdtasdt0 @ SV326 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2692]) ).

thf(2709,plain,
    ! [SV327: $i,SV309: $i] :
      ( ( ( SV309 = sz00 )
        = $true )
      | ( ( SV327 = sz00 )
        = $true )
      | ( ( ( sdtasdt0 @ SV309 @ SV327 )
          = sz00 )
        = $false )
      | ( ( aElement0 @ SV309 )
        = $false )
      | ( ( aElement0 @ SV327 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2693]) ).

thf(2710,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                      | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
                | ( SV317
                 != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2694]) ).

thf(2711,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( ( ( sK2_SY72 @ SV330 @ SV317 )
                = sz00 )
              | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2694]) ).

thf(2712,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i,SX2: $i] :
              ( ~ ( aElementOf0 @ SX1 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SX2 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SX1 @ SX2 )
               != SX0 ) )
          | ( aElementOf0 @ SX0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2695]) ).

thf(2713,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SX0 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SX0 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SX0 ) @ ( sK10_SY73 @ SX0 ) )
               != SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2696]) ).

thf(2714,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xb @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
                | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2697]) ).

thf(2715,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ xa @ SX1 )
                           != SX0 )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                      | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                           != SX0 )
                          | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElementOf0 @ SX1 @ xI )
                                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElementOf0 @ SX0 @ xI )
                                  | ! [SX1: $i] :
                                      ( ~ ( aElement0 @ SX1 )
                                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                      | ~ ( aSet0 @ xI ) )
                | ~ ( aIdeal0 @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2698]) ).

thf(2716,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( ~ ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) ) )
        = $false )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2699]) ).

thf(2717,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
        = $false )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2699]) ).

thf(2718,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
          | ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2700]) ).

thf(2719,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                       != xc )
                                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2701]) ).

thf(2720,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( aDivisorOf0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xb )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ( doDivides0 @ SX0 @ xc ) ) )
                      | ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ! [SX1: $i] :
                                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                       != xa )
                                      | ~ ( aElement0 @ SX1 ) )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aElement0 @ SX0 )
                                  | ~ ( doDivides0 @ SX0 @ xa )
                                  | ~ ( doDivides0 @ SX0 @ xb )
                                  | ( doDivides0 @ SX0 @ xc ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aDivisorOf0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2702]) ).

thf(2721,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                               != xa )
                                              | ~ ( aElement0 @ sK12_W0 ) )
                                        | ~ ( aElement0 @ xc ) )
                                  | ~ ( doDivides0 @ xc @ xa ) )
                            | ~ ( aDivisorOf0 @ xc @ xa ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                       != xb )
                      | ~ ( aElement0 @ sK11_W0 ) ) )
          | ~ ( doDivides0 @ xc @ xb ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2703]) ).

thf(2722,plain,
    ( ( aDivisorOf0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2704]) ).

thf(2723,plain,
    ! [SV351: $i,SV349: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV349 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV351 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2705]) ).

thf(2724,plain,
    ! [SV352: $i,SV350: $i,SV320: $i] :
      ( ( ( ~ ( aElement0 @ SV320 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV350 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV352 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2706]) ).

thf(2725,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                    | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
              | ( SV317
               != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2710]) ).

thf(2726,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ( ( sK2_SY72 @ SV330 @ SV317 )
            = sz00 )
          | ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2711]) ).

thf(2727,plain,
    ! [SV353: $i] :
      ( ( ! [SY245: $i,SY246: $i] :
            ( ~ ( aElementOf0 @ SY245 @ ( slsdtgt0 @ xa ) )
            | ~ ( aElementOf0 @ SY246 @ ( slsdtgt0 @ xb ) )
            | ( ( sdtpldt0 @ SY245 @ SY246 )
             != SV353 ) )
        | ( aElementOf0 @ SV353 @ xI ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2712]) ).

thf(2728,plain,
    ! [SV354: $i] :
      ( ( ~ ( aElementOf0 @ SV354 @ xI )
        | ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
                  | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
            | ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
             != SV354 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2713]) ).

thf(2729,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2714]) ).

thf(2730,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2715]) ).

thf(2731,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2716]) ).

thf(2732,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) ) )
        = $true )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2717]) ).

thf(2733,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2718]) ).

thf(2734,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2718]) ).

thf(2735,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2719]) ).

thf(2736,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2720]) ).

thf(2737,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) )
      | ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2721]) ).

thf(2738,plain,
    ! [SV351: $i,SV349: $i,SV320: $i] :
      ( ( ( aElement0 @ SV320 )
        = $false )
      | ( ( ~ ( aElement0 @ SV349 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV351 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2723]) ).

thf(2739,plain,
    ! [SV352: $i,SV350: $i,SV320: $i] :
      ( ( ( aElement0 @ SV320 )
        = $false )
      | ( ( ~ ( aElement0 @ SV350 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV352 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2724]) ).

thf(2740,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
          | ( SV317
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2725]) ).

thf(2741,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ( sK2_SY72 @ SV330 @ SV317 )
          = sz00 )
        = $true )
      | ( ( iLess0 @ ( sbrdtbr0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) @ ( sbrdtbr0 @ SV330 ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2726]) ).

thf(2742,plain,
    ! [SV353: $i] :
      ( ( ( ! [SY245: $i,SY246: $i] :
              ( ~ ( aElementOf0 @ SY245 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY246 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SY245 @ SY246 )
               != SV353 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2727]) ).

thf(2743,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( aElementOf0 @ SV354 @ xI ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
               != SV354 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2728]) ).

thf(2744,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xb @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2745,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
            | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2746,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ xa @ SX1 )
                       != SX0 )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                  | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                       != SX0 )
                      | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2730]) ).

thf(2747,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElementOf0 @ SX1 @ xI )
                                  | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElementOf0 @ SX0 @ xI )
                              | ! [SX1: $i] :
                                  ( ~ ( aElement0 @ SX1 )
                                  | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                  | ~ ( aSet0 @ xI ) )
            | ~ ( aIdeal0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2730]) ).

thf(2748,plain,
    ! [SV318: $i,SV331: $i,SV355: $i] :
      ( ( ( ! [SY247: $i] :
              ( ~ ( aElement0 @ SV355 )
              | ~ ( aElement0 @ SY247 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY247 @ SV355 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY247 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY247 @ SV355 @ SV331 @ SV318 ) @ SY247 @ SV331 ) ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2731]) ).

thf(2749,plain,
    ! [SV318: $i,SV331: $i] :
      ( ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( ! [SY241: $i,SY242: $i] :
              ( ~ ( aElement0 @ SY241 )
              | ~ ( aElement0 @ SY242 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY241 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY242 @ SY241 @ SV331 @ SV318 ) @ SY242 @ SV331 ) ) ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2732]) ).

thf(2750,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2733]) ).

thf(2751,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 ) )
        = $true )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2734]) ).

thf(2752,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                   != xc )
                                  | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2735]) ).

thf(2753,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2735]) ).

thf(2754,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( aDivisorOf0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xb )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ( doDivides0 @ SX0 @ xc ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ! [SX1: $i] :
                                  ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                   != xa )
                                  | ~ ( aElement0 @ SX1 ) )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aElement0 @ SX0 )
                              | ~ ( doDivides0 @ SX0 @ xa )
                              | ~ ( doDivides0 @ SX0 @ xb )
                              | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2736]) ).

thf(2755,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aDivisorOf0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2736]) ).

thf(2756,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                           != xa )
                                          | ~ ( aElement0 @ sK12_W0 ) )
                                    | ~ ( aElement0 @ xc ) )
                              | ~ ( doDivides0 @ xc @ xa ) )
                        | ~ ( aDivisorOf0 @ xc @ xa ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                   != xb )
                  | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2737]) ).

thf(2757,plain,
    ( ( ~ ( doDivides0 @ xc @ xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2737]) ).

thf(2758,plain,
    ! [SV351: $i,SV320: $i,SV349: $i] :
      ( ( ( aElement0 @ SV349 )
        = $false )
      | ( ( aElement0 @ SV320 )
        = $false )
      | ( ( ~ ( aElement0 @ SV351 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2738]) ).

thf(2759,plain,
    ! [SV352: $i,SV320: $i,SV350: $i] :
      ( ( ( aElement0 @ SV350 )
        = $false )
      | ( ( aElement0 @ SV320 )
        = $false )
      | ( ( ~ ( aElement0 @ SV352 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2739]) ).

thf(2760,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
                | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2740]) ).

thf(2761,plain,
    ! [SV330: $i,SV317: $i] :
      ( ( ( ( SV317
           != ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2740]) ).

thf(2762,plain,
    ! [SV353: $i,SV356: $i] :
      ( ( ( ! [SY248: $i] :
              ( ~ ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ SY248 @ ( slsdtgt0 @ xb ) )
              | ( ( sdtpldt0 @ SV356 @ SY248 )
               != SV353 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2742]) ).

thf(2763,plain,
    ! [SV354: $i] :
      ( ( ( aElementOf0 @ SV354 @ xI )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
                    | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
              | ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
               != SV354 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2743]) ).

thf(2764,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xb @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2744]) ).

thf(2765,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xb ) )
          | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK8_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2745]) ).

thf(2766,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ xa @ SX1 )
                     != SX0 )
                    | ~ ( aElement0 @ SX1 ) )
                | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
                | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                     != SX0 )
                    | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2746]) ).

thf(2767,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElementOf0 @ SX1 @ xI )
                                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElementOf0 @ SX0 @ xI )
                            | ! [SX1: $i] :
                                ( ~ ( aElement0 @ SX1 )
                                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
                | ~ ( aSet0 @ xI ) )
          | ~ ( aIdeal0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2747]) ).

thf(2768,plain,
    ! [SV318: $i,SV331: $i,SV357: $i,SV355: $i] :
      ( ( ( ~ ( aElement0 @ SV355 )
          | ~ ( aElement0 @ SV357 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2748]) ).

thf(2769,plain,
    ! [SV318: $i,SV331: $i,SV358: $i] :
      ( ( ( ! [SY249: $i] :
              ( ~ ( aElement0 @ SV358 )
              | ~ ( aElement0 @ SY249 )
              | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SY249 @ SV358 @ SV331 @ SV318 ) )
                        | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY249 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
                  | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SY249 @ SV358 @ SV331 @ SV318 ) @ SY249 @ SV331 ) ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2749]) ).

thf(2770,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2750]) ).

thf(2771,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( ~ ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
              | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) ) )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2751]) ).

thf(2772,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                                 != xc )
                                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2752]) ).

thf(2773,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2753]) ).

thf(2774,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( aDivisorOf0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xb )
                                | ~ ( aElement0 @ SX1 ) )
                            | ( doDivides0 @ SX0 @ xc ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ! [SX1: $i] :
                                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                                 != xa )
                                | ~ ( aElement0 @ SX1 ) )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aElement0 @ SX0 )
                            | ~ ( doDivides0 @ SX0 @ xa )
                            | ~ ( doDivides0 @ SX0 @ xb )
                            | ( doDivides0 @ SX0 @ xc ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2754]) ).

thf(2775,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aDivisorOf0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2755]) ).

