TSTP Solution File: RNG047+2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG047+2 : 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 20:34:04 EDT 2022

% Result   : Theorem 0.40s 0.74s
% Output   : CNFRefutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   51
% Syntax   : Number of formulae    :  537 ( 281 unt;  17 typ;   0 def)
%            Number of atoms       : 4235 (1493 equ;   0 cnn)
%            Maximal formula atoms :    9 (   8 avg)
%            Number of connectives : 7745 (1467   ~;1488   |; 151   &;4549   @)
%                                         (   0 <=>;  90  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   6 con; 0-2 aty)
%            Number of variables   : 1184 (   0   ^1182   !;   2   ?;1184   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_aDimensionOf0,type,
    aDimensionOf0: $i > $i ).

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

thf(tp_aScalar0,type,
    aScalar0: $i > $o ).

thf(tp_aVector0,type,
    aVector0: $i > $o ).

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

thf(tp_sK1_W1,type,
    sK1_W1: $i > $i ).

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

thf(tp_sdtlbdtrb0,type,
    sdtlbdtrb0: $i > $i > $i ).

thf(tp_sdtlseqdt0,type,
    sdtlseqdt0: $i > $i > $o ).

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

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

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

thf(tp_sz0z00,type,
    sz0z00: $i ).

thf(tp_sziznziztdt0,type,
    sziznziztdt0: $i > $i ).

thf(tp_szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

thf(tp_xs,type,
    xs: $i ).

thf(tp_xt,type,
    xt: $i ).

thf(1,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aVector0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).

thf(2,axiom,
    ! [W0: $i] :
      ( ( aVector0 @ W0 )
     => ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).

thf(3,axiom,
    ! [W0: $i] :
      ( ( aVector0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).

thf(4,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
          & ( sdtlseqdt0 @ sz0z00 @ W1 )
          & ( ( sdtasdt0 @ W0 @ W0 )
            = ( sdtasdt0 @ W1 @ W1 ) ) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).

thf(5,axiom,
    ! [W0: $i] :
      ( ( aScalar0 @ W0 )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

thf(6,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
          & ( sdtlseqdt0 @ sz0z00 @ W1 ) )
       => ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) )
          & ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).

thf(7,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( sdtlseqdt0 @ W0 @ W1 )
        | ( sdtlseqdt0 @ W1 @ W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).

thf(8,axiom,
    ! [W0: $i,W1: $i,W2: $i,W3: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 )
        & ( aScalar0 @ W3 ) )
     => ( ( ( sdtlseqdt0 @ W0 @ W1 )
          & ( sdtlseqdt0 @ sz0z00 @ W2 )
          & ( sdtlseqdt0 @ W2 @ W3 ) )
       => ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).

thf(9,axiom,
    ! [W0: $i,W1: $i,W2: $i,W3: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 )
        & ( aScalar0 @ W3 ) )
     => ( ( ( sdtlseqdt0 @ W0 @ W1 )
          & ( sdtlseqdt0 @ W2 @ W3 ) )
       => ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).

thf(10,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 ) )
     => ( ( ( sdtlseqdt0 @ W0 @ W1 )
          & ( sdtlseqdt0 @ W1 @ W2 ) )
       => ( sdtlseqdt0 @ W0 @ W2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).

thf(11,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( ( sdtlseqdt0 @ W0 @ W1 )
          & ( sdtlseqdt0 @ W1 @ W0 ) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).

thf(12,axiom,
    ! [W0: $i] :
      ( ( aScalar0 @ W0 )
     => ( sdtlseqdt0 @ W0 @ W0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).

thf(13,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( sdtlseqdt0 @ W0 @ W1 )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).

thf(14,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
        = ( sdtasdt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).

thf(15,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
          = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) )
        & ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
          = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

thf(16,axiom,
    ! [W0: $i,W1: $i,W2: $i,W3: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 )
        & ( aScalar0 @ W3 ) )
     => ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
        = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).

thf(17,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 ) )
     => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
          = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).

thf(18,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 )
        & ( aScalar0 @ W2 ) )
     => ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
          = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
        & ( ( sdtpldt0 @ W0 @ W1 )
          = ( sdtpldt0 @ W1 @ W0 ) )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
          = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
        & ( ( sdtasdt0 @ W0 @ W1 )
          = ( sdtasdt0 @ W1 @ W0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

thf(19,axiom,
    ! [W0: $i] :
      ( ( aScalar0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ sz0z00 )
          = W0 )
        & ( ( sdtpldt0 @ sz0z00 @ W0 )
          = W0 )
        & ( ( sdtasdt0 @ W0 @ sz0z00 )
          = sz0z00 )
        & ( ( sdtasdt0 @ sz0z00 @ W0 )
          = sz0z00 )
        & ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
          = sz0z00 )
        & ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
          = sz0z00 )
        & ( ( smndt0 @ ( smndt0 @ W0 ) )
          = W0 )
        & ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

thf(20,axiom,
    ! [W0: $i] :
      ( ( aScalar0 @ W0 )
     => ( aScalar0 @ ( smndt0 @ W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

thf(21,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

thf(22,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aScalar0 @ W0 )
        & ( aScalar0 @ W1 ) )
     => ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

thf(23,axiom,
    aScalar0 @ sz0z00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

thf(24,axiom,
    ! [W0: $i] :
      ( ( aScalar0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).

thf(25,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).

thf(26,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( iLess0 @ W0 @ W1 )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).

thf(27,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( ( szszuzczcdt0 @ W0 )
          = ( szszuzczcdt0 @ W1 ) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).

thf(28,axiom,
    ! [W0: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( W0 != sz00 ) )
     => ? [W1: $i] :
          ( ( aNaturalNumber0 @ W1 )
          & ( W0
            = ( szszuzczcdt0 @ W1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).

thf(29,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
        & ( ( szszuzczcdt0 @ W0 )
         != sz00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).

thf(30,axiom,
    aNaturalNumber0 @ sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).

thf(31,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).

thf(32,axiom,
    ( ( ( aDimensionOf0 @ xs )
      = ( aDimensionOf0 @ xt ) )
    & ( ( aDimensionOf0 @ xt )
     != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).

thf(33,axiom,
    ( ( aVector0 @ xs )
    & ( aVector0 @ xt ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329) ).

thf(34,conjecture,
    ( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
      & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
        = ( aDimensionOf0 @ xs ) )
      & ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
            = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
   => ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
        & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
          = ( aDimensionOf0 @ xt ) )
        & ! [W0: $i] :
            ( ( aNaturalNumber0 @ W0 )
           => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
              = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
     => ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
        = ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(35,negated_conjecture,
    ( ( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
        & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
          = ( aDimensionOf0 @ xs ) )
        & ! [W0: $i] :
            ( ( aNaturalNumber0 @ W0 )
           => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
              = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
     => ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
          & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
            = ( aDimensionOf0 @ xt ) )
          & ! [W0: $i] :
              ( ( aNaturalNumber0 @ W0 )
             => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
                = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
       => ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
          = ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[34]) ).

thf(36,plain,
    ( ( ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
        & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
          = ( aDimensionOf0 @ xs ) )
        & ! [W0: $i] :
            ( ( aNaturalNumber0 @ W0 )
           => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
              = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
     => ( ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
          & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
            = ( aDimensionOf0 @ xt ) )
          & ! [W0: $i] :
              ( ( aNaturalNumber0 @ W0 )
             => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
                = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
       => ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
          = ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(37,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aVector0 @ W0 )
            & ( aNaturalNumber0 @ W1 ) )
         => ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(38,plain,
    ( ( ! [W0: $i] :
          ( ( aVector0 @ W0 )
         => ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(39,plain,
    ( ( ! [W0: $i] :
          ( ( aVector0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(40,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
              & ( sdtlseqdt0 @ sz0z00 @ W1 )
              & ( ( sdtasdt0 @ W0 @ W0 )
                = ( sdtasdt0 @ W1 @ W1 ) ) )
           => ( W0 = W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(41,plain,
    ( ( ! [W0: $i] :
          ( ( aScalar0 @ W0 )
         => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(42,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( ( sdtlseqdt0 @ sz0z00 @ W0 )
              & ( sdtlseqdt0 @ sz0z00 @ W1 ) )
           => ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) )
              & ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(43,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( sdtlseqdt0 @ W0 @ W1 )
            | ( sdtlseqdt0 @ W1 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(44,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 )
            & ( aScalar0 @ W3 ) )
         => ( ( ( sdtlseqdt0 @ W0 @ W1 )
              & ( sdtlseqdt0 @ sz0z00 @ W2 )
              & ( sdtlseqdt0 @ W2 @ W3 ) )
           => ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(45,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 )
            & ( aScalar0 @ W3 ) )
         => ( ( ( sdtlseqdt0 @ W0 @ W1 )
              & ( sdtlseqdt0 @ W2 @ W3 ) )
           => ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(46,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 ) )
         => ( ( ( sdtlseqdt0 @ W0 @ W1 )
              & ( sdtlseqdt0 @ W1 @ W2 ) )
           => ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(47,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( ( sdtlseqdt0 @ W0 @ W1 )
              & ( sdtlseqdt0 @ W1 @ W0 ) )
           => ( W0 = W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(48,plain,
    ( ( ! [W0: $i] :
          ( ( aScalar0 @ W0 )
         => ( sdtlseqdt0 @ W0 @ W0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(49,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( sdtlseqdt0 @ W0 @ W1 )
           => $true ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(50,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
            = ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(51,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
              = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) )
            & ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
              = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(52,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 )
            & ( aScalar0 @ W3 ) )
         => ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
            = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(53,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 ) )
         => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
            & ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
              = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(54,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 )
            & ( aScalar0 @ W2 ) )
         => ( ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
              = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
            & ( ( sdtpldt0 @ W0 @ W1 )
              = ( sdtpldt0 @ W1 @ W0 ) )
            & ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
              = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) )
            & ( ( sdtasdt0 @ W0 @ W1 )
              = ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(55,plain,
    ( ( ! [W0: $i] :
          ( ( aScalar0 @ W0 )
         => ( ( ( sdtpldt0 @ W0 @ sz0z00 )
              = W0 )
            & ( ( sdtpldt0 @ sz0z00 @ W0 )
              = W0 )
            & ( ( sdtasdt0 @ W0 @ sz0z00 )
              = sz0z00 )
            & ( ( sdtasdt0 @ sz0z00 @ W0 )
              = sz0z00 )
            & ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
              = sz0z00 )
            & ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
              = sz0z00 )
            & ( ( smndt0 @ ( smndt0 @ W0 ) )
              = W0 )
            & ( ( smndt0 @ sz0z00 )
              = sz0z00 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(56,plain,
    ( ( ! [W0: $i] :
          ( ( aScalar0 @ W0 )
         => ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(57,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(58,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aScalar0 @ W0 )
            & ( aScalar0 @ W1 ) )
         => ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(59,plain,
    ( ( aScalar0 @ sz0z00 )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(60,plain,
    ( ( ! [W0: $i] :
          ( ( aScalar0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(61,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(62,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aNaturalNumber0 @ W0 )
            & ( aNaturalNumber0 @ W1 ) )
         => ( ( iLess0 @ W0 @ W1 )
           => $true ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(63,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ( ( aNaturalNumber0 @ W0 )
            & ( aNaturalNumber0 @ W1 ) )
         => ( ( ( szszuzczcdt0 @ W0 )
              = ( szszuzczcdt0 @ W1 ) )
           => ( W0 = W1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(64,plain,
    ( ( ! [W0: $i] :
          ( ( ( aNaturalNumber0 @ W0 )
            & ( W0 != sz00 ) )
         => ? [W1: $i] :
              ( ( aNaturalNumber0 @ W1 )
              & ( W0
                = ( szszuzczcdt0 @ W1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(65,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) )
            & ( ( szszuzczcdt0 @ W0 )
             != sz00 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(66,plain,
    ( ( aNaturalNumber0 @ sz00 )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(67,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(68,plain,
    ( ( ( ( aDimensionOf0 @ xs )
        = ( aDimensionOf0 @ xt ) )
      & ( ( aDimensionOf0 @ xt )
       != sz00 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(69,plain,
    ( ( ( aVector0 @ xs )
      & ( aVector0 @ xt ) )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(70,plain,
    ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(71,plain,
    ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
      = ( aDimensionOf0 @ xs ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(72,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
            = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(73,plain,
    ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(74,plain,
    ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
      = ( aDimensionOf0 @ xt ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(75,plain,
    ( ( ! [W0: $i] :
          ( ( aNaturalNumber0 @ W0 )
         => ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
            = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(76,plain,
    ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
      = ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[36]) ).

thf(77,plain,
    ( ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
       != ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[76]) ).

thf(78,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
            = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[72]) ).

thf(79,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
            = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[75]) ).

thf(80,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aNaturalNumber0 @ W1 )
          | ~ ( aVector0 @ W0 )
          | ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(81,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aVector0 @ W0 )
          | ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(82,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[39]) ).

thf(83,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W0 )
           != ( sdtasdt0 @ W1 @ W1 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(84,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(85,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) ) )
      & ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(86,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( sdtlseqdt0 @ W0 @ W1 )
          | ( sdtlseqdt0 @ W1 @ W0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(87,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W2 )
          | ~ ( sdtlseqdt0 @ W2 @ W3 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[44]) ).

thf(88,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W2 @ W3 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[45]) ).

