TSTP Solution File: RNG081+2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG081+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:37:44 EDT 2024

% Result   : Theorem 4.94s 2.44s
% Output   : Refutation 5.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  101 (  12 unt;  17 typ;   0 def)
%            Number of atoms       :  431 ( 144 equ;   0 cnn)
%            Maximal formula atoms :   40 (   5 avg)
%            Number of connectives : 1366 (  15   ~;   2   |; 230   &;1004   @)
%                                         (   1 <=>; 114  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   59 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   6 con; 0-2 aty)
%            Number of variables   :  184 (   0   ^ 140   !;  44   ?; 184   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aVector0_type,type,
    aVector0: $i > $o ).

thf(aDimensionOf0_type,type,
    aDimensionOf0: $i > $i ).

thf(sz00_type,type,
    sz00: $i ).

thf(sziznziztdt0_type,type,
    sziznziztdt0: $i > $i ).

thf(szszuzczcdt0_type,type,
    szszuzczcdt0: $i > $i ).

thf(aNaturalNumber0_type,type,
    aNaturalNumber0: $i > $o ).

thf(sdtlbdtrb0_type,type,
    sdtlbdtrb0: $i > $i > $i ).

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

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

thf(aScalar0_type,type,
    aScalar0: $i > $o ).

thf(sdtasasdt0_type,type,
    sdtasasdt0: $i > $i > $i ).

thf(sdtasdt0_type,type,
    sdtasdt0: $i > $i > $i ).

thf(sdtlseqdt0_type,type,
    sdtlseqdt0: $i > $i > $o ).

thf(sdtpldt0_type,type,
    sdtpldt0: $i > $i > $i ).

thf(iLess0_type,type,
    iLess0: $i > $i > $o ).

thf(sz0z00_type,type,
    sz0z00: $i ).

thf(smndt0_type,type,
    smndt0: $i > $i ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ A )
          & ( sdtlseqdt0 @ sz0z00 @ B ) )
       => ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
          & ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).

thf(138,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ A )
          & ( sdtlseqdt0 @ sz0z00 @ B ) )
       => ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
          & ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).

thf(247,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( aDimensionOf0 @ A )
          = ( aDimensionOf0 @ B ) )
       => ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
         => ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1652) ).

thf(142,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( aDimensionOf0 @ A )
          = ( aDimensionOf0 @ B ) )
       => ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
         => ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

thf(179,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

thf(197,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( iLess0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).

thf(129,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).

thf(181,plain,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).

thf(245,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
           != sz00 ) )
       => ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
          = ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).