thf(2776,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                         != xa )
                                        | ~ ( aElement0 @ sK12_W0 ) )
                                  | ~ ( aElement0 @ xc ) )
                            | ~ ( doDivides0 @ xc @ xa ) )
                      | ~ ( aDivisorOf0 @ xc @ xa ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
                 != xb )
                | ~ ( aElement0 @ sK11_W0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2756]) ).

thf(2777,plain,
    ( ( doDivides0 @ xc @ xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2757]) ).

thf(2778,plain,
    ! [SV349: $i,SV320: $i,SV351: $i] :
      ( ( ( aElement0 @ SV351 )
        = $false )
      | ( ( aElement0 @ SV320 )
        = $false )
      | ( ( aElement0 @ SV349 )
        = $false )
      | ( ( ( sdtasdt0 @ SV320 @ ( sdtpldt0 @ SV349 @ SV351 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV320 @ SV349 ) @ ( sdtasdt0 @ SV320 @ SV351 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2758]) ).

thf(2779,plain,
    ! [SV350: $i,SV320: $i,SV352: $i] :
      ( ( ( aElement0 @ SV352 )
        = $false )
      | ( ( aElement0 @ SV320 )
        = $false )
      | ( ( aElement0 @ SV350 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV350 @ SV352 ) @ SV320 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV350 @ SV320 ) @ ( sdtasdt0 @ SV352 @ SV320 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2759]) ).

thf(2780,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
              | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2760]) ).

thf(2781,plain,
    ! [SV330: $i,SV317: $i] :
      ( ( ( SV317
          = ( sdtpldt0 @ ( sdtasdt0 @ ( sK1_W2 @ SV330 @ SV317 ) @ SV330 ) @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2761]) ).

thf(2782,plain,
    ! [SV353: $i,SV359: $i,SV356: $i] :
      ( ( ( ~ ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) )
          | ( ( sdtpldt0 @ SV356 @ SV359 )
           != SV353 ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2762]) ).

thf(2783,plain,
    ! [SV354: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
          | ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
           != SV354 ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2763]) ).

thf(2784,plain,
    ! [SV360: $i] :
      ( ( ! [SY250: $i] :
            ( ( ( sdtasdt0 @ xb @ SY250 )
             != SV360 )
            | ~ ( aElement0 @ SY250 ) )
        | ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2764]) ).

thf(2785,plain,
    ! [SV361: $i] :
      ( ( ~ ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        | ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
             != SV361 )
            | ~ ( aElement0 @ ( sK8_W1 @ SV361 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2765]) ).

thf(2786,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2766]) ).

thf(2787,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) )
      | ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2767]) ).

thf(2788,plain,
    ! [SV318: $i,SV331: $i,SV357: $i,SV355: $i] :
      ( ( ( ~ ( aElement0 @ SV355 )
          | ~ ( aElement0 @ SV357 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2768]) ).

thf(2789,plain,
    ! [SV318: $i,SV331: $i,SV362: $i,SV358: $i] :
      ( ( ( ~ ( aElement0 @ SV358 )
          | ~ ( aElement0 @ SV362 )
          | ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2769]) ).

thf(2790,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2770]) ).

thf(2791,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2770]) ).

thf(2792,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
          | ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2771]) ).

thf(2793,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2772]) ).

thf(2794,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2773]) ).

thf(2795,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2774]) ).

thf(2796,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2775]) ).

thf(2797,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2776]) ).

thf(2798,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
          | ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2780]) ).

thf(2799,plain,
    ! [SV353: $i,SV359: $i,SV356: $i] :
      ( ( ( ~ ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV356 @ SV359 )
           != SV353 ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2782]) ).

thf(2800,plain,
    ! [SV354: $i] :
      ( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
                | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2783]) ).

thf(2801,plain,
    ! [SV354: $i] :
      ( ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
           != SV354 ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2783]) ).

thf(2802,plain,
    ! [SV360: $i] :
      ( ( ( ! [SY250: $i] :
              ( ( ( sdtasdt0 @ xb @ SY250 )
               != SV360 )
              | ~ ( aElement0 @ SY250 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2784]) ).

thf(2803,plain,
    ! [SV361: $i] :
      ( ( ( ~ ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
               != SV361 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV361 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2785]) ).

thf(2804,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( ( sdtasdt0 @ xa @ SX1 )
                 != SX0 )
                | ~ ( aElement0 @ SX1 ) )
            | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2786]) ).

thf(2805,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
            | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
                 != SX0 )
                | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2786]) ).

thf(2806,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElementOf0 @ SX1 @ xI )
                            | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElementOf0 @ SX0 @ xI )
                        | ! [SX1: $i] :
                            ( ~ ( aElement0 @ SX1 )
                            | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
            | ~ ( aSet0 @ xI ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2787]) ).

thf(2807,plain,
    ( ( ~ ( aIdeal0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2787]) ).

thf(2808,plain,
    ! [SV318: $i,SV331: $i,SV357: $i,SV355: $i] :
      ( ( ( ~ ( aElement0 @ SV355 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV357 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2788]) ).

thf(2809,plain,
    ! [SV318: $i,SV331: $i,SV362: $i,SV358: $i] :
      ( ( ( ~ ( aElement0 @ SV358 )
          | ~ ( aElement0 @ SV362 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2789]) ).

thf(2810,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2790]) ).

thf(2811,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2791]) ).

thf(2812,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2792]) ).

thf(2813,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2792]) ).

thf(2814,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2793]) ).

thf(2815,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                             != xc )
                            | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2793]) ).

thf(2816,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2794]) ).

thf(2817,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2794]) ).

thf(2818,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( aDivisorOf0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2795]) ).

thf(2819,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xb )
                            | ~ ( aElement0 @ SX1 ) )
                        | ( doDivides0 @ SX0 @ xc ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ! [SX1: $i] :
                            ( ( ( sdtasdt0 @ SX0 @ SX1 )
                             != xa )
                            | ~ ( aElement0 @ SX1 ) )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aElement0 @ SX0 )
                        | ~ ( doDivides0 @ SX0 @ xa )
                        | ~ ( doDivides0 @ SX0 @ xb )
                        | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2795]) ).

thf(2820,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2796]) ).

thf(2821,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aDivisorOf0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2796]) ).

thf(2822,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                     != xa )
                                    | ~ ( aElement0 @ sK12_W0 ) )
                              | ~ ( aElement0 @ xc ) )
                        | ~ ( doDivides0 @ xc @ xa ) )
                  | ~ ( aDivisorOf0 @ xc @ xa ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2797]) ).

thf(2823,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
             != xb )
            | ~ ( aElement0 @ sK11_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2797]) ).

thf(2824,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2798]) ).

thf(2825,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( ~ ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) ) )
        = $false )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2798]) ).

thf(2826,plain,
    ! [SV353: $i,SV359: $i,SV356: $i] :
      ( ( ( ~ ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV356 @ SV359 )
           != SV353 ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2799]) ).

thf(2827,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
              | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) ) )
        = $true )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2800]) ).

thf(2828,plain,
    ! [SV354: $i] :
      ( ( ( ( sdtpldt0 @ ( sK9_W1 @ SV354 ) @ ( sK10_SY73 @ SV354 ) )
          = SV354 )
        = $true )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2801]) ).

thf(2829,plain,
    ! [SV360: $i,SV363: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV363 )
           != SV360 )
          | ~ ( aElement0 @ SV363 ) )
        = $true )
      | ( ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2802]) ).

thf(2830,plain,
    ! [SV361: $i] :
      ( ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
               != SV361 )
              | ~ ( aElement0 @ ( sK8_W1 @ SV361 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2803]) ).

thf(2831,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( ( sdtasdt0 @ xa @ SX1 )
               != SX0 )
              | ~ ( aElement0 @ SX1 ) )
          | ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2804]) ).

thf(2832,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ ( slsdtgt0 @ xa ) )
          | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SX0 ) )
               != SX0 )
              | ~ ( aElement0 @ ( sK7_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2805]) ).

thf(2833,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElementOf0 @ SX1 @ xI )
                          | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElementOf0 @ SX0 @ xI )
                      | ! [SX1: $i] :
                          ( ~ ( aElement0 @ SX1 )
                          | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
          | ~ ( aSet0 @ xI ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2806]) ).

thf(2834,plain,
    ( ( aIdeal0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2807]) ).

thf(2835,plain,
    ! [SV318: $i,SV331: $i,SV357: $i,SV355: $i] :
      ( ( ( aElement0 @ SV355 )
        = $false )
      | ( ( ~ ( aElement0 @ SV357 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2808]) ).

thf(2836,plain,
    ! [SV318: $i,SV331: $i,SV362: $i,SV358: $i] :
      ( ( ( ~ ( aElement0 @ SV358 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV362 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2809]) ).

thf(2837,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2811]) ).

thf(2838,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV332 )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2812]) ).

thf(2839,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 ) )
        = $true )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2813]) ).

thf(2840,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2814]) ).

thf(2841,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                           != xc )
                          | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2815]) ).

thf(2842,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK15_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2816]) ).

thf(2843,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2817]) ).

thf(2844,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( aDivisorOf0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2818]) ).

thf(2845,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xb )
                          | ~ ( aElement0 @ SX1 ) )
                      | ( doDivides0 @ SX0 @ xc ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( sdtasdt0 @ SX0 @ SX1 )
                           != xa )
                          | ~ ( aElement0 @ SX1 ) )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aElement0 @ SX0 )
                      | ~ ( doDivides0 @ SX0 @ xa )
                      | ~ ( doDivides0 @ SX0 @ xb )
                      | ( doDivides0 @ SX0 @ xc ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2819]) ).

thf(2846,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2820]) ).

thf(2847,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aDivisorOf0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2821]) ).

thf(2848,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                                   != xa )
                                  | ~ ( aElement0 @ sK12_W0 ) )
                            | ~ ( aElement0 @ xc ) )
                      | ~ ( doDivides0 @ xc @ xa ) )
                | ~ ( aDivisorOf0 @ xc @ xa ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2822]) ).

thf(2849,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK11_W0 )
           != xb )
          | ~ ( aElement0 @ sK11_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2823]) ).

thf(2850,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( aElement0 @ ( sK1_W2 @ SV330 @ SV317 ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2824]) ).

thf(2851,plain,
    ! [SV317: $i,SV330: $i] :
      ( ( ( aElement0 @ ( sK2_SY72 @ SV330 @ SV317 ) )
        = $true )
      | ( ( SV330 = sz00 )
        = $true )
      | ( ( aElement0 @ SV317 )
        = $false )
      | ( ( aElement0 @ SV330 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2825]) ).

thf(2852,plain,
    ! [SV353: $i,SV359: $i,SV356: $i] :
      ( ( ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) ) )
        = $true )
      | ( ( ( ( sdtpldt0 @ SV356 @ SV359 )
           != SV353 ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2826]) ).

thf(2853,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
          | ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2827]) ).

thf(2854,plain,
    ! [SV360: $i,SV363: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ SV363 )
           != SV360 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV363 ) )
        = $true )
      | ( ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2829]) ).

thf(2855,plain,
    ! [SV361: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
           != SV361 )
          | ~ ( aElement0 @ ( sK8_W1 @ SV361 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2830]) ).

thf(2856,plain,
    ! [SV364: $i] :
      ( ( ! [SY251: $i] :
            ( ( ( sdtasdt0 @ xa @ SY251 )
             != SV364 )
            | ~ ( aElement0 @ SY251 ) )
        | ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2831]) ).