thf(89,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W1 @ W2 )
          | ( sdtlseqdt0 @ W0 @ W2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(90,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W1 @ W0 )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(91,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( sdtlseqdt0 @ W0 @ W0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(92,plain,
    ( ( ! [W0: $i] :
          ~ ( aScalar0 @ W0 )
      | ! [W1: $i] :
          ~ ( aScalar0 @ W1 )
      | $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[49]) ).

thf(93,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
            = ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(94,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
            = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
      & ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
            = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[51]) ).

thf(95,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
            = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(96,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[53]) ).

thf(97,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
                = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
          & ! [W1: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ! [W2: $i] :
                  ~ ( aScalar0 @ W2 )
              | ( ( sdtpldt0 @ W0 @ W1 )
                = ( sdtpldt0 @ W1 @ W0 ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
                = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) )
          & ! [W1: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ! [W2: $i] :
                  ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ W1 )
                = ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[54]) ).

thf(98,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz0z00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ sz0z00 @ W0 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz0z00 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtasdt0 @ sz0z00 @ W0 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( smndt0 @ ( smndt0 @ W0 ) )
            = W0 ) )
      & ( ! [W0: $i] :
            ~ ( aScalar0 @ W0 )
        | ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[55]) ).

thf(99,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[56]) ).

thf(100,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[57]) ).

thf(101,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[58]) ).

thf(102,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[60]) ).

thf(103,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[61]) ).

thf(104,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[62]) ).

thf(105,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ~ ( aNaturalNumber0 @ W1 )
          | ( ( szszuzczcdt0 @ W0 )
           != ( szszuzczcdt0 @ W1 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[63]) ).

thf(106,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aNaturalNumber0 @ W0 )
          | ( ( W0
              = ( szszuzczcdt0 @ ( sK1_W1 @ W0 ) ) )
            & ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[64]) ).

thf(107,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( szszuzczcdt0 @ W0 )
           != sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[65]) ).

thf(108,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[67]) ).

thf(109,plain,
    ( ( ( ( aDimensionOf0 @ xt )
       != sz00 )
      & ( ( aDimensionOf0 @ xs )
        = ( aDimensionOf0 @ xt ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[68]) ).

thf(110,plain,
    ( ( ( aVector0 @ xs )
      & ( aVector0 @ xt ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(111,plain,
    ( ( ( ( aDimensionOf0 @ xt )
       != sz00 )
      & ( ( aDimensionOf0 @ xs )
        = ( aDimensionOf0 @ xt ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(112,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(113,plain,
    ( ( aNaturalNumber0 @ sz00 )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(114,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( szszuzczcdt0 @ W0 )
           != sz00 ) )
      & ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( aNaturalNumber0 @ ( szszuzczcdt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(115,plain,
    ( ( ! [W0: $i] :
          ( ( W0 = sz00 )
          | ~ ( aNaturalNumber0 @ W0 )
          | ( ( W0
              = ( szszuzczcdt0 @ ( sK1_W1 @ W0 ) ) )
            & ( aNaturalNumber0 @ ( sK1_W1 @ W0 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(116,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ~ ( aNaturalNumber0 @ W1 )
          | ( ( szszuzczcdt0 @ W0 )
           != ( szszuzczcdt0 @ W1 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(117,plain,
    ( ( ! [W0: $i] :
          ~ ( aNaturalNumber0 @ W0 )
      | ! [W1: $i] :
          ~ ( aNaturalNumber0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(118,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( iLess0 @ W0 @ ( szszuzczcdt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(119,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(120,plain,
    ( ( aScalar0 @ sz0z00 )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(121,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( aScalar0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(122,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( aScalar0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(123,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( aScalar0 @ ( smndt0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(124,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ sz0z00 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ sz0z00 @ W0 )
            = W0 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtasdt0 @ W0 @ sz0z00 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtasdt0 @ sz0z00 @ W0 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 )
            = sz0z00 ) )
      & ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( ( smndt0 @ ( smndt0 @ W0 ) )
            = W0 ) )
      & ( ! [W0: $i] :
            ~ ( aScalar0 @ W0 )
        | ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(125,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
                = ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) )
          & ! [W1: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ! [W2: $i] :
                  ~ ( aScalar0 @ W2 )
              | ( ( sdtpldt0 @ W0 @ W1 )
                = ( sdtpldt0 @ W1 @ W0 ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
                = ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) )
          & ! [W1: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ! [W2: $i] :
                  ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ W1 )
                = ( sdtasdt0 @ W1 @ W0 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(126,plain,
    ( ( ! [W0: $i] :
          ( ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) ) )
          & ! [W1: $i,W2: $i] :
              ( ~ ( aScalar0 @ W0 )
              | ~ ( aScalar0 @ W1 )
              | ~ ( aScalar0 @ W2 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
                = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(127,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ ( sdtpldt0 @ W2 @ W3 ) )
            = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W0 @ W3 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(128,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ W0 @ ( smndt0 @ W1 ) )
            = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
      & ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ W1 )
            = ( smndt0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(129,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( ( sdtasdt0 @ ( smndt0 @ W0 ) @ ( smndt0 @ W1 ) )
            = ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(130,plain,
    ( ( ! [W0: $i] :
          ~ ( aScalar0 @ W0 )
      | ! [W1: $i] :
          ~ ( aScalar0 @ W1 )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(131,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( sdtlseqdt0 @ W0 @ W0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(132,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W1 @ W0 )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(133,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W1 @ W2 )
          | ( sdtlseqdt0 @ W0 @ W2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(134,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ W2 @ W3 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ W0 @ W2 ) @ ( sdtpldt0 @ W1 @ W3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(135,plain,
    ( ( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( aScalar0 @ W2 )
          | ~ ( aScalar0 @ W3 )
          | ~ ( sdtlseqdt0 @ W0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W2 )
          | ~ ( sdtlseqdt0 @ W2 @ W3 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(136,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ( sdtlseqdt0 @ W0 @ W1 )
          | ( sdtlseqdt0 @ W1 @ W0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(137,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ W0 @ W1 ) ) )
      & ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(138,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ W0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(139,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aScalar0 @ W0 )
          | ~ ( aScalar0 @ W1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ W1 )
          | ( ( sdtasdt0 @ W0 @ W0 )
           != ( sdtasdt0 @ W1 @ W1 ) )
          | ( W0 = W1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(140,plain,
    ( ( ! [W0: $i] : $true )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(141,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aVector0 @ W0 )
          | ( aNaturalNumber0 @ ( aDimensionOf0 @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(142,plain,
    ( ( ! [W0: $i,W1: $i] :
          ( ~ ( aNaturalNumber0 @ W1 )
          | ~ ( aVector0 @ W0 )
          | ( aScalar0 @ ( sdtlbdtrb0 @ W0 @ W1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(143,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ W0 )
            = ( sdtlbdtrb0 @ xt @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(144,plain,
    ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
      = ( aDimensionOf0 @ xt ) )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(145,plain,
    ( ( aVector0 @ ( sziznziztdt0 @ xt ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(146,plain,
    ( ( ! [W0: $i] :
          ( ~ ( aNaturalNumber0 @ W0 )
          | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ W0 )
            = ( sdtlbdtrb0 @ xs @ W0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(147,plain,
    ( ( ( szszuzczcdt0 @ ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) ) )
      = ( aDimensionOf0 @ xs ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(148,plain,
    ( ( aVector0 @ ( sziznziztdt0 @ xs ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(149,plain,
    ( ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
       != ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(150,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 = sz00 )
          | ~ ( aNaturalNumber0 @ SX0 )
          | ~ ( ( SX0
               != ( szszuzczcdt0 @ ( sK1_W1 @ SX0 ) ) )
              | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[115]) ).

thf(151,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aNaturalNumber0 @ SX0 )
                | ( ( szszuzczcdt0 @ SX0 )
                 != sz00 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aNaturalNumber0 @ SX0 )
                | ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[114]) ).

thf(152,plain,
    ( ( ~ ( ~ ( aVector0 @ xs )
          | ~ ( aVector0 @ xt ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[110]) ).

thf(153,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ~ ( aScalar0 @ SX1 )
                | ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
                  = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ~ ( aScalar0 @ SX1 )
                | ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
                  = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[128]) ).

thf(154,plain,
    ( ( ~ ( ~ ( ( ( aDimensionOf0 @ xt )
               != sz00 ) )
          | ( ( aDimensionOf0 @ xs )
           != ( aDimensionOf0 @ xt ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[111]) ).

thf(155,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ~ ( aScalar0 @ SX1 )
                  | ~ ( aScalar0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ ( sdtasdt0 @ SX0 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ~ ( aScalar0 @ SX1 )
                  | ~ ( aScalar0 @ SX2 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SX0 @ SX2 ) @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[126]) ).

thf(156,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ~ ( aScalar0 @ SX1 )
                | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
                | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
                | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ~ ( aScalar0 @ SX1 )
                | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
                | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
                | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[137]) ).

thf(157,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ~ ( aScalar0 @ SX1 )
                              | ~ ( aScalar0 @ SX2 )
                              | ( ( sdtpldt0 @ ( sdtpldt0 @ SX0 @ SX1 ) @ SX2 )
                                = ( sdtpldt0 @ SX0 @ ( sdtpldt0 @ SX1 @ SX2 ) ) ) )
                        | ~ ! [SX1: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ~ ( aScalar0 @ SX1 )
                              | ! [SX2: $i] :
                                  ~ ( aScalar0 @ SX2 )
                              | ( ( sdtpldt0 @ SX0 @ SX1 )
                                = ( sdtpldt0 @ SX1 @ SX0 ) ) ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ~ ( aScalar0 @ SX1 )
                        | ~ ( aScalar0 @ SX2 )
                        | ( ( sdtasdt0 @ ( sdtasdt0 @ SX0 @ SX1 ) @ SX2 )
                          = ( sdtasdt0 @ SX0 @ ( sdtasdt0 @ SX1 @ SX2 ) ) ) ) )
            | ~ ! [SX1: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ~ ( aScalar0 @ SX1 )
                  | ! [SX2: $i] :
                      ~ ( aScalar0 @ SX2 )
                  | ( ( sdtasdt0 @ SX0 @ SX1 )
                    = ( sdtasdt0 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[125]) ).

thf(158,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                    ( ~ ( aScalar0 @ SX0 )
                                                    | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                                      = SX0 ) )
                                              | ~ ! [SX0: $i] :
                                                    ( ~ ( aScalar0 @ SX0 )
                                                    | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                                      = SX0 ) ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aScalar0 @ SX0 )
                                              | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                                = sz0z00 ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aScalar0 @ SX0 )
                                        | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                          = sz0z00 ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aScalar0 @ SX0 )
                                  | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                                    = sz0z00 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                              = sz0z00 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( smndt0 @ ( smndt0 @ SX0 ) )
                        = SX0 ) ) )
          | ~ ( ! [SX0: $i] :
                  ~ ( aScalar0 @ SX0 )
              | ( ( smndt0 @ sz0z00 )
                = sz0z00 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[124]) ).

thf(159,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(160,plain,
    ! [SV2: $i] :
      ( ( ! [SY59: $i] :
            ( ~ ( aNaturalNumber0 @ SV2 )
            | ~ ( aNaturalNumber0 @ SY59 )
            | ( ( szszuzczcdt0 @ SV2 )
             != ( szszuzczcdt0 @ SY59 ) )
            | ( SV2 = SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(161,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 )
        | ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[117]) ).