thf(2857,plain,
    ! [SV365: $i] :
      ( ( ~ ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        | ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
             != SV365 )
            | ~ ( aElement0 @ ( sK7_W1 @ SV365 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2832]) ).

thf(2858,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
      | ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2833]) ).

thf(2859,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) ) )
        = $true )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2835]) ).

thf(2860,plain,
    ! [SV318: $i,SV331: $i,SV362: $i,SV358: $i] :
      ( ( ( aElement0 @ SV358 )
        = $false )
      | ( ( ~ ( aElement0 @ SV362 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2836]) ).

thf(2861,plain,
    ! [SV319: $i,SV332: $i] :
      ( ( ( aElementOf0 @ ( sK5_W2 @ SV332 @ SV319 ) @ SV319 )
        = $false )
      | ( ( aElementOf0 @ ( sK6_W2 @ SV332 @ SV319 ) @ SV332 )
        = $false )
      | ( ( SV319 = SV332 )
        = $true )
      | ( ( aSet0 @ SV319 )
        = $false )
      | ( ( aSet0 @ SV332 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2839]) ).

thf(2862,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2840]) ).

thf(2863,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2841]) ).

thf(2864,plain,
    ! [SV366: $i] :
      ( ( ~ ( aDivisorOf0 @ SV366 @ xa )
        | ~ ( aDivisorOf0 @ SV366 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
             != xc )
            | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2842]) ).

thf(2865,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2843]) ).

thf(2866,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2844]) ).

thf(2867,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2845]) ).

thf(2868,plain,
    ! [SV367: $i] :
      ( ( ~ ( aDivisorOf0 @ SV367 @ xa )
        | ~ ( aDivisorOf0 @ SV367 @ xb )
        | ( doDivides0 @ SV367 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2846]) ).

thf(2869,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2847]) ).

thf(2870,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2848]) ).

thf(2871,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb )
      | ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2849]) ).

thf(2872,plain,
    ! [SV353: $i,SV356: $i,SV359: $i] :
      ( ( ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ( ( sdtpldt0 @ SV356 @ SV359 )
           != SV353 ) )
        = $true )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2852]) ).

thf(2873,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2853]) ).

thf(2874,plain,
    ! [SV354: $i] :
      ( ( ( ~ ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) ) )
        = $false )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2853]) ).

thf(2875,plain,
    ! [SV360: $i,SV363: $i] :
      ( ( ( ( sdtasdt0 @ xb @ SV363 )
          = SV360 )
        = $false )
      | ( ( ~ ( aElement0 @ SV363 ) )
        = $true )
      | ( ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2854]) ).

thf(2876,plain,
    ! [SV361: $i] :
      ( ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
           != SV361 ) )
        = $false )
      | ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2855]) ).

thf(2877,plain,
    ! [SV361: $i] :
      ( ( ( ~ ( aElement0 @ ( sK8_W1 @ SV361 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2855]) ).

thf(2878,plain,
    ! [SV364: $i] :
      ( ( ( ! [SY251: $i] :
              ( ( ( sdtasdt0 @ xa @ SY251 )
               != SV364 )
              | ~ ( aElement0 @ SY251 ) ) )
        = $true )
      | ( ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2856]) ).

thf(2879,plain,
    ! [SV365: $i] :
      ( ( ( ~ ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
               != SV365 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV365 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2857]) ).

thf(2880,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElementOf0 @ SX1 @ xI )
                      | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElementOf0 @ SX0 @ xI )
                  | ! [SX1: $i] :
                      ( ~ ( aElement0 @ SX1 )
                      | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2881,plain,
    ( ( ~ ( aSet0 @ xI ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2882,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2859]) ).

thf(2883,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                    | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) ) )
        = $true )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2860]) ).

thf(2884,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2862]) ).

thf(2885,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2862]) ).

thf(2886,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2863]) ).

thf(2887,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                       != xc )
                      | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2863]) ).

thf(2888,plain,
    ! [SV366: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV366 @ xa )
          | ~ ( aDivisorOf0 @ SV366 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2864]) ).

thf(2889,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2865]) ).

thf(2890,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2865]) ).

thf(2891,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2866]) ).

thf(2892,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( aDivisorOf0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2866]) ).

thf(2893,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xb )
                      | ~ ( aElement0 @ SX1 ) )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2867]) ).

thf(2894,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( sdtasdt0 @ SX0 @ SX1 )
                       != xa )
                      | ~ ( aElement0 @ SX1 ) )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aElement0 @ SX0 )
                  | ~ ( doDivides0 @ SX0 @ xa )
                  | ~ ( doDivides0 @ SX0 @ xb )
                  | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2867]) ).

thf(2895,plain,
    ! [SV367: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV367 @ xa )
          | ~ ( aDivisorOf0 @ SV367 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV367 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2868]) ).

thf(2896,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2869]) ).

thf(2897,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aDivisorOf0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2869]) ).

thf(2898,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                               != xa )
                              | ~ ( aElement0 @ sK12_W0 ) )
                        | ~ ( aElement0 @ xc ) )
                  | ~ ( doDivides0 @ xc @ xa ) )
            | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2870]) ).

thf(2899,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2870]) ).

thf(2900,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK11_W0 )
       != xb ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2871]) ).

thf(2901,plain,
    ( ( ~ ( aElement0 @ sK11_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2871]) ).

thf(2902,plain,
    ! [SV353: $i,SV359: $i,SV356: $i] :
      ( ( ( ( sdtpldt0 @ SV356 @ SV359 )
          = SV353 )
        = $false )
      | ( ( aElementOf0 @ SV356 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( aElementOf0 @ SV359 @ ( slsdtgt0 @ xb ) )
        = $false )
      | ( ( aElementOf0 @ SV353 @ xI )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2872]) ).

thf(2903,plain,
    ! [SV354: $i] :
      ( ( ( aElementOf0 @ ( sK9_W1 @ SV354 ) @ ( slsdtgt0 @ xa ) )
        = $true )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2873]) ).

thf(2904,plain,
    ! [SV354: $i] :
      ( ( ( aElementOf0 @ ( sK10_SY73 @ SV354 ) @ ( slsdtgt0 @ xb ) )
        = $true )
      | ( ( aElementOf0 @ SV354 @ xI )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2874]) ).

thf(2905,plain,
    ! [SV360: $i,SV363: $i] :
      ( ( ( aElement0 @ SV363 )
        = $false )
      | ( ( ( sdtasdt0 @ xb @ SV363 )
          = SV360 )
        = $false )
      | ( ( aElementOf0 @ SV360 @ ( slsdtgt0 @ xb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2875]) ).

thf(2906,plain,
    ! [SV361: $i] :
      ( ( ( ( sdtasdt0 @ xb @ ( sK8_W1 @ SV361 ) )
          = SV361 )
        = $true )
      | ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2876]) ).

thf(2907,plain,
    ! [SV361: $i] :
      ( ( ( aElement0 @ ( sK8_W1 @ SV361 ) )
        = $true )
      | ( ( aElementOf0 @ SV361 @ ( slsdtgt0 @ xb ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2877]) ).

thf(2908,plain,
    ! [SV364: $i,SV368: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV368 )
           != SV364 )
          | ~ ( aElement0 @ SV368 ) )
        = $true )
      | ( ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2878]) ).

thf(2909,plain,
    ! [SV365: $i] :
      ( ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
               != SV365 )
              | ~ ( aElement0 @ ( sK7_W1 @ SV365 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2879]) ).

thf(2910,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElementOf0 @ SX1 @ xI )
                    | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElementOf0 @ SX0 @ xI )
                | ! [SX1: $i] :
                    ( ~ ( aElement0 @ SX1 )
                    | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2880]) ).

thf(2911,plain,
    ( ( aSet0 @ xI )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2881]) ).

thf(2912,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2882]) ).

thf(2913,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2882]) ).

thf(2914,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2883]) ).

thf(2915,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK21_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2884]) ).

thf(2916,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK20_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2885]) ).

thf(2917,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2886]) ).

thf(2918,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                     != xc )
                    | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2887]) ).

thf(2919,plain,
    ! [SV366: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV366 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV366 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2888]) ).

thf(2920,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK14_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2889]) ).

thf(2921,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK13_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2890]) ).

thf(2922,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2891]) ).

thf(2923,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( aDivisorOf0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2892]) ).

thf(2924,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xb )
                    | ~ ( aElement0 @ SX1 ) )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2893]) ).

thf(2925,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( sdtasdt0 @ SX0 @ SX1 )
                     != xa )
                    | ~ ( aElement0 @ SX1 ) )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aElement0 @ SX0 )
                | ~ ( doDivides0 @ SX0 @ xa )
                | ~ ( doDivides0 @ SX0 @ xb )
                | ( doDivides0 @ SX0 @ xc ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2894]) ).

thf(2926,plain,
    ! [SV367: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV367 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV367 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV367 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2895]) ).

thf(2927,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2896]) ).

thf(2928,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aDivisorOf0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2897]) ).

thf(2929,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                             != xa )
                            | ~ ( aElement0 @ sK12_W0 ) )
                      | ~ ( aElement0 @ xc ) )
                | ~ ( doDivides0 @ xc @ xa ) )
          | ~ ( aDivisorOf0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2898]) ).

thf(2930,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2899]) ).

thf(2931,plain,
    ( ( ( sdtasdt0 @ xc @ sK11_W0 )
      = xb )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2900]) ).

thf(2932,plain,
    ( ( aElement0 @ sK11_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2901]) ).

thf(2933,plain,
    ! [SV364: $i,SV368: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ SV368 )
           != SV364 ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV368 ) )
        = $true )
      | ( ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2908]) ).

thf(2934,plain,
    ! [SV365: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
           != SV365 )
          | ~ ( aElement0 @ ( sK7_W1 @ SV365 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2909]) ).

thf(2935,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2910]) ).

thf(2936,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) ) )
        = $true )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2912]) ).

thf(2937,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV357 @ SV331 )
        = $true )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2913]) ).

thf(2938,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
                | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2914]) ).

thf(2939,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2914]) ).

thf(2940,plain,
    ! [SV369: $i] :
      ( ( ~ ( aElement0 @ SV369 )
        | ! [SY252: $i] :
            ( ( ( sdtasdt0 @ SV369 @ SY252 )
             != xa )
            | ~ ( aElement0 @ SY252 ) )
        | ~ ( aDivisorOf0 @ SV369 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
             != xc )
            | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2915]) ).

thf(2941,plain,
    ! [SV370: $i] :
      ( ( ~ ( aElement0 @ SV370 )
        | ~ ( doDivides0 @ SV370 @ xa )
        | ~ ( aDivisorOf0 @ SV370 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
             != xc )
            | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2916]) ).

thf(2942,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2917]) ).

thf(2943,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2918]) ).

thf(2944,plain,
    ! [SV366: $i] :
      ( ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV366 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2919]) ).

thf(2945,plain,
    ! [SV371: $i] :
      ( ( ~ ( aDivisorOf0 @ SV371 @ xa )
        | ! [SY253: $i] :
            ( ( ( sdtasdt0 @ SV371 @ SY253 )
             != xb )
            | ~ ( aElement0 @ SY253 ) )
        | ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
             != xc )
            | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2920]) ).

thf(2946,plain,
    ! [SV372: $i] :
      ( ( ~ ( aDivisorOf0 @ SV372 @ xa )
        | ~ ( doDivides0 @ SV372 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
             != xc )
            | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2921]) ).

thf(2947,plain,
    ! [SV373: $i] :
      ( ( ~ ( aElement0 @ SV373 )
        | ! [SY254: $i] :
            ( ( ( sdtasdt0 @ SV373 @ SY254 )
             != xa )
            | ~ ( aElement0 @ SY254 ) )
        | ~ ( aDivisorOf0 @ SV373 @ xb )
        | ( doDivides0 @ SV373 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2922]) ).

thf(2948,plain,
    ! [SV374: $i] :
      ( ( ~ ( aElement0 @ SV374 )
        | ~ ( doDivides0 @ SV374 @ xa )
        | ~ ( aDivisorOf0 @ SV374 @ xb )
        | ( doDivides0 @ SV374 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2923]) ).

thf(2949,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2924]) ).

thf(2950,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2925]) ).

thf(2951,plain,
    ! [SV367: $i] :
      ( ( ( aDivisorOf0 @ SV367 @ xa )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV367 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV367 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2926]) ).

thf(2952,plain,
    ! [SV375: $i] :
      ( ( ~ ( aDivisorOf0 @ SV375 @ xa )
        | ! [SY255: $i] :
            ( ( ( sdtasdt0 @ SV375 @ SY255 )
             != xb )
            | ~ ( aElement0 @ SY255 ) )
        | ( doDivides0 @ SV375 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2927]) ).

thf(2953,plain,
    ! [SV376: $i] :
      ( ( ~ ( aDivisorOf0 @ SV376 @ xa )
        | ~ ( doDivides0 @ SV376 @ xb )
        | ( doDivides0 @ SV376 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2928]) ).

thf(2954,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) )
      | ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2929]) ).

thf(2955,plain,
    ! [SV364: $i,SV368: $i] :
      ( ( ( ( sdtasdt0 @ xa @ SV368 )
          = SV364 )
        = $false )
      | ( ( ~ ( aElement0 @ SV368 ) )
        = $true )
      | ( ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2933]) ).

thf(2956,plain,
    ! [SV365: $i] :
      ( ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
           != SV365 ) )
        = $false )
      | ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2934]) ).

thf(2957,plain,
    ! [SV365: $i] :
      ( ( ( ~ ( aElement0 @ ( sK7_W1 @ SV365 ) ) )
        = $false )
      | ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2934]) ).

thf(2958,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElementOf0 @ SX1 @ xI )
                | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2935]) ).

thf(2959,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElementOf0 @ SX0 @ xI )
            | ! [SX1: $i] :
                ( ~ ( aElement0 @ SX1 )
                | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2935]) ).

thf(2960,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2936]) ).

thf(2961,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
              | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) ) )
        = $true )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2938]) ).

thf(2962,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV362 @ SV331 )
        = $true )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2939]) ).

thf(2963,plain,
    ! [SV369: $i] :
      ( ( ( ~ ( aElement0 @ SV369 )
          | ! [SY252: $i] :
              ( ( ( sdtasdt0 @ SV369 @ SY252 )
               != xa )
              | ~ ( aElement0 @ SY252 ) )
          | ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2940]) ).

thf(2964,plain,
    ! [SV370: $i] :
      ( ( ( ~ ( aElement0 @ SV370 )
          | ~ ( doDivides0 @ SV370 @ xa )
          | ~ ( aDivisorOf0 @ SV370 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2941]) ).

thf(2965,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2942]) ).

thf(2966,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2942]) ).

thf(2967,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2943]) ).

thf(2968,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
                 != xc )
                | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2943]) ).

thf(2969,plain,
    ! [SV366: $i] :
      ( ( ( aDivisorOf0 @ SV366 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
               != xc )
              | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2944]) ).

thf(2970,plain,
    ! [SV371: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV371 @ xa )
          | ! [SY253: $i] :
              ( ( ( sdtasdt0 @ SV371 @ SY253 )
               != xb )
              | ~ ( aElement0 @ SY253 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2945]) ).

thf(2971,plain,
    ! [SV372: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV372 @ xa )
          | ~ ( doDivides0 @ SV372 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2946]) ).

thf(2972,plain,
    ! [SV373: $i] :
      ( ( ( ~ ( aElement0 @ SV373 )
          | ! [SY254: $i] :
              ( ( ( sdtasdt0 @ SV373 @ SY254 )
               != xa )
              | ~ ( aElement0 @ SY254 ) )
          | ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2947]) ).

thf(2973,plain,
    ! [SV374: $i] :
      ( ( ( ~ ( aElement0 @ SV374 )
          | ~ ( doDivides0 @ SV374 @ xa )
          | ~ ( aDivisorOf0 @ SV374 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2948]) ).

thf(2974,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2949]) ).

thf(2975,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xb )
                | ~ ( aElement0 @ SX1 ) )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2949]) ).

thf(2976,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ! [SX1: $i] :
                ( ( ( sdtasdt0 @ SX0 @ SX1 )
                 != xa )
                | ~ ( aElement0 @ SX1 ) )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2950]) ).

thf(2977,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aElement0 @ SX0 )
            | ~ ( doDivides0 @ SX0 @ xa )
            | ~ ( doDivides0 @ SX0 @ xb )
            | ( doDivides0 @ SX0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2950]) ).

thf(2978,plain,
    ! [SV367: $i] :
      ( ( ( aDivisorOf0 @ SV367 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV367 @ xa )
        = $false )
      | ( ( doDivides0 @ SV367 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2951]) ).

thf(2979,plain,
    ! [SV375: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV375 @ xa )
          | ! [SY255: $i] :
              ( ( ( sdtasdt0 @ SV375 @ SY255 )
               != xb )
              | ~ ( aElement0 @ SY255 ) ) )
        = $true )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2952]) ).

thf(2980,plain,
    ! [SV376: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV376 @ xa )
          | ~ ( doDivides0 @ SV376 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV376 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2953]) ).

thf(2981,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                         != xa )
                        | ~ ( aElement0 @ sK12_W0 ) )
                  | ~ ( aElement0 @ xc ) )
            | ~ ( doDivides0 @ xc @ xa ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2954]) ).

thf(2982,plain,
    ( ( ~ ( aDivisorOf0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2954]) ).

thf(2983,plain,
    ! [SV364: $i,SV368: $i] :
      ( ( ( aElement0 @ SV368 )
        = $false )
      | ( ( ( sdtasdt0 @ xa @ SV368 )
          = SV364 )
        = $false )
      | ( ( aElementOf0 @ SV364 @ ( slsdtgt0 @ xa ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2955]) ).

thf(2984,plain,
    ! [SV365: $i] :
      ( ( ( ( sdtasdt0 @ xa @ ( sK7_W1 @ SV365 ) )
          = SV365 )
        = $true )
      | ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2956]) ).

thf(2985,plain,
    ! [SV365: $i] :
      ( ( ( aElement0 @ ( sK7_W1 @ SV365 ) )
        = $true )
      | ( ( aElementOf0 @ SV365 @ ( slsdtgt0 @ xa ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2957]) ).

thf(2986,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElementOf0 @ SX1 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2958]) ).

thf(2987,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElementOf0 @ SX0 @ xI )
          | ! [SX1: $i] :
              ( ~ ( aElement0 @ SX1 )
              | ( aElementOf0 @ ( sdtasdt0 @ SX1 @ SX0 ) @ xI ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2959]) ).

thf(2988,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2960]) ).

thf(2989,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 ) )
        = $false )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2960]) ).

thf(2990,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
          | ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2961]) ).

thf(2991,plain,
    ! [SV369: $i] :
      ( ( ( ~ ( aElement0 @ SV369 )
          | ! [SY252: $i] :
              ( ( ( sdtasdt0 @ SV369 @ SY252 )
               != xa )
              | ~ ( aElement0 @ SY252 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2963]) ).

thf(2992,plain,
    ! [SV370: $i] :
      ( ( ( ~ ( aElement0 @ SV370 )
          | ~ ( doDivides0 @ SV370 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV370 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2964]) ).

thf(2993,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK19_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2965]) ).

thf(2994,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK18_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2966]) ).

thf(2995,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK17_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2967]) ).

thf(2996,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ~ ( ( ( sdtasdt0 @ SX0 @ ( sK16_W1 @ SX0 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2968]) ).

thf(2997,plain,
    ! [SV366: $i] :
      ( ( ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
           != xc )
          | ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2969]) ).

thf(2998,plain,
    ! [SV371: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV371 @ xa ) )
        = $true )
      | ( ( ! [SY253: $i] :
              ( ( ( sdtasdt0 @ SV371 @ SY253 )
               != xb )
              | ~ ( aElement0 @ SY253 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2970]) ).

thf(2999,plain,
    ! [SV372: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV372 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV372 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2971]) ).

thf(3000,plain,
    ! [SV373: $i] :
      ( ( ( ~ ( aElement0 @ SV373 )
          | ! [SY254: $i] :
              ( ( ( sdtasdt0 @ SV373 @ SY254 )
               != xa )
              | ~ ( aElement0 @ SY254 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2972]) ).

thf(3001,plain,
    ! [SV374: $i] :
      ( ( ( ~ ( aElement0 @ SV374 )
          | ~ ( doDivides0 @ SV374 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV374 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2973]) ).

thf(3002,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2974]) ).

thf(3003,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xb )
              | ~ ( aElement0 @ SX1 ) )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2975]) ).

thf(3004,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ! [SX1: $i] :
              ( ( ( sdtasdt0 @ SX0 @ SX1 )
               != xa )
              | ~ ( aElement0 @ SX1 ) )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2976]) ).

thf(3005,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aElement0 @ SX0 )
          | ~ ( doDivides0 @ SX0 @ xa )
          | ~ ( doDivides0 @ SX0 @ xb )
          | ( doDivides0 @ SX0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2977]) ).

thf(3006,plain,
    ! [SV375: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV375 @ xa ) )
        = $true )
      | ( ( ! [SY255: $i] :
              ( ( ( sdtasdt0 @ SV375 @ SY255 )
               != xb )
              | ~ ( aElement0 @ SY255 ) ) )
        = $true )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2979]) ).

thf(3007,plain,
    ! [SV376: $i] :
      ( ( ( ~ ( aDivisorOf0 @ SV376 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV376 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV376 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2980]) ).

thf(3008,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                       != xa )
                      | ~ ( aElement0 @ sK12_W0 ) )
                | ~ ( aElement0 @ xc ) )
          | ~ ( doDivides0 @ xc @ xa ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2981]) ).

thf(3009,plain,
    ( ( aDivisorOf0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2982]) ).

thf(3010,plain,
    ! [SV377: $i] :
      ( ( ~ ( aElementOf0 @ SV377 @ xI )
        | ! [SY256: $i] :
            ( ~ ( aElementOf0 @ SY256 @ xI )
            | ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SY256 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2986]) ).