thf(162,plain,
    ! [SV3: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV3 )
        | ( iLess0 @ SV3 @ ( szszuzczcdt0 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(163,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(164,plain,
    ! [SV5: $i] :
      ( ( ! [SY60: $i] :
            ( ~ ( aScalar0 @ SV5 )
            | ~ ( aScalar0 @ SY60 )
            | ( aScalar0 @ ( sdtpldt0 @ SV5 @ SY60 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(165,plain,
    ! [SV6: $i] :
      ( ( ! [SY61: $i] :
            ( ~ ( aScalar0 @ SV6 )
            | ~ ( aScalar0 @ SY61 )
            | ( aScalar0 @ ( sdtasdt0 @ SV6 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(166,plain,
    ! [SV7: $i] :
      ( ( ~ ( aScalar0 @ SV7 )
        | ( aScalar0 @ ( smndt0 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(167,plain,
    ! [SV8: $i] :
      ( ( ! [SY62: $i,SY63: $i,SY64: $i] :
            ( ~ ( aScalar0 @ SV8 )
            | ~ ( aScalar0 @ SY62 )
            | ~ ( aScalar0 @ SY63 )
            | ~ ( aScalar0 @ SY64 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SY62 ) @ ( sdtpldt0 @ SY63 @ SY64 ) )
              = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SY63 ) @ ( sdtasdt0 @ SV8 @ SY64 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SY62 @ SY63 ) @ ( sdtasdt0 @ SY62 @ SY64 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(168,plain,
    ! [SV9: $i] :
      ( ( ! [SY65: $i] :
            ( ~ ( aScalar0 @ SV9 )
            | ~ ( aScalar0 @ SY65 )
            | ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SY65 ) )
              = ( sdtasdt0 @ SV9 @ SY65 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(169,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aScalar0 @ W0 )
        | ! [W1: $i] :
            ~ ( aScalar0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(170,plain,
    ! [SV10: $i] :
      ( ( ~ ( aScalar0 @ SV10 )
        | ( sdtlseqdt0 @ SV10 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(171,plain,
    ! [SV11: $i] :
      ( ( ! [SY66: $i] :
            ( ~ ( aScalar0 @ SV11 )
            | ~ ( aScalar0 @ SY66 )
            | ~ ( sdtlseqdt0 @ SV11 @ SY66 )
            | ~ ( sdtlseqdt0 @ SY66 @ SV11 )
            | ( SV11 = SY66 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(172,plain,
    ! [SV12: $i] :
      ( ( ! [SY67: $i,SY68: $i] :
            ( ~ ( aScalar0 @ SV12 )
            | ~ ( aScalar0 @ SY67 )
            | ~ ( aScalar0 @ SY68 )
            | ~ ( sdtlseqdt0 @ SV12 @ SY67 )
            | ~ ( sdtlseqdt0 @ SY67 @ SY68 )
            | ( sdtlseqdt0 @ SV12 @ SY68 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(173,plain,
    ! [SV13: $i] :
      ( ( ! [SY69: $i,SY70: $i,SY71: $i] :
            ( ~ ( aScalar0 @ SV13 )
            | ~ ( aScalar0 @ SY69 )
            | ~ ( aScalar0 @ SY70 )
            | ~ ( aScalar0 @ SY71 )
            | ~ ( sdtlseqdt0 @ SV13 @ SY69 )
            | ~ ( sdtlseqdt0 @ SY70 @ SY71 )
            | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SY70 ) @ ( sdtpldt0 @ SY69 @ SY71 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(174,plain,
    ! [SV14: $i] :
      ( ( ! [SY72: $i,SY73: $i,SY74: $i] :
            ( ~ ( aScalar0 @ SV14 )
            | ~ ( aScalar0 @ SY72 )
            | ~ ( aScalar0 @ SY73 )
            | ~ ( aScalar0 @ SY74 )
            | ~ ( sdtlseqdt0 @ SV14 @ SY72 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SY73 )
            | ~ ( sdtlseqdt0 @ SY73 @ SY74 )
            | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SY73 ) @ ( sdtasdt0 @ SY72 @ SY74 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(175,plain,
    ! [SV15: $i] :
      ( ( ! [SY75: $i] :
            ( ~ ( aScalar0 @ SV15 )
            | ~ ( aScalar0 @ SY75 )
            | ( sdtlseqdt0 @ SV15 @ SY75 )
            | ( sdtlseqdt0 @ SY75 @ SV15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(176,plain,
    ! [SV16: $i] :
      ( ( ~ ( aScalar0 @ SV16 )
        | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV16 @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(177,plain,
    ! [SV17: $i] :
      ( ( ! [SY76: $i] :
            ( ~ ( aScalar0 @ SV17 )
            | ~ ( aScalar0 @ SY76 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SY76 )
            | ( ( sdtasdt0 @ SV17 @ SV17 )
             != ( sdtasdt0 @ SY76 @ SY76 ) )
            | ( SV17 = SY76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(178,plain,
    $true = $true,
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(179,plain,
    ! [SV19: $i] :
      ( ( ~ ( aVector0 @ SV19 )
        | ( aNaturalNumber0 @ ( aDimensionOf0 @ SV19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(180,plain,
    ! [SV20: $i] :
      ( ( ! [SY77: $i] :
            ( ~ ( aNaturalNumber0 @ SY77 )
            | ~ ( aVector0 @ SV20 )
            | ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SY77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(181,plain,
    ! [SV21: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV21 )
        | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV21 )
          = ( sdtlbdtrb0 @ xt @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(182,plain,
    ! [SV22: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV22 )
        | ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV22 )
          = ( sdtlbdtrb0 @ xs @ SV22 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(183,plain,
    ( ( ( aDimensionOf0 @ ( sziznziztdt0 @ xs ) )
      = ( aDimensionOf0 @ ( sziznziztdt0 @ xt ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(184,plain,
    ! [SV23: $i] :
      ( ( ( SV23 = sz00 )
        | ~ ( aNaturalNumber0 @ SV23 )
        | ~ ( ( SV23
             != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
            | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[150]) ).

thf(185,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aNaturalNumber0 @ SX0 )
            | ( ( szszuzczcdt0 @ SX0 )
             != sz00 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aNaturalNumber0 @ SX0 )
            | ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(186,plain,
    ( ( ~ ( aVector0 @ xs )
      | ~ ( aVector0 @ xt ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(187,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
              = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
              = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(188,plain,
    ( ( ~ ( ( ( aDimensionOf0 @ xt )
           != sz00 ) )
      | ( ( aDimensionOf0 @ xs )
       != ( aDimensionOf0 @ xt ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(189,plain,
    ! [SV24: $i] :
      ( ( ~ ( ~ ! [SY78: $i,SY79: $i] :
                  ( ~ ( aScalar0 @ SV24 )
                  | ~ ( aScalar0 @ SY78 )
                  | ~ ( aScalar0 @ SY79 )
                  | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SY78 @ SY79 ) )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY78 ) @ ( sdtasdt0 @ SV24 @ SY79 ) ) ) )
            | ~ ! [SY80: $i,SY81: $i] :
                  ( ~ ( aScalar0 @ SV24 )
                  | ~ ( aScalar0 @ SY80 )
                  | ~ ( aScalar0 @ SY81 )
                  | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SY80 ) @ SY81 )
                    = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY81 ) @ ( sdtasdt0 @ SY80 @ SY81 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(190,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(191,plain,
    ! [SV25: $i] :
      ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                              ( ~ ( aScalar0 @ SV25 )
                              | ~ ( aScalar0 @ SY82 )
                              | ~ ( aScalar0 @ SY83 )
                              | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                                = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
                        | ~ ! [SY84: $i] :
                              ( ~ ( aScalar0 @ SV25 )
                              | ~ ( aScalar0 @ SY84 )
                              | ! [SX2: $i] :
                                  ~ ( aScalar0 @ SX2 )
                              | ( ( sdtpldt0 @ SV25 @ SY84 )
                                = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
                  | ~ ! [SY86: $i,SY87: $i] :
                        ( ~ ( aScalar0 @ SV25 )
                        | ~ ( aScalar0 @ SY86 )
                        | ~ ( aScalar0 @ SY87 )
                        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) )
            | ~ ! [SY88: $i] :
                  ( ~ ( aScalar0 @ SV25 )
                  | ~ ( aScalar0 @ SY88 )
                  | ! [SX2: $i] :
                      ~ ( aScalar0 @ SX2 )
                  | ( ( sdtasdt0 @ SV25 @ SY88 )
                    = ( sdtasdt0 @ SY88 @ SV25 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(192,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aScalar0 @ SX0 )
                                                | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                                  = SX0 ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aScalar0 @ SX0 )
                                                | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                                  = SX0 ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                            = sz0z00 ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                      = sz0z00 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( smndt0 @ ( smndt0 @ SX0 ) )
                    = SX0 ) ) )
      | ~ ( ! [SX0: $i] :
              ~ ( aScalar0 @ SX0 )
          | ( ( smndt0 @ sz0z00 )
            = sz0z00 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(193,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV2 )
        | ~ ( aNaturalNumber0 @ SV26 )
        | ( ( szszuzczcdt0 @ SV2 )
         != ( szszuzczcdt0 @ SV26 ) )
        | ( SV2 = SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(194,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aNaturalNumber0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aNaturalNumber0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(195,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV3 ) )
        = $true )
      | ( ( iLess0 @ SV3 @ ( szszuzczcdt0 @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[162]) ).

thf(196,plain,
    ! [SV27: $i,SV5: $i] :
      ( ( ~ ( aScalar0 @ SV5 )
        | ~ ( aScalar0 @ SV27 )
        | ( aScalar0 @ ( sdtpldt0 @ SV5 @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(197,plain,
    ! [SV28: $i,SV6: $i] :
      ( ( ~ ( aScalar0 @ SV6 )
        | ~ ( aScalar0 @ SV28 )
        | ( aScalar0 @ ( sdtasdt0 @ SV6 @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(198,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( aScalar0 @ SV7 ) )
        = $true )
      | ( ( aScalar0 @ ( smndt0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[166]) ).

thf(199,plain,
    ! [SV29: $i,SV8: $i] :
      ( ( ! [SY90: $i,SY91: $i] :
            ( ~ ( aScalar0 @ SV8 )
            | ~ ( aScalar0 @ SV29 )
            | ~ ( aScalar0 @ SY90 )
            | ~ ( aScalar0 @ SY91 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SY90 @ SY91 ) )
              = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SY90 ) @ ( sdtasdt0 @ SV8 @ SY91 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SY90 ) @ ( sdtasdt0 @ SV29 @ SY91 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(200,plain,
    ! [SV30: $i,SV9: $i] :
      ( ( ~ ( aScalar0 @ SV9 )
        | ~ ( aScalar0 @ SV30 )
        | ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SV30 ) )
          = ( sdtasdt0 @ SV9 @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[168]) ).

thf(201,plain,
    ( ( ( ! [W0: $i] :
            ~ ( aScalar0 @ W0 ) )
      = $true )
    | ( ( ! [W1: $i] :
            ~ ( aScalar0 @ W1 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(202,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( aScalar0 @ SV10 ) )
        = $true )
      | ( ( sdtlseqdt0 @ SV10 @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[170]) ).

thf(203,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ~ ( aScalar0 @ SV11 )
        | ~ ( aScalar0 @ SV31 )
        | ~ ( sdtlseqdt0 @ SV11 @ SV31 )
        | ~ ( sdtlseqdt0 @ SV31 @ SV11 )
        | ( SV11 = SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(204,plain,
    ! [SV32: $i,SV12: $i] :
      ( ( ! [SY92: $i] :
            ( ~ ( aScalar0 @ SV12 )
            | ~ ( aScalar0 @ SV32 )
            | ~ ( aScalar0 @ SY92 )
            | ~ ( sdtlseqdt0 @ SV12 @ SV32 )
            | ~ ( sdtlseqdt0 @ SV32 @ SY92 )
            | ( sdtlseqdt0 @ SV12 @ SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(205,plain,
    ! [SV33: $i,SV13: $i] :
      ( ( ! [SY93: $i,SY94: $i] :
            ( ~ ( aScalar0 @ SV13 )
            | ~ ( aScalar0 @ SV33 )
            | ~ ( aScalar0 @ SY93 )
            | ~ ( aScalar0 @ SY94 )
            | ~ ( sdtlseqdt0 @ SV13 @ SV33 )
            | ~ ( sdtlseqdt0 @ SY93 @ SY94 )
            | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SY93 ) @ ( sdtpldt0 @ SV33 @ SY94 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(206,plain,
    ! [SV34: $i,SV14: $i] :
      ( ( ! [SY95: $i,SY96: $i] :
            ( ~ ( aScalar0 @ SV14 )
            | ~ ( aScalar0 @ SV34 )
            | ~ ( aScalar0 @ SY95 )
            | ~ ( aScalar0 @ SY96 )
            | ~ ( sdtlseqdt0 @ SV14 @ SV34 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SY95 )
            | ~ ( sdtlseqdt0 @ SY95 @ SY96 )
            | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SY95 ) @ ( sdtasdt0 @ SV34 @ SY96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(207,plain,
    ! [SV35: $i,SV15: $i] :
      ( ( ~ ( aScalar0 @ SV15 )
        | ~ ( aScalar0 @ SV35 )
        | ( sdtlseqdt0 @ SV15 @ SV35 )
        | ( sdtlseqdt0 @ SV35 @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(208,plain,
    ! [SV16: $i] :
      ( ( ( ~ ( aScalar0 @ SV16 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV16 @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(209,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ~ ( aScalar0 @ SV17 )
        | ~ ( aScalar0 @ SV36 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
        | ( ( sdtasdt0 @ SV17 @ SV17 )
         != ( sdtasdt0 @ SV36 @ SV36 ) )
        | ( SV17 = SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[177]) ).

thf(210,plain,
    ! [SV19: $i] :
      ( ( ( ~ ( aVector0 @ SV19 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV19 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(211,plain,
    ! [SV20: $i,SV37: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV37 )
        | ~ ( aVector0 @ SV20 )
        | ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SV37 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[180]) ).

thf(212,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV21 ) )
        = $true )
      | ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV21 )
          = ( sdtlbdtrb0 @ xt @ SV21 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(213,plain,
    ! [SV22: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV22 ) )
        = $true )
      | ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV22 )
          = ( sdtlbdtrb0 @ xs @ SV22 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[182]) ).

thf(214,plain,
    ! [SV23: $i] :
      ( ( ( ( SV23 = sz00 )
          | ~ ( aNaturalNumber0 @ SV23 ) )
        = $true )
      | ( ( ~ ( ( SV23
               != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
              | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[184]) ).

thf(215,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aNaturalNumber0 @ SX0 )
            | ( ( szszuzczcdt0 @ SX0 )
             != sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[185]) ).

thf(216,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aNaturalNumber0 @ SX0 )
            | ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[185]) ).