thf(3011,plain,
    ! [SV378: $i] :
      ( ( ~ ( aElementOf0 @ SV378 @ xI )
        | ! [SY257: $i] :
            ( ~ ( aElement0 @ SY257 )
            | ( aElementOf0 @ ( sdtasdt0 @ SY257 @ SV378 ) @ xI ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2987]) ).

thf(3012,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2988]) ).

thf(3013,plain,
    ! [SV318: $i,SV331: $i,SV355: $i,SV357: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV357 @ SV355 @ SV331 @ SV318 ) @ SV355 @ SV318 )
        = $true )
      | ( ( aElement0 @ SV355 )
        = $false )
      | ( ( aElement0 @ SV357 )
        = $false )
      | ( ( aElement0 @ ( sK4_W2 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2989]) ).

thf(3014,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3015,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( ~ ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 ) )
        = $false )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3016,plain,
    ! [SV369: $i] :
      ( ( ( ~ ( aElement0 @ SV369 ) )
        = $true )
      | ( ( ! [SY252: $i] :
              ( ( ( sdtasdt0 @ SV369 @ SY252 )
               != xa )
              | ~ ( aElement0 @ SY252 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2991]) ).

thf(3017,plain,
    ! [SV370: $i] :
      ( ( ( ~ ( aElement0 @ SV370 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV370 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV370 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2992]) ).

thf(3018,plain,
    ! [SV379: $i] :
      ( ( ~ ( aElement0 @ SV379 )
        | ! [SY258: $i] :
            ( ( ( sdtasdt0 @ SV379 @ SY258 )
             != xa )
            | ~ ( aElement0 @ SY258 ) )
        | ! [SY259: $i] :
            ( ( ( sdtasdt0 @ SV379 @ SY259 )
             != xb )
            | ~ ( aElement0 @ SY259 ) )
        | ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
             != xc )
            | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2993]) ).

thf(3019,plain,
    ! [SV380: $i] :
      ( ( ~ ( aElement0 @ SV380 )
        | ~ ( doDivides0 @ SV380 @ xa )
        | ! [SY260: $i] :
            ( ( ( sdtasdt0 @ SV380 @ SY260 )
             != xb )
            | ~ ( aElement0 @ SY260 ) )
        | ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
             != xc )
            | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2994]) ).

thf(3020,plain,
    ! [SV381: $i] :
      ( ( ~ ( aElement0 @ SV381 )
        | ! [SY261: $i] :
            ( ( ( sdtasdt0 @ SV381 @ SY261 )
             != xa )
            | ~ ( aElement0 @ SY261 ) )
        | ~ ( doDivides0 @ SV381 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
             != xc )
            | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2995]) ).

thf(3021,plain,
    ! [SV382: $i] :
      ( ( ~ ( aElement0 @ SV382 )
        | ~ ( doDivides0 @ SV382 @ xa )
        | ~ ( doDivides0 @ SV382 @ xb )
        | ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
             != xc )
            | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2996]) ).

thf(3022,plain,
    ! [SV366: $i] :
      ( ( ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2997]) ).

thf(3023,plain,
    ! [SV366: $i] :
      ( ( ( ~ ( aElement0 @ ( sK15_W1 @ SV366 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2997]) ).

thf(3024,plain,
    ! [SV371: $i] :
      ( ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ! [SY253: $i] :
              ( ( ( sdtasdt0 @ SV371 @ SY253 )
               != xb )
              | ~ ( aElement0 @ SY253 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2998]) ).

thf(3025,plain,
    ! [SV372: $i] :
      ( ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV372 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2999]) ).

thf(3026,plain,
    ! [SV373: $i] :
      ( ( ( ~ ( aElement0 @ SV373 ) )
        = $true )
      | ( ( ! [SY254: $i] :
              ( ( ( sdtasdt0 @ SV373 @ SY254 )
               != xa )
              | ~ ( aElement0 @ SY254 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3000]) ).

thf(3027,plain,
    ! [SV374: $i] :
      ( ( ( ~ ( aElement0 @ SV374 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV374 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV374 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3001]) ).

thf(3028,plain,
    ! [SV383: $i] :
      ( ( ~ ( aElement0 @ SV383 )
        | ! [SY262: $i] :
            ( ( ( sdtasdt0 @ SV383 @ SY262 )
             != xa )
            | ~ ( aElement0 @ SY262 ) )
        | ! [SY263: $i] :
            ( ( ( sdtasdt0 @ SV383 @ SY263 )
             != xb )
            | ~ ( aElement0 @ SY263 ) )
        | ( doDivides0 @ SV383 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3002]) ).

thf(3029,plain,
    ! [SV384: $i] :
      ( ( ~ ( aElement0 @ SV384 )
        | ~ ( doDivides0 @ SV384 @ xa )
        | ! [SY264: $i] :
            ( ( ( sdtasdt0 @ SV384 @ SY264 )
             != xb )
            | ~ ( aElement0 @ SY264 ) )
        | ( doDivides0 @ SV384 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3003]) ).

thf(3030,plain,
    ! [SV385: $i] :
      ( ( ~ ( aElement0 @ SV385 )
        | ! [SY265: $i] :
            ( ( ( sdtasdt0 @ SV385 @ SY265 )
             != xa )
            | ~ ( aElement0 @ SY265 ) )
        | ~ ( doDivides0 @ SV385 @ xb )
        | ( doDivides0 @ SV385 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3004]) ).

thf(3031,plain,
    ! [SV386: $i] :
      ( ( ~ ( aElement0 @ SV386 )
        | ~ ( doDivides0 @ SV386 @ xa )
        | ~ ( doDivides0 @ SV386 @ xb )
        | ( doDivides0 @ SV386 @ xc ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3005]) ).

thf(3032,plain,
    ! [SV375: $i] :
      ( ( ( aDivisorOf0 @ SV375 @ xa )
        = $false )
      | ( ( ! [SY255: $i] :
              ( ( ( sdtasdt0 @ SV375 @ SY255 )
               != xb )
              | ~ ( aElement0 @ SY255 ) ) )
        = $true )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3006]) ).

thf(3033,plain,
    ! [SV376: $i] :
      ( ( ( aDivisorOf0 @ SV376 @ xa )
        = $false )
      | ( ( ~ ( doDivides0 @ SV376 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV376 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3007]) ).

thf(3034,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) )
      | ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3008]) ).

thf(3035,plain,
    ! [SV377: $i] :
      ( ( ( ~ ( aElementOf0 @ SV377 @ xI ) )
        = $true )
      | ( ( ! [SY256: $i] :
              ( ~ ( aElementOf0 @ SY256 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SY256 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3010]) ).

thf(3036,plain,
    ! [SV378: $i] :
      ( ( ( ~ ( aElementOf0 @ SV378 @ xI ) )
        = $true )
      | ( ( ! [SY257: $i] :
              ( ~ ( aElement0 @ SY257 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY257 @ SV378 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3011]) ).

thf(3037,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( aElement0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) )
        = $true )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3014]) ).

thf(3038,plain,
    ! [SV318: $i,SV331: $i,SV358: $i,SV362: $i] :
      ( ( ( sdteqdtlpzmzozddtrp0 @ ( sK3_W4 @ SV362 @ SV358 @ SV331 @ SV318 ) @ SV358 @ SV318 )
        = $true )
      | ( ( aElement0 @ SV358 )
        = $false )
      | ( ( aElement0 @ SV362 )
        = $false )
      | ( ( aElementOf0 @ ( sK4_W2 @ SV331 @ SV318 ) @ ( sdtpldt1 @ SV318 @ SV331 ) )
        = $false )
      | ( ( aIdeal0 @ SV318 )
        = $false )
      | ( ( aIdeal0 @ SV331 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3015]) ).

thf(3039,plain,
    ! [SV369: $i] :
      ( ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ! [SY252: $i] :
              ( ( ( sdtasdt0 @ SV369 @ SY252 )
               != xa )
              | ~ ( aElement0 @ SY252 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3016]) ).

thf(3040,plain,
    ! [SV370: $i] :
      ( ( ( aElement0 @ SV370 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV370 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV370 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3017]) ).

thf(3041,plain,
    ! [SV379: $i] :
      ( ( ( ~ ( aElement0 @ SV379 )
          | ! [SY258: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY258 )
               != xa )
              | ~ ( aElement0 @ SY258 ) )
          | ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3018]) ).

thf(3042,plain,
    ! [SV380: $i] :
      ( ( ( ~ ( aElement0 @ SV380 )
          | ~ ( doDivides0 @ SV380 @ xa )
          | ! [SY260: $i] :
              ( ( ( sdtasdt0 @ SV380 @ SY260 )
               != xb )
              | ~ ( aElement0 @ SY260 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3019]) ).

thf(3043,plain,
    ! [SV381: $i] :
      ( ( ( ~ ( aElement0 @ SV381 )
          | ! [SY261: $i] :
              ( ( ( sdtasdt0 @ SV381 @ SY261 )
               != xa )
              | ~ ( aElement0 @ SY261 ) )
          | ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3020]) ).

thf(3044,plain,
    ! [SV382: $i] :
      ( ( ( ~ ( aElement0 @ SV382 )
          | ~ ( doDivides0 @ SV382 @ xa )
          | ~ ( doDivides0 @ SV382 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3021]) ).

thf(3045,plain,
    ! [SV366: $i] :
      ( ( ( ( sdtasdt0 @ SV366 @ ( sK15_W1 @ SV366 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3022]) ).

thf(3046,plain,
    ! [SV366: $i] :
      ( ( ( aElement0 @ ( sK15_W1 @ SV366 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV366 @ xa )
        = $false )
      | ( ( aDivisorOf0 @ SV366 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3023]) ).

thf(3047,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( ( sdtasdt0 @ SV371 @ SV387 )
           != xb )
          | ~ ( aElement0 @ SV387 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3024]) ).

thf(3048,plain,
    ! [SV372: $i] :
      ( ( ( doDivides0 @ SV372 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
               != xc )
              | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3025]) ).

thf(3049,plain,
    ! [SV373: $i] :
      ( ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ! [SY254: $i] :
              ( ( ( sdtasdt0 @ SV373 @ SY254 )
               != xa )
              | ~ ( aElement0 @ SY254 ) ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3026]) ).

thf(3050,plain,
    ! [SV374: $i] :
      ( ( ( aElement0 @ SV374 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV374 @ xa ) )
        = $true )
      | ( ( ~ ( aDivisorOf0 @ SV374 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3027]) ).

thf(3051,plain,
    ! [SV383: $i] :
      ( ( ( ~ ( aElement0 @ SV383 )
          | ! [SY262: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY262 )
               != xa )
              | ~ ( aElement0 @ SY262 ) )
          | ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3028]) ).

thf(3052,plain,
    ! [SV384: $i] :
      ( ( ( ~ ( aElement0 @ SV384 )
          | ~ ( doDivides0 @ SV384 @ xa )
          | ! [SY264: $i] :
              ( ( ( sdtasdt0 @ SV384 @ SY264 )
               != xb )
              | ~ ( aElement0 @ SY264 ) ) )
        = $true )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3029]) ).

thf(3053,plain,
    ! [SV385: $i] :
      ( ( ( ~ ( aElement0 @ SV385 )
          | ! [SY265: $i] :
              ( ( ( sdtasdt0 @ SV385 @ SY265 )
               != xa )
              | ~ ( aElement0 @ SY265 ) )
          | ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3030]) ).