thf(217,plain,
    ( ( ~ ( aVector0 @ xs ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(218,plain,
    ( ( ~ ( aVector0 @ xt ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(219,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
              = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(220,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
              = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(221,plain,
    ( ( ~ ( ( ( aDimensionOf0 @ xt )
           != sz00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(222,plain,
    ( ( ( ( aDimensionOf0 @ xs )
       != ( aDimensionOf0 @ xt ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(223,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY78: $i,SY79: $i] :
              ( ~ ( aScalar0 @ SV24 )
              | ~ ( aScalar0 @ SY78 )
              | ~ ( aScalar0 @ SY79 )
              | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SY78 @ SY79 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY78 ) @ ( sdtasdt0 @ SV24 @ SY79 ) ) ) )
        | ~ ! [SY80: $i,SY81: $i] :
              ( ~ ( aScalar0 @ SV24 )
              | ~ ( aScalar0 @ SY80 )
              | ~ ( aScalar0 @ SY81 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SY80 ) @ SY81 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY81 ) @ ( sdtasdt0 @ SY80 @ SY81 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(224,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(225,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ~ ( aScalar0 @ SX1 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(226,plain,
    ! [SV25: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                          ( ~ ( aScalar0 @ SV25 )
                          | ~ ( aScalar0 @ SY82 )
                          | ~ ( aScalar0 @ SY83 )
                          | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                            = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
                    | ~ ! [SY84: $i] :
                          ( ~ ( aScalar0 @ SV25 )
                          | ~ ( aScalar0 @ SY84 )
                          | ! [SX2: $i] :
                              ~ ( aScalar0 @ SX2 )
                          | ( ( sdtpldt0 @ SV25 @ SY84 )
                            = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
              | ~ ! [SY86: $i,SY87: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY86 )
                    | ~ ( aScalar0 @ SY87 )
                    | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                      = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) )
        | ~ ! [SY88: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY88 )
              | ! [SX2: $i] :
                  ~ ( aScalar0 @ SX2 )
              | ( ( sdtasdt0 @ SV25 @ SY88 )
                = ( sdtasdt0 @ SY88 @ SV25 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(227,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                                ( ~ ( aScalar0 @ SX0 )
                                                | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                                  = SX0 ) )
                                          | ~ ! [SX0: $i] :
                                                ( ~ ( aScalar0 @ SX0 )
                                                | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                                  = SX0 ) ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                            = sz0z00 ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                      = sz0z00 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( smndt0 @ ( smndt0 @ SX0 ) )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[192]) ).

thf(228,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( aScalar0 @ SX0 )
          | ( ( smndt0 @ sz0z00 )
            = sz0z00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[192]) ).

thf(229,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV2 )
          | ~ ( aNaturalNumber0 @ SV26 ) )
        = $true )
      | ( ( ( ( szszuzczcdt0 @ SV2 )
           != ( szszuzczcdt0 @ SV26 ) )
          | ( SV2 = SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[193]) ).

thf(230,plain,
    ! [SV38: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV38 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[194]) ).

thf(231,plain,
    ! [SV3: $i] :
      ( ( ( aNaturalNumber0 @ SV3 )
        = $false )
      | ( ( iLess0 @ SV3 @ ( szszuzczcdt0 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[195]) ).

thf(232,plain,
    ! [SV27: $i,SV5: $i] :
      ( ( ( ~ ( aScalar0 @ SV5 )
          | ~ ( aScalar0 @ SV27 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtpldt0 @ SV5 @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[196]) ).

thf(233,plain,
    ! [SV28: $i,SV6: $i] :
      ( ( ( ~ ( aScalar0 @ SV6 )
          | ~ ( aScalar0 @ SV28 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtasdt0 @ SV6 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[197]) ).

thf(234,plain,
    ! [SV7: $i] :
      ( ( ( aScalar0 @ SV7 )
        = $false )
      | ( ( aScalar0 @ ( smndt0 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[198]) ).

thf(235,plain,
    ! [SV39: $i,SV29: $i,SV8: $i] :
      ( ( ! [SY97: $i] :
            ( ~ ( aScalar0 @ SV8 )
            | ~ ( aScalar0 @ SV29 )
            | ~ ( aScalar0 @ SV39 )
            | ~ ( aScalar0 @ SY97 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SY97 ) )
              = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SY97 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SY97 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(236,plain,
    ! [SV30: $i,SV9: $i] :
      ( ( ( ~ ( aScalar0 @ SV9 )
          | ~ ( aScalar0 @ SV30 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SV30 ) )
          = ( sdtasdt0 @ SV9 @ SV30 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[200]) ).

thf(237,plain,
    ! [SV40: $i] :
      ( ( ( ~ ( aScalar0 @ SV40 ) )
        = $true )
      | ( ( ! [W1: $i] :
              ~ ( aScalar0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(238,plain,
    ! [SV10: $i] :
      ( ( ( aScalar0 @ SV10 )
        = $false )
      | ( ( sdtlseqdt0 @ SV10 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[202]) ).

thf(239,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( ~ ( aScalar0 @ SV11 )
          | ~ ( aScalar0 @ SV31 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 )
          | ~ ( sdtlseqdt0 @ SV31 @ SV11 )
          | ( SV11 = SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[203]) ).

thf(240,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ~ ( aScalar0 @ SV12 )
        | ~ ( aScalar0 @ SV32 )
        | ~ ( aScalar0 @ SV41 )
        | ~ ( sdtlseqdt0 @ SV12 @ SV32 )
        | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
        | ( sdtlseqdt0 @ SV12 @ SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(241,plain,
    ! [SV42: $i,SV33: $i,SV13: $i] :
      ( ( ! [SY98: $i] :
            ( ~ ( aScalar0 @ SV13 )
            | ~ ( aScalar0 @ SV33 )
            | ~ ( aScalar0 @ SV42 )
            | ~ ( aScalar0 @ SY98 )
            | ~ ( sdtlseqdt0 @ SV13 @ SV33 )
            | ~ ( sdtlseqdt0 @ SV42 @ SY98 )
            | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SY98 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[205]) ).

thf(242,plain,
    ! [SV43: $i,SV34: $i,SV14: $i] :
      ( ( ! [SY99: $i] :
            ( ~ ( aScalar0 @ SV14 )
            | ~ ( aScalar0 @ SV34 )
            | ~ ( aScalar0 @ SV43 )
            | ~ ( aScalar0 @ SY99 )
            | ~ ( sdtlseqdt0 @ SV14 @ SV34 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
            | ~ ( sdtlseqdt0 @ SV43 @ SY99 )
            | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SY99 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[206]) ).

thf(243,plain,
    ! [SV35: $i,SV15: $i] :
      ( ( ( ~ ( aScalar0 @ SV15 )
          | ~ ( aScalar0 @ SV35 ) )
        = $true )
      | ( ( ( sdtlseqdt0 @ SV15 @ SV35 )
          | ( sdtlseqdt0 @ SV35 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[207]) ).

thf(244,plain,
    ! [SV16: $i] :
      ( ( ( aScalar0 @ SV16 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV16 @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[208]) ).

thf(245,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ~ ( aScalar0 @ SV17 )
          | ~ ( aScalar0 @ SV36 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
          | ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) )
          | ( SV17 = SV36 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[209]) ).

thf(246,plain,
    ! [SV19: $i] :
      ( ( ( aVector0 @ SV19 )
        = $false )
      | ( ( aNaturalNumber0 @ ( aDimensionOf0 @ SV19 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[210]) ).

thf(247,plain,
    ! [SV20: $i,SV37: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV37 )
          | ~ ( aVector0 @ SV20 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[211]) ).

thf(248,plain,
    ! [SV21: $i] :
      ( ( ( aNaturalNumber0 @ SV21 )
        = $false )
      | ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xt ) @ SV21 )
          = ( sdtlbdtrb0 @ xt @ SV21 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[212]) ).

thf(249,plain,
    ! [SV22: $i] :
      ( ( ( aNaturalNumber0 @ SV22 )
        = $false )
      | ( ( ( sdtlbdtrb0 @ ( sziznziztdt0 @ xs ) @ SV22 )
          = ( sdtlbdtrb0 @ xs @ SV22 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[213]) ).

thf(250,plain,
    ! [SV23: $i] :
      ( ( ( SV23 = sz00 )
        = $true )
      | ( ( ~ ( aNaturalNumber0 @ SV23 ) )
        = $true )
      | ( ( ~ ( ( SV23
               != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
              | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[214]) ).

thf(251,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aNaturalNumber0 @ SX0 )
          | ( ( szszuzczcdt0 @ SX0 )
           != sz00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[215]) ).

thf(252,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aNaturalNumber0 @ SX0 )
          | ( aNaturalNumber0 @ ( szszuzczcdt0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[216]) ).

thf(253,plain,
    ( ( aVector0 @ xs )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[217]) ).

thf(254,plain,
    ( ( aVector0 @ xt )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[218]) ).

thf(255,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ~ ( aScalar0 @ SX1 )
          | ( ( sdtasdt0 @ SX0 @ ( smndt0 @ SX1 ) )
            = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[219]) ).

thf(256,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ~ ( aScalar0 @ SX1 )
          | ( ( sdtasdt0 @ ( smndt0 @ SX0 ) @ SX1 )
            = ( smndt0 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[220]) ).

thf(257,plain,
    ( ( ( ( aDimensionOf0 @ xt )
       != sz00 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[221]) ).

thf(258,plain,
    ( ( ( aDimensionOf0 @ xs )
      = ( aDimensionOf0 @ xt ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[222]) ).

thf(259,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY78: $i,SY79: $i] :
              ( ~ ( aScalar0 @ SV24 )
              | ~ ( aScalar0 @ SY78 )
              | ~ ( aScalar0 @ SY79 )
              | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SY78 @ SY79 ) )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY78 ) @ ( sdtasdt0 @ SV24 @ SY79 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[223]) ).

thf(260,plain,
    ! [SV24: $i] :
      ( ( ~ ! [SY80: $i,SY81: $i] :
              ( ~ ( aScalar0 @ SV24 )
              | ~ ( aScalar0 @ SY80 )
              | ~ ( aScalar0 @ SY81 )
              | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SY80 ) @ SY81 )
                = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY81 ) @ ( sdtasdt0 @ SY80 @ SY81 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[223]) ).

thf(261,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ~ ( aScalar0 @ SX1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[224]) ).

thf(262,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ~ ( aScalar0 @ SX1 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SX0 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SX1 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[225]) ).

thf(263,plain,
    ! [SV25: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                          ( ~ ( aScalar0 @ SV25 )
                          | ~ ( aScalar0 @ SY82 )
                          | ~ ( aScalar0 @ SY83 )
                          | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                            = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
                    | ~ ! [SY84: $i] :
                          ( ~ ( aScalar0 @ SV25 )
                          | ~ ( aScalar0 @ SY84 )
                          | ! [SX2: $i] :
                              ~ ( aScalar0 @ SX2 )
                          | ( ( sdtpldt0 @ SV25 @ SY84 )
                            = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
              | ~ ! [SY86: $i,SY87: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY86 )
                    | ~ ( aScalar0 @ SY87 )
                    | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                      = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[226]) ).

thf(264,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY88: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY88 )
              | ! [SX2: $i] :
                  ~ ( aScalar0 @ SX2 )
              | ( ( sdtasdt0 @ SV25 @ SY88 )
                = ( sdtasdt0 @ SY88 @ SV25 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[226]) ).

thf(265,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                              ( ~ ( aScalar0 @ SX0 )
                                              | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                                = SX0 ) )
                                        | ~ ! [SX0: $i] :
                                              ( ~ ( aScalar0 @ SX0 )
                                              | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                                = SX0 ) ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aScalar0 @ SX0 )
                                        | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                          = sz0z00 ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aScalar0 @ SX0 )
                                  | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                    = sz0z00 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                              = sz0z00 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                        = sz0z00 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( smndt0 @ ( smndt0 @ SX0 ) )
                  = SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[227]) ).

thf(266,plain,
    ( ( ! [SX0: $i] :
          ~ ( aScalar0 @ SX0 )
      | ( ( smndt0 @ sz0z00 )
        = sz0z00 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[228]) ).

thf(267,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV2 ) )
        = $true )
      | ( ( ~ ( aNaturalNumber0 @ SV26 ) )
        = $true )
      | ( ( ( ( szszuzczcdt0 @ SV2 )
           != ( szszuzczcdt0 @ SV26 ) )
          | ( SV2 = SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[229]) ).

thf(268,plain,
    ! [SV38: $i] :
      ( ( ( aNaturalNumber0 @ SV38 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aNaturalNumber0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[230]) ).

thf(269,plain,
    ! [SV27: $i,SV5: $i] :
      ( ( ( ~ ( aScalar0 @ SV5 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV27 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtpldt0 @ SV5 @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[232]) ).

thf(270,plain,
    ! [SV28: $i,SV6: $i] :
      ( ( ( ~ ( aScalar0 @ SV6 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV28 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtasdt0 @ SV6 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[233]) ).

thf(271,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ~ ( aScalar0 @ SV8 )
        | ~ ( aScalar0 @ SV29 )
        | ~ ( aScalar0 @ SV39 )
        | ~ ( aScalar0 @ SV44 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[235]) ).

thf(272,plain,
    ! [SV30: $i,SV9: $i] :
      ( ( ( ~ ( aScalar0 @ SV9 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV30 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SV30 ) )
          = ( sdtasdt0 @ SV9 @ SV30 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[236]) ).

thf(273,plain,
    ! [SV40: $i] :
      ( ( ( aScalar0 @ SV40 )
        = $false )
      | ( ( ! [W1: $i] :
              ~ ( aScalar0 @ W1 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[237]) ).

thf(274,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( ~ ( aScalar0 @ SV11 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV31 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 )
          | ~ ( sdtlseqdt0 @ SV31 @ SV11 )
          | ( SV11 = SV31 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[239]) ).

thf(275,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( ~ ( aScalar0 @ SV12 )
          | ~ ( aScalar0 @ SV32 )
          | ~ ( aScalar0 @ SV41 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[240]) ).

thf(276,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ~ ( aScalar0 @ SV13 )
        | ~ ( aScalar0 @ SV33 )
        | ~ ( aScalar0 @ SV42 )
        | ~ ( aScalar0 @ SV45 )
        | ~ ( sdtlseqdt0 @ SV13 @ SV33 )
        | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
        | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[241]) ).