thf(3054,plain,
    ! [SV386: $i] :
      ( ( ( ~ ( aElement0 @ SV386 )
          | ~ ( doDivides0 @ SV386 @ xa )
          | ~ ( doDivides0 @ SV386 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3031]) ).

thf(3055,plain,
    ! [SV388: $i,SV375: $i] :
      ( ( ( ( ( sdtasdt0 @ SV375 @ SV388 )
           != xb )
          | ~ ( aElement0 @ SV388 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV375 @ xa )
        = $false )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3032]) ).

thf(3056,plain,
    ! [SV376: $i] :
      ( ( ( doDivides0 @ SV376 @ xb )
        = $false )
      | ( ( aDivisorOf0 @ SV376 @ xa )
        = $false )
      | ( ( doDivides0 @ SV376 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3033]) ).

thf(3057,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                   != xa )
                  | ~ ( aElement0 @ sK12_W0 ) )
            | ~ ( aElement0 @ xc ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3034]) ).

thf(3058,plain,
    ( ( ~ ( doDivides0 @ xc @ xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3034]) ).

thf(3059,plain,
    ! [SV377: $i] :
      ( ( ( aElementOf0 @ SV377 @ xI )
        = $false )
      | ( ( ! [SY256: $i] :
              ( ~ ( aElementOf0 @ SY256 @ xI )
              | ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SY256 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3035]) ).

thf(3060,plain,
    ! [SV378: $i] :
      ( ( ( aElementOf0 @ SV378 @ xI )
        = $false )
      | ( ( ! [SY257: $i] :
              ( ~ ( aElement0 @ SY257 )
              | ( aElementOf0 @ ( sdtasdt0 @ SY257 @ SV378 ) @ xI ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3036]) ).

thf(3061,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( ( sdtasdt0 @ SV369 @ SV389 )
           != xa )
          | ~ ( aElement0 @ SV389 ) )
        = $true )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3039]) ).

thf(3062,plain,
    ! [SV370: $i] :
      ( ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV370 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3040]) ).

thf(3063,plain,
    ! [SV379: $i] :
      ( ( ( ~ ( aElement0 @ SV379 )
          | ! [SY258: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY258 )
               != xa )
              | ~ ( aElement0 @ SY258 ) ) )
        = $true )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3041]) ).

thf(3064,plain,
    ! [SV380: $i] :
      ( ( ( ~ ( aElement0 @ SV380 )
          | ~ ( doDivides0 @ SV380 @ xa ) )
        = $true )
      | ( ( ! [SY260: $i] :
              ( ( ( sdtasdt0 @ SV380 @ SY260 )
               != xb )
              | ~ ( aElement0 @ SY260 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3042]) ).

thf(3065,plain,
    ! [SV381: $i] :
      ( ( ( ~ ( aElement0 @ SV381 )
          | ! [SY261: $i] :
              ( ( ( sdtasdt0 @ SV381 @ SY261 )
               != xa )
              | ~ ( aElement0 @ SY261 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3043]) ).

thf(3066,plain,
    ! [SV382: $i] :
      ( ( ( ~ ( aElement0 @ SV382 )
          | ~ ( doDivides0 @ SV382 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV382 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3044]) ).

thf(3067,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( ( sdtasdt0 @ SV371 @ SV387 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV387 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3047]) ).

thf(3068,plain,
    ! [SV372: $i] :
      ( ( ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
           != xc )
          | ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( doDivides0 @ SV372 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3048]) ).

thf(3069,plain,
    ! [SV390: $i,SV373: $i] :
      ( ( ( ( ( sdtasdt0 @ SV373 @ SV390 )
           != xa )
          | ~ ( aElement0 @ SV390 ) )
        = $true )
      | ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3049]) ).

thf(3070,plain,
    ! [SV374: $i] :
      ( ( ( doDivides0 @ SV374 @ xa )
        = $false )
      | ( ( aElement0 @ SV374 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV374 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3050]) ).

thf(3071,plain,
    ! [SV383: $i] :
      ( ( ( ~ ( aElement0 @ SV383 )
          | ! [SY262: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY262 )
               != xa )
              | ~ ( aElement0 @ SY262 ) ) )
        = $true )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3051]) ).

thf(3072,plain,
    ! [SV384: $i] :
      ( ( ( ~ ( aElement0 @ SV384 )
          | ~ ( doDivides0 @ SV384 @ xa ) )
        = $true )
      | ( ( ! [SY264: $i] :
              ( ( ( sdtasdt0 @ SV384 @ SY264 )
               != xb )
              | ~ ( aElement0 @ SY264 ) ) )
        = $true )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3052]) ).

thf(3073,plain,
    ! [SV385: $i] :
      ( ( ( ~ ( aElement0 @ SV385 )
          | ! [SY265: $i] :
              ( ( ( sdtasdt0 @ SV385 @ SY265 )
               != xa )
              | ~ ( aElement0 @ SY265 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3053]) ).

thf(3074,plain,
    ! [SV386: $i] :
      ( ( ( ~ ( aElement0 @ SV386 )
          | ~ ( doDivides0 @ SV386 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV386 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3054]) ).

thf(3075,plain,
    ! [SV388: $i,SV375: $i] :
      ( ( ( ( ( sdtasdt0 @ SV375 @ SV388 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV388 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV375 @ xa )
        = $false )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3055]) ).

thf(3076,plain,
    ( ( ~ ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
                 != xa )
                | ~ ( aElement0 @ sK12_W0 ) )
          | ~ ( aElement0 @ xc ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3057]) ).

thf(3077,plain,
    ( ( doDivides0 @ xc @ xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3058]) ).

thf(3078,plain,
    ! [SV377: $i,SV391: $i] :
      ( ( ( ~ ( aElementOf0 @ SV391 @ xI )
          | ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SV391 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV377 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3059]) ).

thf(3079,plain,
    ! [SV378: $i,SV392: $i] :
      ( ( ( ~ ( aElement0 @ SV392 )
          | ( aElementOf0 @ ( sdtasdt0 @ SV392 @ SV378 ) @ xI ) )
        = $true )
      | ( ( aElementOf0 @ SV378 @ xI )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3060]) ).

thf(3080,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( ( sdtasdt0 @ SV369 @ SV389 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV389 ) )
        = $true )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3061]) ).

thf(3081,plain,
    ! [SV370: $i] :
      ( ( ( aDivisorOf0 @ SV370 @ xb )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
               != xc )
              | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3062]) ).

thf(3082,plain,
    ! [SV379: $i] :
      ( ( ( ~ ( aElement0 @ SV379 ) )
        = $true )
      | ( ( ! [SY258: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY258 )
               != xa )
              | ~ ( aElement0 @ SY258 ) ) )
        = $true )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3063]) ).

thf(3083,plain,
    ! [SV380: $i] :
      ( ( ( ~ ( aElement0 @ SV380 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV380 @ xa ) )
        = $true )
      | ( ( ! [SY260: $i] :
              ( ( ( sdtasdt0 @ SV380 @ SY260 )
               != xb )
              | ~ ( aElement0 @ SY260 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3064]) ).

thf(3084,plain,
    ! [SV381: $i] :
      ( ( ( ~ ( aElement0 @ SV381 ) )
        = $true )
      | ( ( ! [SY261: $i] :
              ( ( ( sdtasdt0 @ SV381 @ SY261 )
               != xa )
              | ~ ( aElement0 @ SY261 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3065]) ).

thf(3085,plain,
    ! [SV382: $i] :
      ( ( ( ~ ( aElement0 @ SV382 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV382 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV382 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3066]) ).

thf(3086,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV387 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3067]) ).

thf(3087,plain,
    ! [SV372: $i] :
      ( ( ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( doDivides0 @ SV372 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3068]) ).

thf(3088,plain,
    ! [SV372: $i] :
      ( ( ( ~ ( aElement0 @ ( sK13_W1 @ SV372 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( doDivides0 @ SV372 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3068]) ).

thf(3089,plain,
    ! [SV390: $i,SV373: $i] :
      ( ( ( ( ( sdtasdt0 @ SV373 @ SV390 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV390 ) )
        = $true )
      | ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3069]) ).

thf(3090,plain,
    ! [SV374: $i] :
      ( ( ( aDivisorOf0 @ SV374 @ xb )
        = $false )
      | ( ( aElement0 @ SV374 )
        = $false )
      | ( ( doDivides0 @ SV374 @ xa )
        = $false )
      | ( ( doDivides0 @ SV374 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3070]) ).

thf(3091,plain,
    ! [SV383: $i] :
      ( ( ( ~ ( aElement0 @ SV383 ) )
        = $true )
      | ( ( ! [SY262: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY262 )
               != xa )
              | ~ ( aElement0 @ SY262 ) ) )
        = $true )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3071]) ).

thf(3092,plain,
    ! [SV384: $i] :
      ( ( ( ~ ( aElement0 @ SV384 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV384 @ xa ) )
        = $true )
      | ( ( ! [SY264: $i] :
              ( ( ( sdtasdt0 @ SV384 @ SY264 )
               != xb )
              | ~ ( aElement0 @ SY264 ) ) )
        = $true )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3072]) ).

thf(3093,plain,
    ! [SV385: $i] :
      ( ( ( ~ ( aElement0 @ SV385 ) )
        = $true )
      | ( ( ! [SY265: $i] :
              ( ( ( sdtasdt0 @ SV385 @ SY265 )
               != xa )
              | ~ ( aElement0 @ SY265 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3073]) ).

thf(3094,plain,
    ! [SV386: $i] :
      ( ( ( ~ ( aElement0 @ SV386 ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV386 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV386 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3074]) ).

thf(3095,plain,
    ! [SV388: $i,SV375: $i] :
      ( ( ( ( sdtasdt0 @ SV375 @ SV388 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV388 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV375 @ xa )
        = $false )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3075]) ).

thf(3096,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) )
      | ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3076]) ).

thf(3097,plain,
    ! [SV377: $i,SV391: $i] :
      ( ( ( ~ ( aElementOf0 @ SV391 @ xI ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SV391 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV377 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3078]) ).

thf(3098,plain,
    ! [SV378: $i,SV392: $i] :
      ( ( ( ~ ( aElement0 @ SV392 ) )
        = $true )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV392 @ SV378 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV378 @ xI )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3079]) ).

thf(3099,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV389 ) )
        = $true )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3080]) ).

thf(3100,plain,
    ! [SV370: $i] :
      ( ( ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
           != xc )
          | ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) )
        = $false )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( aDivisorOf0 @ SV370 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3081]) ).

thf(3101,plain,
    ! [SV379: $i] :
      ( ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ! [SY258: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY258 )
               != xa )
              | ~ ( aElement0 @ SY258 ) ) )
        = $true )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3082]) ).

thf(3102,plain,
    ! [SV380: $i] :
      ( ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV380 @ xa ) )
        = $true )
      | ( ( ! [SY260: $i] :
              ( ( ( sdtasdt0 @ SV380 @ SY260 )
               != xb )
              | ~ ( aElement0 @ SY260 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3083]) ).

thf(3103,plain,
    ! [SV381: $i] :
      ( ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ! [SY261: $i] :
              ( ( ( sdtasdt0 @ SV381 @ SY261 )
               != xa )
              | ~ ( aElement0 @ SY261 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3084]) ).