thf(277,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ~ ( aScalar0 @ SV14 )
        | ~ ( aScalar0 @ SV34 )
        | ~ ( aScalar0 @ SV43 )
        | ~ ( aScalar0 @ SV46 )
        | ~ ( sdtlseqdt0 @ SV14 @ SV34 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
        | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
        | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[242]) ).

thf(278,plain,
    ! [SV35: $i,SV15: $i] :
      ( ( ( ~ ( aScalar0 @ SV15 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV35 ) )
        = $true )
      | ( ( ( sdtlseqdt0 @ SV15 @ SV35 )
          | ( sdtlseqdt0 @ SV35 @ SV15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[243]) ).

thf(279,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ~ ( aScalar0 @ SV17 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV36 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
          | ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) )
          | ( SV17 = SV36 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[245]) ).

thf(280,plain,
    ! [SV20: $i,SV37: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV37 ) )
        = $true )
      | ( ( ~ ( aVector0 @ SV20 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[247]) ).

thf(281,plain,
    ! [SV23: $i] :
      ( ( ( aNaturalNumber0 @ SV23 )
        = $false )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( ~ ( ( SV23
               != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
              | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[250]) ).

thf(282,plain,
    ! [SV47: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV47 )
        | ( ( szszuzczcdt0 @ SV47 )
         != sz00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[251]) ).

thf(283,plain,
    ! [SV48: $i] :
      ( ( ~ ( aNaturalNumber0 @ SV48 )
        | ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[252]) ).

thf(284,plain,
    ! [SV49: $i] :
      ( ( ! [SY100: $i] :
            ( ~ ( aScalar0 @ SV49 )
            | ~ ( aScalar0 @ SY100 )
            | ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SY100 ) )
              = ( smndt0 @ ( sdtasdt0 @ SV49 @ SY100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(285,plain,
    ! [SV50: $i] :
      ( ( ! [SY101: $i] :
            ( ~ ( aScalar0 @ SV50 )
            | ~ ( aScalar0 @ SY101 )
            | ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SY101 )
              = ( smndt0 @ ( sdtasdt0 @ SV50 @ SY101 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(286,plain,
    ( ( ( aDimensionOf0 @ xt )
      = sz00 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[257]) ).

thf(287,plain,
    ! [SV24: $i] :
      ( ( ! [SY78: $i,SY79: $i] :
            ( ~ ( aScalar0 @ SV24 )
            | ~ ( aScalar0 @ SY78 )
            | ~ ( aScalar0 @ SY79 )
            | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SY78 @ SY79 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY78 ) @ ( sdtasdt0 @ SV24 @ SY79 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[259]) ).

thf(288,plain,
    ! [SV24: $i] :
      ( ( ! [SY80: $i,SY81: $i] :
            ( ~ ( aScalar0 @ SV24 )
            | ~ ( aScalar0 @ SY80 )
            | ~ ( aScalar0 @ SY81 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SY80 ) @ SY81 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY81 ) @ ( sdtasdt0 @ SY80 @ SY81 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[260]) ).

thf(289,plain,
    ! [SV51: $i] :
      ( ( ! [SY102: $i] :
            ( ~ ( aScalar0 @ SV51 )
            | ~ ( aScalar0 @ SY102 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SY102 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SY102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[261]) ).

thf(290,plain,
    ! [SV52: $i] :
      ( ( ! [SY103: $i] :
            ( ~ ( aScalar0 @ SV52 )
            | ~ ( aScalar0 @ SY103 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
            | ~ ( sdtlseqdt0 @ sz0z00 @ SY103 )
            | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SY103 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[262]) ).

thf(291,plain,
    ! [SV25: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                        ( ~ ( aScalar0 @ SV25 )
                        | ~ ( aScalar0 @ SY82 )
                        | ~ ( aScalar0 @ SY83 )
                        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
                  | ~ ! [SY84: $i] :
                        ( ~ ( aScalar0 @ SV25 )
                        | ~ ( aScalar0 @ SY84 )
                        | ! [SX2: $i] :
                            ~ ( aScalar0 @ SX2 )
                        | ( ( sdtpldt0 @ SV25 @ SY84 )
                          = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
            | ~ ! [SY86: $i,SY87: $i] :
                  ( ~ ( aScalar0 @ SV25 )
                  | ~ ( aScalar0 @ SY86 )
                  | ~ ( aScalar0 @ SY87 )
                  | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                    = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[263]) ).

thf(292,plain,
    ! [SV25: $i] :
      ( ( ! [SY88: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SY88 )
            | ! [SX2: $i] :
                ~ ( aScalar0 @ SX2 )
            | ( ( sdtasdt0 @ SV25 @ SY88 )
              = ( sdtasdt0 @ SY88 @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[264]) ).

thf(293,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                            = SX0 ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                            = SX0 ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                      = sz0z00 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                    = sz0z00 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( smndt0 @ ( smndt0 @ SX0 ) )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[265]) ).

thf(294,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( aScalar0 @ SX0 ) )
      = $true )
    | ( ( ( smndt0 @ sz0z00 )
        = sz0z00 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[266]) ).

thf(295,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ( aNaturalNumber0 @ SV2 )
        = $false )
      | ( ( ~ ( aNaturalNumber0 @ SV26 ) )
        = $true )
      | ( ( ( ( szszuzczcdt0 @ SV2 )
           != ( szszuzczcdt0 @ SV26 ) )
          | ( SV2 = SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[267]) ).

thf(296,plain,
    ! [SV38: $i,SV53: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV53 ) )
        = $true )
      | ( ( aNaturalNumber0 @ SV38 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(297,plain,
    ! [SV27: $i,SV5: $i] :
      ( ( ( aScalar0 @ SV5 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV27 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtpldt0 @ SV5 @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[269]) ).

thf(298,plain,
    ! [SV28: $i,SV6: $i] :
      ( ( ( aScalar0 @ SV6 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV28 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtasdt0 @ SV6 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[270]) ).

thf(299,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ( ~ ( aScalar0 @ SV8 )
          | ~ ( aScalar0 @ SV29 )
          | ~ ( aScalar0 @ SV39 )
          | ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[271]) ).

thf(300,plain,
    ! [SV30: $i,SV9: $i] :
      ( ( ( aScalar0 @ SV9 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV30 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SV30 ) )
          = ( sdtasdt0 @ SV9 @ SV30 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(301,plain,
    ! [SV40: $i,SV54: $i] :
      ( ( ( ~ ( aScalar0 @ SV54 ) )
        = $true )
      | ( ( aScalar0 @ SV40 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[273]) ).

thf(302,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV31 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 )
          | ~ ( sdtlseqdt0 @ SV31 @ SV11 )
          | ( SV11 = SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[274]) ).

thf(303,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( ~ ( aScalar0 @ SV12 )
          | ~ ( aScalar0 @ SV32 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV41 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[275]) ).

thf(304,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( aScalar0 @ SV13 )
          | ~ ( aScalar0 @ SV33 )
          | ~ ( aScalar0 @ SV42 )
          | ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[276]) ).

thf(305,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( aScalar0 @ SV14 )
          | ~ ( aScalar0 @ SV34 )
          | ~ ( aScalar0 @ SV43 )
          | ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[277]) ).

thf(306,plain,
    ! [SV35: $i,SV15: $i] :
      ( ( ( aScalar0 @ SV15 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV35 ) )
        = $true )
      | ( ( ( sdtlseqdt0 @ SV15 @ SV35 )
          | ( sdtlseqdt0 @ SV35 @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[278]) ).

thf(307,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV36 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
          | ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) )
          | ( SV17 = SV36 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[279]) ).

thf(308,plain,
    ! [SV20: $i,SV37: $i] :
      ( ( ( aNaturalNumber0 @ SV37 )
        = $false )
      | ( ( ~ ( aVector0 @ SV20 ) )
        = $true )
      | ( ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[280]) ).

thf(309,plain,
    ! [SV23: $i] :
      ( ( ( ( SV23
           != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
          | ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) )
        = $false )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[281]) ).

thf(310,plain,
    ! [SV47: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV47 ) )
        = $true )
      | ( ( ( ( szszuzczcdt0 @ SV47 )
           != sz00 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[282]) ).

thf(311,plain,
    ! [SV48: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ SV48 ) )
        = $true )
      | ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV48 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[283]) ).

thf(312,plain,
    ! [SV55: $i,SV49: $i] :
      ( ( ~ ( aScalar0 @ SV49 )
        | ~ ( aScalar0 @ SV55 )
        | ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SV55 ) )
          = ( smndt0 @ ( sdtasdt0 @ SV49 @ SV55 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[284]) ).

thf(313,plain,
    ! [SV56: $i,SV50: $i] :
      ( ( ~ ( aScalar0 @ SV50 )
        | ~ ( aScalar0 @ SV56 )
        | ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SV56 )
          = ( smndt0 @ ( sdtasdt0 @ SV50 @ SV56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(314,plain,
    ! [SV57: $i,SV24: $i] :
      ( ( ! [SY104: $i] :
            ( ~ ( aScalar0 @ SV24 )
            | ~ ( aScalar0 @ SV57 )
            | ~ ( aScalar0 @ SY104 )
            | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SY104 ) )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SY104 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[287]) ).

thf(315,plain,
    ! [SV58: $i,SV24: $i] :
      ( ( ! [SY105: $i] :
            ( ~ ( aScalar0 @ SV24 )
            | ~ ( aScalar0 @ SV58 )
            | ~ ( aScalar0 @ SY105 )
            | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SY105 )
              = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SY105 ) @ ( sdtasdt0 @ SV58 @ SY105 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[288]) ).

thf(316,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ~ ( aScalar0 @ SV51 )
        | ~ ( aScalar0 @ SV59 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
        | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[289]) ).

thf(317,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ~ ( aScalar0 @ SV52 )
        | ~ ( aScalar0 @ SV60 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
        | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 )
        | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[290]) ).

thf(318,plain,
    ! [SV25: $i] :
      ( ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY82 )
                    | ~ ( aScalar0 @ SY83 )
                    | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                      = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
              | ~ ! [SY84: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY84 )
                    | ! [SX2: $i] :
                        ~ ( aScalar0 @ SX2 )
                    | ( ( sdtpldt0 @ SV25 @ SY84 )
                      = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
        | ~ ! [SY86: $i,SY87: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY86 )
              | ~ ( aScalar0 @ SY87 )
              | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[291]) ).

thf(319,plain,
    ! [SV61: $i,SV25: $i] :
      ( ( ~ ( aScalar0 @ SV25 )
        | ~ ( aScalar0 @ SV61 )
        | ! [SX2: $i] :
            ~ ( aScalar0 @ SX2 )
        | ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[292]) ).

thf(320,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                            = SX0 ) )
                                    | ~ ! [SX0: $i] :
                                          ( ~ ( aScalar0 @ SX0 )
                                          | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                            = SX0 ) ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                      = sz0z00 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                    = sz0z00 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[293]) ).

thf(321,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( smndt0 @ ( smndt0 @ SX0 ) )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[293]) ).

thf(322,plain,
    ! [SV62: $i] :
      ( ( ( ~ ( aScalar0 @ SV62 ) )
        = $true )
      | ( ( ( smndt0 @ sz0z00 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[294]) ).

thf(323,plain,
    ! [SV2: $i,SV26: $i] :
      ( ( ( aNaturalNumber0 @ SV26 )
        = $false )
      | ( ( aNaturalNumber0 @ SV2 )
        = $false )
      | ( ( ( ( szszuzczcdt0 @ SV2 )
           != ( szszuzczcdt0 @ SV26 ) )
          | ( SV2 = SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[295]) ).

thf(324,plain,
    ! [SV38: $i,SV53: $i] :
      ( ( ( aNaturalNumber0 @ SV53 )
        = $false )
      | ( ( aNaturalNumber0 @ SV38 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[296]) ).

thf(325,plain,
    ! [SV5: $i,SV27: $i] :
      ( ( ( aScalar0 @ SV27 )
        = $false )
      | ( ( aScalar0 @ SV5 )
        = $false )
      | ( ( aScalar0 @ ( sdtpldt0 @ SV5 @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[297]) ).

thf(326,plain,
    ! [SV6: $i,SV28: $i] :
      ( ( ( aScalar0 @ SV28 )
        = $false )
      | ( ( aScalar0 @ SV6 )
        = $false )
      | ( ( aScalar0 @ ( sdtasdt0 @ SV6 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[298]) ).

thf(327,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ( ~ ( aScalar0 @ SV8 )
          | ~ ( aScalar0 @ SV29 )
          | ~ ( aScalar0 @ SV39 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[299]) ).

thf(328,plain,
    ! [SV9: $i,SV30: $i] :
      ( ( ( aScalar0 @ SV30 )
        = $false )
      | ( ( aScalar0 @ SV9 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV9 ) @ ( smndt0 @ SV30 ) )
          = ( sdtasdt0 @ SV9 @ SV30 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[300]) ).

thf(329,plain,
    ! [SV40: $i,SV54: $i] :
      ( ( ( aScalar0 @ SV54 )
        = $false )
      | ( ( aScalar0 @ SV40 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[301]) ).

thf(330,plain,
    ! [SV11: $i,SV31: $i] :
      ( ( ( aScalar0 @ SV31 )
        = $false )
      | ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 )
          | ~ ( sdtlseqdt0 @ SV31 @ SV11 )
          | ( SV11 = SV31 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[302]) ).

thf(331,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( ~ ( aScalar0 @ SV12 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV32 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV41 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[303]) ).

thf(332,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( aScalar0 @ SV13 )
          | ~ ( aScalar0 @ SV33 )
          | ~ ( aScalar0 @ SV42 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[304]) ).

thf(333,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( aScalar0 @ SV14 )
          | ~ ( aScalar0 @ SV34 )
          | ~ ( aScalar0 @ SV43 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[305]) ).

thf(334,plain,
    ! [SV15: $i,SV35: $i] :
      ( ( ( aScalar0 @ SV35 )
        = $false )
      | ( ( aScalar0 @ SV15 )
        = $false )
      | ( ( ( sdtlseqdt0 @ SV15 @ SV35 )
          | ( sdtlseqdt0 @ SV35 @ SV15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[306]) ).

thf(335,plain,
    ! [SV17: $i,SV36: $i] :
      ( ( ( aScalar0 @ SV36 )
        = $false )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
          | ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) )
          | ( SV17 = SV36 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[307]) ).

thf(336,plain,
    ! [SV37: $i,SV20: $i] :
      ( ( ( aVector0 @ SV20 )
        = $false )
      | ( ( aNaturalNumber0 @ SV37 )
        = $false )
      | ( ( aScalar0 @ ( sdtlbdtrb0 @ SV20 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[308]) ).

thf(337,plain,
    ! [SV23: $i] :
      ( ( ( ( SV23
           != ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) ) )
        = $false )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ SV23 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[309]) ).

thf(338,plain,
    ! [SV23: $i] :
      ( ( ( ~ ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) ) )
        = $false )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ SV23 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[309]) ).

thf(339,plain,
    ! [SV47: $i] :
      ( ( ( aNaturalNumber0 @ SV47 )
        = $false )
      | ( ( ( ( szszuzczcdt0 @ SV47 )
           != sz00 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[310]) ).

thf(340,plain,
    ! [SV48: $i] :
      ( ( ( aNaturalNumber0 @ SV48 )
        = $false )
      | ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[311]) ).

thf(341,plain,
    ! [SV55: $i,SV49: $i] :
      ( ( ( ~ ( aScalar0 @ SV49 )
          | ~ ( aScalar0 @ SV55 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SV55 ) )
          = ( smndt0 @ ( sdtasdt0 @ SV49 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[312]) ).

thf(342,plain,
    ! [SV56: $i,SV50: $i] :
      ( ( ( ~ ( aScalar0 @ SV50 )
          | ~ ( aScalar0 @ SV56 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SV56 )
          = ( smndt0 @ ( sdtasdt0 @ SV50 @ SV56 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[313]) ).

thf(343,plain,
    ! [SV63: $i,SV57: $i,SV24: $i] :
      ( ( ~ ( aScalar0 @ SV24 )
        | ~ ( aScalar0 @ SV57 )
        | ~ ( aScalar0 @ SV63 )
        | ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[314]) ).

thf(344,plain,
    ! [SV64: $i,SV58: $i,SV24: $i] :
      ( ( ~ ( aScalar0 @ SV24 )
        | ~ ( aScalar0 @ SV58 )
        | ~ ( aScalar0 @ SV64 )
        | ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[315]) ).

thf(345,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( ~ ( aScalar0 @ SV51 )
          | ~ ( aScalar0 @ SV59 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[316]) ).

thf(346,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( ~ ( aScalar0 @ SV52 )
          | ~ ( aScalar0 @ SV60 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[317]) ).

thf(347,plain,
    ! [SV25: $i] :
      ( ( ~ ~ ( ~ ! [SY82: $i,SY83: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY82 )
                    | ~ ( aScalar0 @ SY83 )
                    | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                      = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
              | ~ ! [SY84: $i] :
                    ( ~ ( aScalar0 @ SV25 )
                    | ~ ( aScalar0 @ SY84 )
                    | ! [SX2: $i] :
                        ~ ( aScalar0 @ SX2 )
                    | ( ( sdtpldt0 @ SV25 @ SY84 )
                      = ( sdtpldt0 @ SY84 @ SV25 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[318]) ).

thf(348,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY86: $i,SY87: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY86 )
              | ~ ( aScalar0 @ SY87 )
              | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
                = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[318]) ).

thf(349,plain,
    ! [SV61: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV61 )
          | ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[319]) ).

thf(350,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                        ( ~ ( aScalar0 @ SX0 )
                                        | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                          = SX0 ) )
                                  | ~ ! [SX0: $i] :
                                        ( ~ ( aScalar0 @ SX0 )
                                        | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                          = SX0 ) ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aScalar0 @ SX0 )
                                  | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                    = sz0z00 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                              = sz0z00 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                        = sz0z00 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
                  = sz0z00 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[320]) ).

thf(351,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( smndt0 @ ( smndt0 @ SX0 ) )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[321]) ).

thf(352,plain,
    ! [SV62: $i] :
      ( ( ( aScalar0 @ SV62 )
        = $false )
      | ( ( ( smndt0 @ sz0z00 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[322]) ).

thf(353,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ( ( ( szszuzczcdt0 @ SV2 )
           != ( szszuzczcdt0 @ SV26 ) ) )
        = $true )
      | ( ( SV2 = SV26 )
        = $true )
      | ( ( aNaturalNumber0 @ SV2 )
        = $false )
      | ( ( aNaturalNumber0 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[323]) ).

thf(354,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ( ~ ( aScalar0 @ SV8 )
          | ~ ( aScalar0 @ SV29 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV39 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[327]) ).

thf(355,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 )
          | ~ ( sdtlseqdt0 @ SV31 @ SV11 ) )
        = $true )
      | ( ( SV11 = SV31 )
        = $true )
      | ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( aScalar0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[330]) ).

thf(356,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV32 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV41 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(357,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( aScalar0 @ SV13 )
          | ~ ( aScalar0 @ SV33 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV42 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[332]) ).

thf(358,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( aScalar0 @ SV14 )
          | ~ ( aScalar0 @ SV34 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV43 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[333]) ).

thf(359,plain,
    ! [SV35: $i,SV15: $i] :
      ( ( ( sdtlseqdt0 @ SV15 @ SV35 )
        = $true )
      | ( ( sdtlseqdt0 @ SV35 @ SV15 )
        = $true )
      | ( ( aScalar0 @ SV15 )
        = $false )
      | ( ( aScalar0 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[334]) ).

thf(360,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 )
          | ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) ) )
        = $true )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[335]) ).

thf(361,plain,
    ! [SV23: $i] :
      ( ( ( SV23
          = ( szszuzczcdt0 @ ( sK1_W1 @ SV23 ) ) )
        = $true )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ SV23 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[337]) ).

thf(362,plain,
    ! [SV23: $i] :
      ( ( ( aNaturalNumber0 @ ( sK1_W1 @ SV23 ) )
        = $true )
      | ( ( SV23 = sz00 )
        = $true )
      | ( ( aNaturalNumber0 @ SV23 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[338]) ).

thf(363,plain,
    ! [SV47: $i] :
      ( ( ( ( szszuzczcdt0 @ SV47 )
          = sz00 )
        = $false )
      | ( ( aNaturalNumber0 @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(364,plain,
    ! [SV55: $i,SV49: $i] :
      ( ( ( ~ ( aScalar0 @ SV49 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV55 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SV55 ) )
          = ( smndt0 @ ( sdtasdt0 @ SV49 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[341]) ).

thf(365,plain,
    ! [SV56: $i,SV50: $i] :
      ( ( ( ~ ( aScalar0 @ SV50 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV56 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SV56 )
          = ( smndt0 @ ( sdtasdt0 @ SV50 @ SV56 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[342]) ).

thf(366,plain,
    ! [SV63: $i,SV57: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 )
          | ~ ( aScalar0 @ SV57 )
          | ~ ( aScalar0 @ SV63 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(367,plain,
    ! [SV64: $i,SV58: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 )
          | ~ ( aScalar0 @ SV58 )
          | ~ ( aScalar0 @ SV64 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[344]) ).

thf(368,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( ~ ( aScalar0 @ SV51 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV59 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[345]) ).

thf(369,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( ~ ( aScalar0 @ SV52 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV60 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[346]) ).

thf(370,plain,
    ! [SV25: $i] :
      ( ( ~ ( ~ ! [SY82: $i,SY83: $i] :
                  ( ~ ( aScalar0 @ SV25 )
                  | ~ ( aScalar0 @ SY82 )
                  | ~ ( aScalar0 @ SY83 )
                  | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                    = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
            | ~ ! [SY84: $i] :
                  ( ~ ( aScalar0 @ SV25 )
                  | ~ ( aScalar0 @ SY84 )
                  | ! [SX2: $i] :
                      ~ ( aScalar0 @ SX2 )
                  | ( ( sdtpldt0 @ SV25 @ SY84 )
                    = ( sdtpldt0 @ SY84 @ SV25 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[347]) ).

thf(371,plain,
    ! [SV25: $i] :
      ( ( ! [SY86: $i,SY87: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SY86 )
            | ~ ( aScalar0 @ SY87 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SY86 ) @ SY87 )
              = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SY86 @ SY87 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[348]) ).

thf(372,plain,
    ! [SV61: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV61 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[349]) ).

thf(373,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                      = SX0 ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                      = SX0 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                    = sz0z00 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[350]) ).

thf(374,plain,
    ! [SV65: $i] :
      ( ( ~ ( aScalar0 @ SV65 )
        | ( ( smndt0 @ ( smndt0 @ SV65 ) )
          = SV65 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[351]) ).

thf(375,plain,
    ! [SV26: $i,SV2: $i] :
      ( ( ( ( szszuzczcdt0 @ SV2 )
          = ( szszuzczcdt0 @ SV26 ) )
        = $false )
      | ( ( SV2 = SV26 )
        = $true )
      | ( ( aNaturalNumber0 @ SV2 )
        = $false )
      | ( ( aNaturalNumber0 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[353]) ).

thf(376,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ( ~ ( aScalar0 @ SV8 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV29 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV39 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[354]) ).

thf(377,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV11 @ SV31 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV31 @ SV11 ) )
        = $true )
      | ( ( SV11 = SV31 )
        = $true )
      | ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( aScalar0 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[355]) ).

thf(378,plain,
    ! [SV41: $i,SV12: $i,SV32: $i] :
      ( ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV41 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[356]) ).

thf(379,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( aScalar0 @ SV13 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV33 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV42 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[357]) ).

thf(380,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( aScalar0 @ SV14 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV34 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV43 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[358]) ).

thf(381,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV36 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) ) )
        = $true )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[360]) ).

thf(382,plain,
    ! [SV55: $i,SV49: $i] :
      ( ( ( aScalar0 @ SV49 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV55 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SV55 ) )
          = ( smndt0 @ ( sdtasdt0 @ SV49 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[364]) ).

thf(383,plain,
    ! [SV56: $i,SV50: $i] :
      ( ( ( aScalar0 @ SV50 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV56 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SV56 )
          = ( smndt0 @ ( sdtasdt0 @ SV50 @ SV56 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[365]) ).

thf(384,plain,
    ! [SV63: $i,SV57: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 )
          | ~ ( aScalar0 @ SV57 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV63 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[366]) ).

thf(385,plain,
    ! [SV64: $i,SV58: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 )
          | ~ ( aScalar0 @ SV58 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV64 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[367]) ).

thf(386,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV59 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[368]) ).

thf(387,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV60 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[369]) ).

thf(388,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY82: $i,SY83: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY82 )
              | ~ ( aScalar0 @ SY83 )
              | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) )
        | ~ ! [SY84: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY84 )
              | ! [SX2: $i] :
                  ~ ( aScalar0 @ SX2 )
              | ( ( sdtpldt0 @ SV25 @ SY84 )
                = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[370]) ).

thf(389,plain,
    ! [SV66: $i,SV25: $i] :
      ( ( ! [SY107: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SV66 )
            | ~ ( aScalar0 @ SY107 )
            | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SY107 )
              = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SY107 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[371]) ).

thf(390,plain,
    ! [SV61: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV61 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[372]) ).

thf(391,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                      = SX0 ) )
                              | ~ ! [SX0: $i] :
                                    ( ~ ( aScalar0 @ SX0 )
                                    | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                      = SX0 ) ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                                = sz0z00 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                    = sz0z00 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[373]) ).

thf(392,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[373]) ).

thf(393,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( aScalar0 @ SV65 ) )
        = $true )
      | ( ( ( smndt0 @ ( smndt0 @ SV65 ) )
          = SV65 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[374]) ).

thf(394,plain,
    ! [SV44: $i,SV39: $i,SV29: $i,SV8: $i] :
      ( ( ( aScalar0 @ SV8 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV29 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV39 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[376]) ).

thf(395,plain,
    ! [SV31: $i,SV11: $i] :
      ( ( ( sdtlseqdt0 @ SV11 @ SV31 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV31 @ SV11 ) )
        = $true )
      | ( ( SV11 = SV31 )
        = $true )
      | ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( aScalar0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[377]) ).

thf(396,plain,
    ! [SV32: $i,SV12: $i,SV41: $i] :
      ( ( ( aScalar0 @ SV41 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 )
          | ( sdtlseqdt0 @ SV12 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[378]) ).

thf(397,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV33 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV42 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[379]) ).

thf(398,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV34 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV43 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[380]) ).

thf(399,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV17 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV36 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) ) )
        = $true )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[381]) ).

thf(400,plain,
    ! [SV49: $i,SV55: $i] :
      ( ( ( aScalar0 @ SV55 )
        = $false )
      | ( ( aScalar0 @ SV49 )
        = $false )
      | ( ( ( sdtasdt0 @ SV49 @ ( smndt0 @ SV55 ) )
          = ( smndt0 @ ( sdtasdt0 @ SV49 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[382]) ).