thf(3104,plain,
    ! [SV382: $i] :
      ( ( ( aElement0 @ SV382 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV382 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV382 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3085]) ).

thf(3105,plain,
    ! [SV371: $i,SV387: $i] :
      ( ( ( aElement0 @ SV387 )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
               != xc )
              | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3086]) ).

thf(3106,plain,
    ! [SV372: $i] :
      ( ( ( ( sdtasdt0 @ SV372 @ ( sK13_W1 @ SV372 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( doDivides0 @ SV372 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3087]) ).

thf(3107,plain,
    ! [SV372: $i] :
      ( ( ( aElement0 @ ( sK13_W1 @ SV372 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV372 @ xa )
        = $false )
      | ( ( doDivides0 @ SV372 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3088]) ).

thf(3108,plain,
    ! [SV390: $i,SV373: $i] :
      ( ( ( ( sdtasdt0 @ SV373 @ SV390 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV390 ) )
        = $true )
      | ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3089]) ).

thf(3109,plain,
    ! [SV383: $i] :
      ( ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ! [SY262: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY262 )
               != xa )
              | ~ ( aElement0 @ SY262 ) ) )
        = $true )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3091]) ).

thf(3110,plain,
    ! [SV384: $i] :
      ( ( ( aElement0 @ SV384 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV384 @ xa ) )
        = $true )
      | ( ( ! [SY264: $i] :
              ( ( ( sdtasdt0 @ SV384 @ SY264 )
               != xb )
              | ~ ( aElement0 @ SY264 ) ) )
        = $true )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3092]) ).

thf(3111,plain,
    ! [SV385: $i] :
      ( ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ! [SY265: $i] :
              ( ( ( sdtasdt0 @ SV385 @ SY265 )
               != xa )
              | ~ ( aElement0 @ SY265 ) ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3093]) ).

thf(3112,plain,
    ! [SV386: $i] :
      ( ( ( aElement0 @ SV386 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV386 @ xa ) )
        = $true )
      | ( ( ~ ( doDivides0 @ SV386 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3094]) ).

thf(3113,plain,
    ! [SV375: $i,SV388: $i] :
      ( ( ( aElement0 @ SV388 )
        = $false )
      | ( ( ( sdtasdt0 @ SV375 @ SV388 )
          = xb )
        = $false )
      | ( ( aDivisorOf0 @ SV375 @ xa )
        = $false )
      | ( ( doDivides0 @ SV375 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3095]) ).

thf(3114,plain,
    ( ( ~ ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
             != xa )
            | ~ ( aElement0 @ sK12_W0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3096]) ).

thf(3115,plain,
    ( ( ~ ( aElement0 @ xc ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3096]) ).

thf(3116,plain,
    ! [SV377: $i,SV391: $i] :
      ( ( ( aElementOf0 @ SV391 @ xI )
        = $false )
      | ( ( aElementOf0 @ ( sdtpldt0 @ SV377 @ SV391 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV377 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3097]) ).

thf(3117,plain,
    ! [SV378: $i,SV392: $i] :
      ( ( ( aElement0 @ SV392 )
        = $false )
      | ( ( aElementOf0 @ ( sdtasdt0 @ SV392 @ SV378 ) @ xI )
        = $true )
      | ( ( aElementOf0 @ SV378 @ xI )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3098]) ).

thf(3118,plain,
    ! [SV369: $i,SV389: $i] :
      ( ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV369 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3099]) ).

thf(3119,plain,
    ! [SV370: $i] :
      ( ( ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( aDivisorOf0 @ SV370 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3100]) ).

thf(3120,plain,
    ! [SV370: $i] :
      ( ( ( ~ ( aElement0 @ ( sK20_W1 @ SV370 ) ) )
        = $false )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( aDivisorOf0 @ SV370 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3100]) ).

thf(3121,plain,
    ! [SV393: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ SV393 )
           != xa )
          | ~ ( aElement0 @ SV393 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3101]) ).

thf(3122,plain,
    ! [SV380: $i] :
      ( ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ! [SY260: $i] :
              ( ( ( sdtasdt0 @ SV380 @ SY260 )
               != xb )
              | ~ ( aElement0 @ SY260 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3102]) ).

thf(3123,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( ( sdtasdt0 @ SV381 @ SV394 )
           != xa )
          | ~ ( aElement0 @ SV394 ) )
        = $true )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3103]) ).

thf(3124,plain,
    ! [SV382: $i] :
      ( ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV382 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3104]) ).

thf(3125,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
           != xc )
          | ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV387 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3105]) ).

thf(3126,plain,
    ! [SV373: $i,SV390: $i] :
      ( ( ( aElement0 @ SV390 )
        = $false )
      | ( ( ( sdtasdt0 @ SV373 @ SV390 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ~ ( aDivisorOf0 @ SV373 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3108]) ).

thf(3127,plain,
    ! [SV395: $i,SV383: $i] :
      ( ( ( ( ( sdtasdt0 @ SV383 @ SV395 )
           != xa )
          | ~ ( aElement0 @ SV395 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3109]) ).

thf(3128,plain,
    ! [SV384: $i] :
      ( ( ( doDivides0 @ SV384 @ xa )
        = $false )
      | ( ( aElement0 @ SV384 )
        = $false )
      | ( ( ! [SY264: $i] :
              ( ( ( sdtasdt0 @ SV384 @ SY264 )
               != xb )
              | ~ ( aElement0 @ SY264 ) ) )
        = $true )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3110]) ).

thf(3129,plain,
    ! [SV396: $i,SV385: $i] :
      ( ( ( ( ( sdtasdt0 @ SV385 @ SV396 )
           != xa )
          | ~ ( aElement0 @ SV396 ) )
        = $true )
      | ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3111]) ).

thf(3130,plain,
    ! [SV386: $i] :
      ( ( ( doDivides0 @ SV386 @ xa )
        = $false )
      | ( ( aElement0 @ SV386 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV386 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3112]) ).

thf(3131,plain,
    ( ( ~ ( ( ( sdtasdt0 @ xc @ sK12_W0 )
           != xa )
          | ~ ( aElement0 @ sK12_W0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3114]) ).

thf(3132,plain,
    ( ( aElement0 @ xc )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3115]) ).

thf(3133,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( aDivisorOf0 @ SV369 @ xb )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
               != xc )
              | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3118]) ).

thf(3134,plain,
    ! [SV370: $i] :
      ( ( ( ( sdtasdt0 @ SV370 @ ( sK20_W1 @ SV370 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( aDivisorOf0 @ SV370 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3119]) ).

thf(3135,plain,
    ! [SV370: $i] :
      ( ( ( aElement0 @ ( sK20_W1 @ SV370 ) )
        = $true )
      | ( ( doDivides0 @ SV370 @ xa )
        = $false )
      | ( ( aElement0 @ SV370 )
        = $false )
      | ( ( aDivisorOf0 @ SV370 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3120]) ).

thf(3136,plain,
    ! [SV393: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ SV393 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV393 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3121]) ).

thf(3137,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( ( sdtasdt0 @ SV380 @ SV397 )
           != xb )
          | ~ ( aElement0 @ SV397 ) )
        = $true )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3122]) ).

thf(3138,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( ( sdtasdt0 @ SV381 @ SV394 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV394 ) )
        = $true )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3123]) ).

thf(3139,plain,
    ! [SV382: $i] :
      ( ( ( doDivides0 @ SV382 @ xb )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
               != xc )
              | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3124]) ).

thf(3140,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
           != xc ) )
        = $false )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV387 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3125]) ).

thf(3141,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ~ ( aElement0 @ ( sK14_W1 @ SV371 ) ) )
        = $false )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV387 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3125]) ).

thf(3142,plain,
    ! [SV390: $i,SV373: $i] :
      ( ( ( aDivisorOf0 @ SV373 @ xb )
        = $false )
      | ( ( aElement0 @ SV373 )
        = $false )
      | ( ( ( sdtasdt0 @ SV373 @ SV390 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV390 )
        = $false )
      | ( ( doDivides0 @ SV373 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3126]) ).

thf(3143,plain,
    ! [SV395: $i,SV383: $i] :
      ( ( ( ( ( sdtasdt0 @ SV383 @ SV395 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV395 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3127]) ).

thf(3144,plain,
    ! [SV398: $i,SV384: $i] :
      ( ( ( ( ( sdtasdt0 @ SV384 @ SV398 )
           != xb )
          | ~ ( aElement0 @ SV398 ) )
        = $true )
      | ( ( aElement0 @ SV384 )
        = $false )
      | ( ( doDivides0 @ SV384 @ xa )
        = $false )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3128]) ).

thf(3145,plain,
    ! [SV396: $i,SV385: $i] :
      ( ( ( ( ( sdtasdt0 @ SV385 @ SV396 )
           != xa ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV396 ) )
        = $true )
      | ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3129]) ).

thf(3146,plain,
    ! [SV386: $i] :
      ( ( ( doDivides0 @ SV386 @ xb )
        = $false )
      | ( ( aElement0 @ SV386 )
        = $false )
      | ( ( doDivides0 @ SV386 @ xa )
        = $false )
      | ( ( doDivides0 @ SV386 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3130]) ).

thf(3147,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa )
      | ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3131]) ).

thf(3148,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
           != xc )
          | ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) )
        = $false )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( aDivisorOf0 @ SV369 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3133]) ).

thf(3149,plain,
    ! [SV393: $i,SV379: $i] :
      ( ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV393 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3136]) ).

thf(3150,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( ( sdtasdt0 @ SV380 @ SV397 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV397 ) )
        = $true )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3137]) ).

thf(3151,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV394 ) )
        = $true )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3138]) ).

thf(3152,plain,
    ! [SV382: $i] :
      ( ( ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
           != xc )
          | ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) )
        = $false )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3139]) ).

thf(3153,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( ( sdtasdt0 @ SV371 @ ( sK14_W1 @ SV371 ) )
          = xc )
        = $true )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV387 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3140]) ).

thf(3154,plain,
    ! [SV387: $i,SV371: $i] :
      ( ( ( aElement0 @ ( sK14_W1 @ SV371 ) )
        = $true )
      | ( ( aDivisorOf0 @ SV371 @ xa )
        = $false )
      | ( ( ( sdtasdt0 @ SV371 @ SV387 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV387 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3141]) ).

thf(3155,plain,
    ! [SV395: $i,SV383: $i] :
      ( ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV395 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3143]) ).

thf(3156,plain,
    ! [SV398: $i,SV384: $i] :
      ( ( ( ( ( sdtasdt0 @ SV384 @ SV398 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV398 ) )
        = $true )
      | ( ( aElement0 @ SV384 )
        = $false )
      | ( ( doDivides0 @ SV384 @ xa )
        = $false )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3144]) ).

thf(3157,plain,
    ! [SV396: $i,SV385: $i] :
      ( ( ( ( sdtasdt0 @ SV385 @ SV396 )
          = xa )
        = $false )
      | ( ( ~ ( aElement0 @ SV396 ) )
        = $true )
      | ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3145]) ).

thf(3158,plain,
    ( ( ( ( sdtasdt0 @ xc @ sK12_W0 )
       != xa ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3147]) ).