thf(401,plain,
    ! [SV50: $i,SV56: $i] :
      ( ( ( aScalar0 @ SV56 )
        = $false )
      | ( ( aScalar0 @ SV50 )
        = $false )
      | ( ( ( sdtasdt0 @ ( smndt0 @ SV50 ) @ SV56 )
          = ( smndt0 @ ( sdtasdt0 @ SV50 @ SV56 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[383]) ).

thf(402,plain,
    ! [SV63: $i,SV57: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV57 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV63 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[384]) ).

thf(403,plain,
    ! [SV64: $i,SV58: $i,SV24: $i] :
      ( ( ( ~ ( aScalar0 @ SV24 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV58 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV64 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[385]) ).

thf(404,plain,
    ! [SV51: $i,SV59: $i] :
      ( ( ( aScalar0 @ SV59 )
        = $false )
      | ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[386]) ).

thf(405,plain,
    ! [SV52: $i,SV60: $i] :
      ( ( ( aScalar0 @ SV60 )
        = $false )
      | ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 )
          | ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[387]) ).

thf(406,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY82: $i,SY83: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY82 )
              | ~ ( aScalar0 @ SY83 )
              | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
                = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[388]) ).

thf(407,plain,
    ! [SV25: $i] :
      ( ( ~ ! [SY84: $i] :
              ( ~ ( aScalar0 @ SV25 )
              | ~ ( aScalar0 @ SY84 )
              | ! [SX2: $i] :
                  ~ ( aScalar0 @ SX2 )
              | ( ( sdtpldt0 @ SV25 @ SY84 )
                = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[388]) ).

thf(408,plain,
    ! [SV67: $i,SV66: $i,SV25: $i] :
      ( ( ~ ( aScalar0 @ SV25 )
        | ~ ( aScalar0 @ SV66 )
        | ~ ( aScalar0 @ SV67 )
        | ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[389]) ).

thf(409,plain,
    ! [SV61: $i,SV25: $i] :
      ( ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV61 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[390]) ).

thf(410,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                  ( ~ ( aScalar0 @ SX0 )
                                  | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                    = SX0 ) )
                            | ~ ! [SX0: $i] :
                                  ( ~ ( aScalar0 @ SX0 )
                                  | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                    = SX0 ) ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                              = sz0z00 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                        = sz0z00 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
                  = sz0z00 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[391]) ).

thf(411,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtpldt0 @ ( smndt0 @ SX0 ) @ SX0 )
            = sz0z00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[392]) ).

thf(412,plain,
    ! [SV65: $i] :
      ( ( ( aScalar0 @ SV65 )
        = $false )
      | ( ( ( smndt0 @ ( smndt0 @ SV65 ) )
          = SV65 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[393]) ).

thf(413,plain,
    ! [SV44: $i,SV39: $i,SV8: $i,SV29: $i] :
      ( ( ( aScalar0 @ SV29 )
        = $false )
      | ( ( aScalar0 @ SV8 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV39 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[394]) ).

thf(414,plain,
    ! [SV11: $i,SV31: $i] :
      ( ( ( sdtlseqdt0 @ SV31 @ SV11 )
        = $false )
      | ( ( sdtlseqdt0 @ SV11 @ SV31 )
        = $false )
      | ( ( SV11 = SV31 )
        = $true )
      | ( ( aScalar0 @ SV11 )
        = $false )
      | ( ( aScalar0 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[395]) ).

thf(415,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 )
          | ~ ( sdtlseqdt0 @ SV32 @ SV41 ) )
        = $true )
      | ( ( sdtlseqdt0 @ SV12 @ SV41 )
        = $true )
      | ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( aScalar0 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[396]) ).

thf(416,plain,
    ! [SV45: $i,SV42: $i,SV13: $i,SV33: $i] :
      ( ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV42 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[397]) ).

thf(417,plain,
    ! [SV46: $i,SV43: $i,SV14: $i,SV34: $i] :
      ( ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV43 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[398]) ).

thf(418,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV17 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV36 ) )
        = $true )
      | ( ( ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) ) )
        = $true )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[399]) ).

thf(419,plain,
    ! [SV63: $i,SV57: $i,SV24: $i] :
      ( ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV57 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV63 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[402]) ).

thf(420,plain,
    ! [SV64: $i,SV58: $i,SV24: $i] :
      ( ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV58 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV64 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[403]) ).

thf(421,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV59 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) )
        = $true )
      | ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( aScalar0 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[404]) ).

thf(422,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV60 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) )
        = $true )
      | ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( aScalar0 @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[405]) ).

thf(423,plain,
    ! [SV25: $i] :
      ( ( ! [SY82: $i,SY83: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SY82 )
            | ~ ( aScalar0 @ SY83 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SY82 ) @ SY83 )
              = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SY82 @ SY83 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[406]) ).

thf(424,plain,
    ! [SV25: $i] :
      ( ( ! [SY84: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SY84 )
            | ! [SX2: $i] :
                ~ ( aScalar0 @ SX2 )
            | ( ( sdtpldt0 @ SV25 @ SY84 )
              = ( sdtpldt0 @ SY84 @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[407]) ).

thf(425,plain,
    ! [SV67: $i,SV66: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV66 )
          | ~ ( aScalar0 @ SV67 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[408]) ).

thf(426,plain,
    ! [SV25: $i,SV61: $i] :
      ( ( ( aScalar0 @ SV61 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[409]) ).

thf(427,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                = SX0 ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                = SX0 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                    = sz0z00 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[410]) ).

thf(428,plain,
    ! [SV68: $i] :
      ( ( ~ ( aScalar0 @ SV68 )
        | ( ( sdtpldt0 @ ( smndt0 @ SV68 ) @ SV68 )
          = sz0z00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[411]) ).

thf(429,plain,
    ! [SV44: $i,SV29: $i,SV8: $i,SV39: $i] :
      ( ( ( aScalar0 @ SV39 )
        = $false )
      | ( ( aScalar0 @ SV8 )
        = $false )
      | ( ( aScalar0 @ SV29 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV44 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[413]) ).

thf(430,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV12 @ SV32 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV32 @ SV41 ) )
        = $true )
      | ( ( sdtlseqdt0 @ SV12 @ SV41 )
        = $true )
      | ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( aScalar0 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[415]) ).

thf(431,plain,
    ! [SV45: $i,SV33: $i,SV13: $i,SV42: $i] :
      ( ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV45 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[416]) ).

thf(432,plain,
    ! [SV46: $i,SV34: $i,SV14: $i,SV43: $i] :
      ( ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV46 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[417]) ).

thf(433,plain,
    ! [SV17: $i,SV36: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV36 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV17 )
        = $false )
      | ( ( ( ( sdtasdt0 @ SV17 @ SV17 )
           != ( sdtasdt0 @ SV36 @ SV36 ) ) )
        = $true )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[418]) ).

thf(434,plain,
    ! [SV63: $i,SV24: $i,SV57: $i] :
      ( ( ( aScalar0 @ SV57 )
        = $false )
      | ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV63 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[419]) ).

thf(435,plain,
    ! [SV64: $i,SV24: $i,SV58: $i] :
      ( ( ( aScalar0 @ SV58 )
        = $false )
      | ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV64 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[420]) ).

thf(436,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV51 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) )
        = $true )
      | ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( aScalar0 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[421]) ).

thf(437,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV52 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV60 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) )
        = $true )
      | ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( aScalar0 @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[422]) ).

thf(438,plain,
    ! [SV69: $i,SV25: $i] :
      ( ( ! [SY108: $i] :
            ( ~ ( aScalar0 @ SV25 )
            | ~ ( aScalar0 @ SV69 )
            | ~ ( aScalar0 @ SY108 )
            | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SY108 )
              = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SY108 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[423]) ).

thf(439,plain,
    ! [SV70: $i,SV25: $i] :
      ( ( ~ ( aScalar0 @ SV25 )
        | ~ ( aScalar0 @ SV70 )
        | ! [SX2: $i] :
            ~ ( aScalar0 @ SX2 )
        | ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[424]) ).

thf(440,plain,
    ! [SV67: $i,SV66: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV66 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV67 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[425]) ).

thf(441,plain,
    ! [SV61: $i,SV25: $i,SV71: $i] :
      ( ( ( ~ ( aScalar0 @ SV71 ) )
        = $true )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV61 )
        = $false )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[426]) ).

thf(442,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                                = SX0 ) )
                        | ~ ! [SX0: $i] :
                              ( ~ ( aScalar0 @ SX0 )
                              | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                                = SX0 ) ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                          = sz0z00 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                    = sz0z00 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[427]) ).

thf(443,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[427]) ).

thf(444,plain,
    ! [SV68: $i] :
      ( ( ( ~ ( aScalar0 @ SV68 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( smndt0 @ SV68 ) @ SV68 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[428]) ).

thf(445,plain,
    ! [SV39: $i,SV8: $i,SV29: $i,SV44: $i] :
      ( ( ( aScalar0 @ SV44 )
        = $false )
      | ( ( aScalar0 @ SV29 )
        = $false )
      | ( ( aScalar0 @ SV8 )
        = $false )
      | ( ( aScalar0 @ SV39 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV8 @ SV29 ) @ ( sdtpldt0 @ SV39 @ SV44 ) )
          = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ SV8 @ SV39 ) @ ( sdtasdt0 @ SV8 @ SV44 ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ SV29 @ SV39 ) @ ( sdtasdt0 @ SV29 @ SV44 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[429]) ).

thf(446,plain,
    ! [SV41: $i,SV32: $i,SV12: $i] :
      ( ( ( sdtlseqdt0 @ SV12 @ SV32 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV32 @ SV41 ) )
        = $true )
      | ( ( sdtlseqdt0 @ SV12 @ SV41 )
        = $true )
      | ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( aScalar0 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[430]) ).

thf(447,plain,
    ! [SV42: $i,SV13: $i,SV33: $i,SV45: $i] :
      ( ( ( aScalar0 @ SV45 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 )
          | ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[431]) ).

thf(448,plain,
    ! [SV43: $i,SV14: $i,SV34: $i,SV46: $i] :
      ( ( ( aScalar0 @ SV46 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 )
          | ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[432]) ).

thf(449,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( ( sdtasdt0 @ SV17 @ SV17 )
          = ( sdtasdt0 @ SV36 @ SV36 ) )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV17 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV36 )
        = $false )
      | ( ( SV17 = SV36 )
        = $true )
      | ( ( aScalar0 @ SV17 )
        = $false )
      | ( ( aScalar0 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[433]) ).

thf(450,plain,
    ! [SV57: $i,SV24: $i,SV63: $i] :
      ( ( ( aScalar0 @ SV63 )
        = $false )
      | ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( aScalar0 @ SV57 )
        = $false )
      | ( ( ( sdtasdt0 @ SV24 @ ( sdtpldt0 @ SV57 @ SV63 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV57 ) @ ( sdtasdt0 @ SV24 @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[434]) ).

thf(451,plain,
    ! [SV58: $i,SV24: $i,SV64: $i] :
      ( ( ( aScalar0 @ SV64 )
        = $false )
      | ( ( aScalar0 @ SV24 )
        = $false )
      | ( ( aScalar0 @ SV58 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtpldt0 @ SV24 @ SV58 ) @ SV64 )
          = ( sdtpldt0 @ ( sdtasdt0 @ SV24 @ SV64 ) @ ( sdtasdt0 @ SV58 @ SV64 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[435]) ).

thf(452,plain,
    ! [SV59: $i,SV51: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV51 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV59 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) )
        = $true )
      | ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( aScalar0 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[436]) ).

thf(453,plain,
    ! [SV60: $i,SV52: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV52 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV60 ) )
        = $true )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) )
        = $true )
      | ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( aScalar0 @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[437]) ).

thf(454,plain,
    ! [SV72: $i,SV69: $i,SV25: $i] :
      ( ( ~ ( aScalar0 @ SV25 )
        | ~ ( aScalar0 @ SV69 )
        | ~ ( aScalar0 @ SV72 )
        | ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[438]) ).

thf(455,plain,
    ! [SV70: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV70 )
          | ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[439]) ).

thf(456,plain,
    ! [SV67: $i,SV66: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV66 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV67 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[440]) ).

thf(457,plain,
    ! [SV61: $i,SV25: $i,SV71: $i] :
      ( ( ( aScalar0 @ SV71 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV61 )
        = $false )
      | ( ( ( sdtasdt0 @ SV25 @ SV61 )
          = ( sdtasdt0 @ SV61 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[441]) ).

thf(458,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                              = SX0 ) )
                      | ~ ! [SX0: $i] :
                            ( ~ ( aScalar0 @ SX0 )
                            | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                              = SX0 ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                        = sz0z00 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtasdt0 @ sz0z00 @ SX0 )
                  = sz0z00 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[442]) ).

thf(459,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ ( smndt0 @ SX0 ) )
            = sz0z00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[443]) ).

thf(460,plain,
    ! [SV68: $i] :
      ( ( ( aScalar0 @ SV68 )
        = $false )
      | ( ( ( sdtpldt0 @ ( smndt0 @ SV68 ) @ SV68 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[444]) ).

thf(461,plain,
    ! [SV12: $i,SV41: $i,SV32: $i] :
      ( ( ( sdtlseqdt0 @ SV32 @ SV41 )
        = $false )
      | ( ( sdtlseqdt0 @ SV12 @ SV32 )
        = $false )
      | ( ( sdtlseqdt0 @ SV12 @ SV41 )
        = $true )
      | ( ( aScalar0 @ SV32 )
        = $false )
      | ( ( aScalar0 @ SV12 )
        = $false )
      | ( ( aScalar0 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[446]) ).

thf(462,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 )
          | ~ ( sdtlseqdt0 @ SV42 @ SV45 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) )
        = $true )
      | ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[447]) ).

thf(463,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 )
          | ~ ( sdtlseqdt0 @ SV43 @ SV46 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[448]) ).

thf(464,plain,
    ! [SV51: $i,SV59: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV59 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV51 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ SV51 @ SV59 ) )
        = $true )
      | ( ( aScalar0 @ SV51 )
        = $false )
      | ( ( aScalar0 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[452]) ).

thf(465,plain,
    ! [SV52: $i,SV60: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV60 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV52 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ SV52 @ SV60 ) )
        = $true )
      | ( ( aScalar0 @ SV52 )
        = $false )
      | ( ( aScalar0 @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[453]) ).

thf(466,plain,
    ! [SV72: $i,SV69: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV69 )
          | ~ ( aScalar0 @ SV72 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[454]) ).

thf(467,plain,
    ! [SV70: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV70 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[455]) ).

thf(468,plain,
    ! [SV67: $i,SV66: $i,SV25: $i] :
      ( ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV66 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV67 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[456]) ).

thf(469,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                          = SX0 ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                          = SX0 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                    = sz0z00 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtasdt0 @ sz0z00 @ SX0 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[458]) ).

thf(470,plain,
    ! [SV73: $i] :
      ( ( ~ ( aScalar0 @ SV73 )
        | ( ( sdtpldt0 @ SV73 @ ( smndt0 @ SV73 ) )
          = sz0z00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[459]) ).

thf(471,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV13 @ SV33 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV42 @ SV45 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) )
        = $true )
      | ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[462]) ).

thf(472,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 )
          | ~ ( sdtlseqdt0 @ sz0z00 @ SV43 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV43 @ SV46 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[463]) ).

thf(473,plain,
    ! [SV72: $i,SV69: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 )
          | ~ ( aScalar0 @ SV69 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV72 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[466]) ).

thf(474,plain,
    ! [SV70: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV70 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[467]) ).

thf(475,plain,
    ! [SV67: $i,SV25: $i,SV66: $i] :
      ( ( ( aScalar0 @ SV66 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV67 ) )
        = $true )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[468]) ).

thf(476,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                          = SX0 ) )
                  | ~ ! [SX0: $i] :
                        ( ~ ( aScalar0 @ SX0 )
                        | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                          = SX0 ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                    = sz0z00 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[469]) ).

thf(477,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtasdt0 @ sz0z00 @ SX0 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[469]) ).

thf(478,plain,
    ! [SV73: $i] :
      ( ( ( ~ ( aScalar0 @ SV73 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV73 @ ( smndt0 @ SV73 ) )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[470]) ).

thf(479,plain,
    ! [SV45: $i,SV42: $i,SV33: $i,SV13: $i] :
      ( ( ( sdtlseqdt0 @ SV13 @ SV33 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV42 @ SV45 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) )
        = $true )
      | ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[471]) ).

thf(480,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( ~ ( sdtlseqdt0 @ SV14 @ SV34 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV43 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV43 @ SV46 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[472]) ).

thf(481,plain,
    ! [SV72: $i,SV69: $i,SV25: $i] :
      ( ( ( ~ ( aScalar0 @ SV25 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV69 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV72 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[473]) ).

thf(482,plain,
    ! [SV70: $i,SV25: $i] :
      ( ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV70 ) )
        = $true )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[474]) ).

thf(483,plain,
    ! [SV66: $i,SV25: $i,SV67: $i] :
      ( ( ( aScalar0 @ SV67 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV66 )
        = $false )
      | ( ( ( sdtasdt0 @ ( sdtasdt0 @ SV25 @ SV66 ) @ SV67 )
          = ( sdtasdt0 @ SV25 @ ( sdtasdt0 @ SV66 @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[475]) ).

thf(484,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                        = SX0 ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( aScalar0 @ SX0 )
                      | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                        = SX0 ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtasdt0 @ SX0 @ sz0z00 )
                  = sz0z00 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[476]) ).

thf(485,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtasdt0 @ sz0z00 @ SX0 )
            = sz0z00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[477]) ).

thf(486,plain,
    ! [SV73: $i] :
      ( ( ( aScalar0 @ SV73 )
        = $false )
      | ( ( ( sdtpldt0 @ SV73 @ ( smndt0 @ SV73 ) )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[478]) ).

thf(487,plain,
    ! [SV33: $i,SV13: $i,SV45: $i,SV42: $i] :
      ( ( ( sdtlseqdt0 @ SV42 @ SV45 )
        = $false )
      | ( ( sdtlseqdt0 @ SV13 @ SV33 )
        = $false )
      | ( ( sdtlseqdt0 @ ( sdtpldt0 @ SV13 @ SV42 ) @ ( sdtpldt0 @ SV33 @ SV45 ) )
        = $true )
      | ( ( aScalar0 @ SV42 )
        = $false )
      | ( ( aScalar0 @ SV13 )
        = $false )
      | ( ( aScalar0 @ SV33 )
        = $false )
      | ( ( aScalar0 @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[479]) ).

thf(488,plain,
    ! [SV46: $i,SV43: $i,SV34: $i,SV14: $i] :
      ( ( ( sdtlseqdt0 @ SV14 @ SV34 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ sz0z00 @ SV43 ) )
        = $true )
      | ( ( ~ ( sdtlseqdt0 @ SV43 @ SV46 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[480]) ).

thf(489,plain,
    ! [SV72: $i,SV69: $i,SV25: $i] :
      ( ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV69 ) )
        = $true )
      | ( ( ~ ( aScalar0 @ SV72 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[481]) ).

thf(490,plain,
    ! [SV25: $i,SV70: $i] :
      ( ( ( aScalar0 @ SV70 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ! [SX2: $i] :
              ~ ( aScalar0 @ SX2 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[482]) ).

thf(491,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                    = SX0 ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                    = SX0 ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz0z00 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[484]) ).

thf(492,plain,
    ! [SV74: $i] :
      ( ( ~ ( aScalar0 @ SV74 )
        | ( ( sdtasdt0 @ sz0z00 @ SV74 )
          = sz0z00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[485]) ).

thf(493,plain,
    ! [SV46: $i,SV34: $i,SV14: $i,SV43: $i] :
      ( ( ( sdtlseqdt0 @ sz0z00 @ SV43 )
        = $false )
      | ( ( sdtlseqdt0 @ SV14 @ SV34 )
        = $false )
      | ( ( ~ ( sdtlseqdt0 @ SV43 @ SV46 ) )
        = $true )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[488]) ).

thf(494,plain,
    ! [SV72: $i,SV25: $i,SV69: $i] :
      ( ( ( aScalar0 @ SV69 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( ~ ( aScalar0 @ SV72 ) )
        = $true )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[489]) ).

thf(495,plain,
    ! [SV70: $i,SV25: $i,SV75: $i] :
      ( ( ( ~ ( aScalar0 @ SV75 ) )
        = $true )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV70 )
        = $false )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[490]) ).

thf(496,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                    = SX0 ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( aScalar0 @ SX0 )
                  | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[491]) ).

thf(497,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtasdt0 @ SX0 @ sz0z00 )
              = sz0z00 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[491]) ).

thf(498,plain,
    ! [SV74: $i] :
      ( ( ( ~ ( aScalar0 @ SV74 ) )
        = $true )
      | ( ( ( sdtasdt0 @ sz0z00 @ SV74 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[492]) ).

thf(499,plain,
    ! [SV34: $i,SV14: $i,SV46: $i,SV43: $i] :
      ( ( ( sdtlseqdt0 @ SV43 @ SV46 )
        = $false )
      | ( ( sdtlseqdt0 @ SV14 @ SV34 )
        = $false )
      | ( ( sdtlseqdt0 @ sz0z00 @ SV43 )
        = $false )
      | ( ( sdtlseqdt0 @ ( sdtasdt0 @ SV14 @ SV43 ) @ ( sdtasdt0 @ SV34 @ SV46 ) )
        = $true )
      | ( ( aScalar0 @ SV43 )
        = $false )
      | ( ( aScalar0 @ SV14 )
        = $false )
      | ( ( aScalar0 @ SV34 )
        = $false )
      | ( ( aScalar0 @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[493]) ).

thf(500,plain,
    ! [SV69: $i,SV25: $i,SV72: $i] :
      ( ( ( aScalar0 @ SV72 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV69 )
        = $false )
      | ( ( ( sdtpldt0 @ ( sdtpldt0 @ SV25 @ SV69 ) @ SV72 )
          = ( sdtpldt0 @ SV25 @ ( sdtpldt0 @ SV69 @ SV72 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[494]) ).

thf(501,plain,
    ! [SV70: $i,SV25: $i,SV75: $i] :
      ( ( ( aScalar0 @ SV75 )
        = $false )
      | ( ( aScalar0 @ SV25 )
        = $false )
      | ( ( aScalar0 @ SV70 )
        = $false )
      | ( ( ( sdtpldt0 @ SV25 @ SV70 )
          = ( sdtpldt0 @ SV70 @ SV25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[495]) ).

thf(502,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtpldt0 @ SX0 @ sz0z00 )
                  = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( aScalar0 @ SX0 )
                | ( ( sdtpldt0 @ sz0z00 @ SX0 )
                  = SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[496]) ).

thf(503,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtasdt0 @ SX0 @ sz0z00 )
            = sz0z00 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[497]) ).

thf(504,plain,
    ! [SV74: $i] :
      ( ( ( aScalar0 @ SV74 )
        = $false )
      | ( ( ( sdtasdt0 @ sz0z00 @ SV74 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[498]) ).

thf(505,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz0z00 )
              = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ sz0z00 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[502]) ).

thf(506,plain,
    ! [SV76: $i] :
      ( ( ~ ( aScalar0 @ SV76 )
        | ( ( sdtasdt0 @ SV76 @ sz0z00 )
          = sz0z00 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[503]) ).

thf(507,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ SX0 @ sz0z00 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[505]) ).

thf(508,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( aScalar0 @ SX0 )
            | ( ( sdtpldt0 @ sz0z00 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[505]) ).

thf(509,plain,
    ! [SV76: $i] :
      ( ( ( ~ ( aScalar0 @ SV76 ) )
        = $true )
      | ( ( ( sdtasdt0 @ SV76 @ sz0z00 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[506]) ).

thf(510,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtpldt0 @ SX0 @ sz0z00 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[507]) ).

thf(511,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( aScalar0 @ SX0 )
          | ( ( sdtpldt0 @ sz0z00 @ SX0 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[508]) ).

thf(512,plain,
    ! [SV76: $i] :
      ( ( ( aScalar0 @ SV76 )
        = $false )
      | ( ( ( sdtasdt0 @ SV76 @ sz0z00 )
          = sz0z00 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[509]) ).

thf(513,plain,
    ! [SV77: $i] :
      ( ( ~ ( aScalar0 @ SV77 )
        | ( ( sdtpldt0 @ SV77 @ sz0z00 )
          = SV77 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[510]) ).

thf(514,plain,
    ! [SV78: $i] :
      ( ( ~ ( aScalar0 @ SV78 )
        | ( ( sdtpldt0 @ sz0z00 @ SV78 )
          = SV78 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[511]) ).

thf(515,plain,
    ! [SV77: $i] :
      ( ( ( ~ ( aScalar0 @ SV77 ) )
        = $true )
      | ( ( ( sdtpldt0 @ SV77 @ sz0z00 )
          = SV77 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[513]) ).

thf(516,plain,
    ! [SV78: $i] :
      ( ( ( ~ ( aScalar0 @ SV78 ) )
        = $true )
      | ( ( ( sdtpldt0 @ sz0z00 @ SV78 )
          = SV78 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[514]) ).

thf(517,plain,
    ! [SV77: $i] :
      ( ( ( aScalar0 @ SV77 )
        = $false )
      | ( ( ( sdtpldt0 @ SV77 @ sz0z00 )
          = SV77 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[515]) ).

thf(518,plain,
    ! [SV78: $i] :
      ( ( ( aScalar0 @ SV78 )
        = $false )
      | ( ( ( sdtpldt0 @ sz0z00 @ SV78 )
          = SV78 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[516]) ).

thf(519,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[113,518,517,512,504,501,500,499,487,486,483,465,464,461,460,457,451,450,449,445,414,412,401,400,375,363,362,361,359,352,340,336,329,328,326,325,324,286,258,254,253,249,248,246,244,238,234,231,183,178,163,159,148,147,145,144,120]) ).

thf(520,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[519]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG047+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon May 30 19:08:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.38  
% 0.12/0.38   No.of.Axioms: 33
% 0.12/0.38  
% 0.12/0.38   Length.of.Defs: 0
% 0.12/0.38  
% 0.12/0.38   Contains.Choice.Funs: false
% 0.12/0.39  .
% 0.19/0.41  (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).............................
% 0.40/0.74  
% 0.40/0.74  ********************************
% 0.40/0.74  *   All subproblems solved!    *
% 0.40/0.74  ********************************
% 0.40/0.74  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:39,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:519,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.66/0.91  
% 0.66/0.91  %**** Beginning of derivation protocol ****
% 0.66/0.91  % SZS output start CNFRefutation
% See solution above
% 0.66/0.91  
% 0.66/0.91  %**** End of derivation protocol ****
% 0.66/0.91  %**** no. of clauses in derivation: 520 ****
% 0.66/0.91  %**** clause counter: 519 ****
% 0.66/0.91  
% 0.66/0.91  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:39,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:519,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------