thf(3159,plain,
    ( ( ~ ( aElement0 @ sK12_W0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3147]) ).

thf(3160,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( aDivisorOf0 @ SV369 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3148]) ).

thf(3161,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ~ ( aElement0 @ ( sK21_W1 @ SV369 ) ) )
        = $false )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( aDivisorOf0 @ SV369 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3148]) ).

thf(3162,plain,
    ! [SV379: $i,SV393: $i] :
      ( ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ! [SY259: $i] :
              ( ( ( sdtasdt0 @ SV379 @ SY259 )
               != xb )
              | ~ ( aElement0 @ SY259 ) ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3149]) ).

thf(3163,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV397 ) )
        = $true )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3150]) ).

thf(3164,plain,
    ! [SV381: $i,SV394: $i] :
      ( ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV381 @ xb ) )
        = $true )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3151]) ).

thf(3165,plain,
    ! [SV382: $i] :
      ( ( ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3152]) ).

thf(3166,plain,
    ! [SV382: $i] :
      ( ( ( ~ ( aElement0 @ ( sK16_W1 @ SV382 ) ) )
        = $false )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3152]) ).

thf(3167,plain,
    ! [SV383: $i,SV395: $i] :
      ( ( ( aElement0 @ SV395 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ! [SY263: $i] :
              ( ( ( sdtasdt0 @ SV383 @ SY263 )
               != xb )
              | ~ ( aElement0 @ SY263 ) ) )
        = $true )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3155]) ).

thf(3168,plain,
    ! [SV398: $i,SV384: $i] :
      ( ( ( ( sdtasdt0 @ SV384 @ SV398 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV398 ) )
        = $true )
      | ( ( aElement0 @ SV384 )
        = $false )
      | ( ( doDivides0 @ SV384 @ xa )
        = $false )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3156]) ).

thf(3169,plain,
    ! [SV385: $i,SV396: $i] :
      ( ( ( aElement0 @ SV396 )
        = $false )
      | ( ( ( sdtasdt0 @ SV385 @ SV396 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ~ ( doDivides0 @ SV385 @ xb ) )
        = $true )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3157]) ).

thf(3170,plain,
    ( ( ( sdtasdt0 @ xc @ sK12_W0 )
      = xa )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3158]) ).

thf(3171,plain,
    ( ( aElement0 @ sK12_W0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3159]) ).

thf(3172,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( ( sdtasdt0 @ SV369 @ ( sK21_W1 @ SV369 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( aDivisorOf0 @ SV369 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3160]) ).

thf(3173,plain,
    ! [SV389: $i,SV369: $i] :
      ( ( ( aElement0 @ ( sK21_W1 @ SV369 ) )
        = $true )
      | ( ( aElement0 @ SV389 )
        = $false )
      | ( ( ( sdtasdt0 @ SV369 @ SV389 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV369 )
        = $false )
      | ( ( aDivisorOf0 @ SV369 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3161]) ).

thf(3174,plain,
    ! [SV393: $i,SV399: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ SV399 )
           != xb )
          | ~ ( aElement0 @ SV399 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3162]) ).

thf(3175,plain,
    ! [SV380: $i,SV397: $i] :
      ( ( ( aElement0 @ SV397 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
               != xc )
              | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3163]) ).

thf(3176,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( doDivides0 @ SV381 @ xb )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
               != xc )
              | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3164]) ).

thf(3177,plain,
    ! [SV382: $i] :
      ( ( ( ( sdtasdt0 @ SV382 @ ( sK16_W1 @ SV382 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3165]) ).

thf(3178,plain,
    ! [SV382: $i] :
      ( ( ( aElement0 @ ( sK16_W1 @ SV382 ) )
        = $true )
      | ( ( doDivides0 @ SV382 @ xa )
        = $false )
      | ( ( aElement0 @ SV382 )
        = $false )
      | ( ( doDivides0 @ SV382 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3166]) ).

thf(3179,plain,
    ! [SV395: $i,SV400: $i,SV383: $i] :
      ( ( ( ( ( sdtasdt0 @ SV383 @ SV400 )
           != xb )
          | ~ ( aElement0 @ SV400 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV395 )
        = $false )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3167]) ).

thf(3180,plain,
    ! [SV384: $i,SV398: $i] :
      ( ( ( aElement0 @ SV398 )
        = $false )
      | ( ( ( sdtasdt0 @ SV384 @ SV398 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV384 )
        = $false )
      | ( ( doDivides0 @ SV384 @ xa )
        = $false )
      | ( ( doDivides0 @ SV384 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3168]) ).

thf(3181,plain,
    ! [SV396: $i,SV385: $i] :
      ( ( ( doDivides0 @ SV385 @ xb )
        = $false )
      | ( ( aElement0 @ SV385 )
        = $false )
      | ( ( ( sdtasdt0 @ SV385 @ SV396 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV396 )
        = $false )
      | ( ( doDivides0 @ SV385 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3169]) ).

thf(3182,plain,
    ! [SV393: $i,SV399: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ SV399 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV399 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3174]) ).

thf(3183,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
           != xc )
          | ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV397 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3175]) ).

thf(3184,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
           != xc )
          | ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) )
        = $false )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( doDivides0 @ SV381 @ xb )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3176]) ).

thf(3185,plain,
    ! [SV395: $i,SV400: $i,SV383: $i] :
      ( ( ( ( ( sdtasdt0 @ SV383 @ SV400 )
           != xb ) )
        = $true )
      | ( ( ~ ( aElement0 @ SV400 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV395 )
        = $false )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3179]) ).

thf(3186,plain,
    ! [SV393: $i,SV399: $i,SV379: $i] :
      ( ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV399 ) )
        = $true )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3182]) ).

thf(3187,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
           != xc ) )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV397 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3183]) ).

thf(3188,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ~ ( aElement0 @ ( sK18_W1 @ SV380 ) ) )
        = $false )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV397 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3183]) ).

thf(3189,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( doDivides0 @ SV381 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3184]) ).

thf(3190,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ~ ( aElement0 @ ( sK17_W1 @ SV381 ) ) )
        = $false )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( doDivides0 @ SV381 @ xb )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3184]) ).

thf(3191,plain,
    ! [SV395: $i,SV400: $i,SV383: $i] :
      ( ( ( ( sdtasdt0 @ SV383 @ SV400 )
          = xb )
        = $false )
      | ( ( ~ ( aElement0 @ SV400 ) )
        = $true )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV395 )
        = $false )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3185]) ).

thf(3192,plain,
    ! [SV393: $i,SV379: $i,SV399: $i] :
      ( ( ( aElement0 @ SV399 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ~ ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
               != xc )
              | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3186]) ).

thf(3193,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( ( sdtasdt0 @ SV380 @ ( sK18_W1 @ SV380 ) )
          = xc )
        = $true )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV397 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3187]) ).

thf(3194,plain,
    ! [SV397: $i,SV380: $i] :
      ( ( ( aElement0 @ ( sK18_W1 @ SV380 ) )
        = $true )
      | ( ( doDivides0 @ SV380 @ xa )
        = $false )
      | ( ( aElement0 @ SV380 )
        = $false )
      | ( ( ( sdtasdt0 @ SV380 @ SV397 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV397 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3188]) ).

thf(3195,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( ( sdtasdt0 @ SV381 @ ( sK17_W1 @ SV381 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( doDivides0 @ SV381 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3189]) ).

thf(3196,plain,
    ! [SV394: $i,SV381: $i] :
      ( ( ( aElement0 @ ( sK17_W1 @ SV381 ) )
        = $true )
      | ( ( aElement0 @ SV394 )
        = $false )
      | ( ( ( sdtasdt0 @ SV381 @ SV394 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV381 )
        = $false )
      | ( ( doDivides0 @ SV381 @ xb )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3190]) ).

thf(3197,plain,
    ! [SV395: $i,SV383: $i,SV400: $i] :
      ( ( ( aElement0 @ SV400 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV400 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV383 )
        = $false )
      | ( ( ( sdtasdt0 @ SV383 @ SV395 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV395 )
        = $false )
      | ( ( doDivides0 @ SV383 @ xc )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3191]) ).

thf(3198,plain,
    ! [SV399: $i,SV393: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
           != xc )
          | ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV399 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3192]) ).

thf(3199,plain,
    ! [SV399: $i,SV393: $i,SV379: $i] :
      ( ( ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
           != xc ) )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV399 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3198]) ).

thf(3200,plain,
    ! [SV399: $i,SV393: $i,SV379: $i] :
      ( ( ( ~ ( aElement0 @ ( sK19_W1 @ SV379 ) ) )
        = $false )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV399 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3198]) ).

thf(3201,plain,
    ! [SV399: $i,SV393: $i,SV379: $i] :
      ( ( ( ( sdtasdt0 @ SV379 @ ( sK19_W1 @ SV379 ) )
          = xc )
        = $true )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV399 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3199]) ).

thf(3202,plain,
    ! [SV399: $i,SV393: $i,SV379: $i] :
      ( ( ( aElement0 @ ( sK19_W1 @ SV379 ) )
        = $true )
      | ( ( aElement0 @ SV393 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV393 )
          = xa )
        = $false )
      | ( ( aElement0 @ SV379 )
        = $false )
      | ( ( ( sdtasdt0 @ SV379 @ SV399 )
          = xb )
        = $false )
      | ( ( aElement0 @ SV399 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3200]) ).

thf(3203,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[2436,3202,3201,3197,3196,3195,3194,3193,3181,3180,3178,3177,3173,3172,3171,3170,3154,3153,3146,3142,3135,3134,3132,3117,3116,3113,3107,3106,3090,3077,3056,3046,3045,3038,3037,3013,3012,3009,2985,2984,2983,2978,2962,2937,2932,2931,2930,2911,2907,2906,2905,2904,2903,2902,2861,2851,2850,2838,2837,2834,2828,2810,2781,2779,2778,2777,2741,2722,2709,2708,2707,2685,2671,2670,2669,2668,2667,2666,2664,2663,2659,2658,2657,2656,2655,2654,2651,2649,2648,2647,2611,2595,2582,2570,2569,2566,2561,2548,2547,2493,2489,2488,2479,2437]) ).

thf(3204,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[3203,884,1657,2430]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG108+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon May 30 07:56:55 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.39  
% 0.20/0.39   No.of.Axioms: 33
% 0.20/0.39  
% 0.20/0.39   Length.of.Defs: 0
% 0.20/0.39  
% 0.20/0.39   Contains.Choice.Funs: false
% 0.20/0.42  .
% 0.20/0.43  (rf:0,axioms:33,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:0,translation:fof_full)................................................................................................................................................................................................................................
% 1.44/1.66  
% 1.44/1.66  ********************************
% 1.44/1.66  *   All subproblems solved!    *
% 1.44/1.66  ********************************
% 1.44/1.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:33,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3203,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.05/6.24  
% 6.05/6.24  %**** Beginning of derivation protocol ****
% 6.05/6.24  % SZS output start CNFRefutation
% See solution above
% 6.05/6.26  
% 6.05/6.26  %**** End of derivation protocol ****
% 6.05/6.26  %**** no. of clauses in derivation: 3204 ****
% 6.05/6.26  %**** clause counter: 3203 ****
% 6.05/6.26  
% 6.05/6.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:33,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3203,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------