thf(240,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
           != sz00 ) )
       => ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
          = ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1,conjecture,
    ( ( ( ( aDimensionOf0 @ xs )
       != sz00 )
     => ? [A: $i] :
          ( ( aVector0 @ A )
          & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ A ) )
            = ( aDimensionOf0 @ xs ) )
          & ! [B: $i] :
              ( ( aNaturalNumber0 @ B )
             => ( ( sdtlbdtrb0 @ A @ B )
                = ( sdtlbdtrb0 @ xs @ B ) ) )
          & ( A
            = ( sziznziztdt0 @ xs ) )
          & ? [B: $i] :
              ( ( aVector0 @ B )
              & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                = ( aDimensionOf0 @ xt ) )
              & ! [C: $i] :
                  ( ( aNaturalNumber0 @ C )
                 => ( ( sdtlbdtrb0 @ B @ C )
                    = ( sdtlbdtrb0 @ xt @ C ) ) )
              & ( B
                = ( sziznziztdt0 @ xt ) )
              & ? [C: $i] :
                  ( ( aScalar0 @ C )
                  & ( C
                    = ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
                  & ? [D: $i] :
                      ( ( aScalar0 @ D )
                      & ( D
                        = ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
                      & ? [E: $i] :
                          ( ( aScalar0 @ E )
                          & ( E
                            = ( sdtasasdt0 @ A @ A ) )
                          & ? [F: $i] :
                              ( ( aScalar0 @ F )
                              & ( F
                                = ( sdtasasdt0 @ B @ B ) )
                              & ? [G: $i] :
                                  ( ( aScalar0 @ G )
                                  & ( G
                                    = ( sdtasasdt0 @ A @ B ) )
                                  & ? [H: $i] :
                                      ( ( aScalar0 @ H )
                                      & ( H
                                        = ( sdtasdt0 @ C @ C ) )
                                      & ? [I: $i] :
                                          ( ( aScalar0 @ I )
                                          & ( I
                                            = ( sdtasdt0 @ D @ D ) )
                                          & ? [J: $i] :
                                              ( ( aScalar0 @ J )
                                              & ( J
                                                = ( sdtasdt0 @ C @ D ) )
                                              & ? [K: $i] :
                                                  ( ( aScalar0 @ K )
                                                  & ( K
                                                    = ( sdtasdt0 @ E @ I ) )
                                                  & ? [L: $i] :
                                                      ( ( aScalar0 @ L )
                                                      & ( L
                                                        = ( sdtasdt0 @ G @ J ) )
                                                      & ? [M: $i] :
                                                          ( ( aScalar0 @ M )
                                                          & ( M
                                                            = ( sdtasdt0 @ H @ F ) )
                                                          & ? [N: $i] :
                                                              ( ( aScalar0 @ N )
                                                              & ( N
                                                                = ( sdtasdt0 @ K @ M ) )
                                                              & ( sdtlseqdt0 @ ( sdtasdt0 @ G @ G ) @ ( sdtasdt0 @ E @ F ) )
                                                              & ( sdtlseqdt0 @ ( sdtpldt0 @ L @ L ) @ ( sdtpldt0 @ K @ M ) )
                                                              & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ G @ J ) @ ( sdtpldt0 @ G @ J ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ E @ H ) @ ( sdtpldt0 @ F @ I ) ) )
                                                              & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
   => ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ? [A: $i] :
            ( ( aVector0 @ A )
            & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ A ) )
              = ( aDimensionOf0 @ xs ) )
            & ! [B: $i] :
                ( ( aNaturalNumber0 @ B )
               => ( ( sdtlbdtrb0 @ A @ B )
                  = ( sdtlbdtrb0 @ xs @ B ) ) )
            & ( A
              = ( sziznziztdt0 @ xs ) )
            & ? [B: $i] :
                ( ( aVector0 @ B )
                & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                  = ( aDimensionOf0 @ xt ) )
                & ! [C: $i] :
                    ( ( aNaturalNumber0 @ C )
                   => ( ( sdtlbdtrb0 @ B @ C )
                      = ( sdtlbdtrb0 @ xt @ C ) ) )
                & ( B
                  = ( sziznziztdt0 @ xt ) )
                & ? [C: $i] :
                    ( ( aScalar0 @ C )
                    & ( C
                      = ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
                    & ? [D: $i] :
                        ( ( aScalar0 @ D )
                        & ( D
                          = ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
                        & ? [E: $i] :
                            ( ( aScalar0 @ E )
                            & ( E
                              = ( sdtasasdt0 @ A @ A ) )
                            & ? [F: $i] :
                                ( ( aScalar0 @ F )
                                & ( F
                                  = ( sdtasasdt0 @ B @ B ) )
                                & ? [G: $i] :
                                    ( ( aScalar0 @ G )
                                    & ( G
                                      = ( sdtasasdt0 @ A @ B ) )
                                    & ? [H: $i] :
                                        ( ( aScalar0 @ H )
                                        & ( H
                                          = ( sdtasdt0 @ C @ C ) )
                                        & ? [I: $i] :
                                            ( ( aScalar0 @ I )
                                            & ( I
                                              = ( sdtasdt0 @ D @ D ) )
                                            & ? [J: $i] :
                                                ( ( aScalar0 @ J )
                                                & ( J
                                                  = ( sdtasdt0 @ C @ D ) )
                                                & ? [K: $i] :
                                                    ( ( aScalar0 @ K )
                                                    & ( K
                                                      = ( sdtasdt0 @ E @ I ) )
                                                    & ? [L: $i] :
                                                        ( ( aScalar0 @ L )
                                                        & ( L
                                                          = ( sdtasdt0 @ G @ J ) )
                                                        & ? [M: $i] :
                                                            ( ( aScalar0 @ M )
                                                            & ( M
                                                              = ( sdtasdt0 @ H @ F ) )
                                                            & ? [N: $i] :
                                                                ( ( aScalar0 @ N )
                                                                & ( N
                                                                  = ( sdtasdt0 @ K @ M ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ G @ G ) @ ( sdtasdt0 @ E @ F ) )
                                                                & ( sdtlseqdt0 @ ( sdtpldt0 @ L @ L ) @ ( sdtpldt0 @ K @ M ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ G @ J ) @ ( sdtpldt0 @ G @ J ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ E @ H ) @ ( sdtpldt0 @ F @ I ) ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
     => ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(43,plain,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ? [A: $i] :
            ( ( aVector0 @ A )
            & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ A ) )
              = ( aDimensionOf0 @ xs ) )
            & ! [B: $i] :
                ( ( aNaturalNumber0 @ B )
               => ( ( sdtlbdtrb0 @ A @ B )
                  = ( sdtlbdtrb0 @ xs @ B ) ) )
            & ( A
              = ( sziznziztdt0 @ xs ) )
            & ? [B: $i] :
                ( ( aVector0 @ B )
                & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                  = ( aDimensionOf0 @ xt ) )
                & ! [C: $i] :
                    ( ( aNaturalNumber0 @ C )
                   => ( ( sdtlbdtrb0 @ B @ C )
                      = ( sdtlbdtrb0 @ xt @ C ) ) )
                & ( B
                  = ( sziznziztdt0 @ xt ) )
                & ? [C: $i] :
                    ( ( aScalar0 @ C )
                    & ( C
                      = ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) )
                    & ? [D: $i] :
                        ( ( aScalar0 @ D )
                        & ( D
                          = ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) )
                        & ? [E: $i] :
                            ( ( aScalar0 @ E )
                            & ( E
                              = ( sdtasasdt0 @ A @ A ) )
                            & ? [F: $i] :
                                ( ( aScalar0 @ F )
                                & ( F
                                  = ( sdtasasdt0 @ B @ B ) )
                                & ? [G: $i] :
                                    ( ( aScalar0 @ G )
                                    & ( G
                                      = ( sdtasasdt0 @ A @ B ) )
                                    & ? [H: $i] :
                                        ( ( aScalar0 @ H )
                                        & ( H
                                          = ( sdtasdt0 @ C @ C ) )
                                        & ? [I: $i] :
                                            ( ( aScalar0 @ I )
                                            & ( I
                                              = ( sdtasdt0 @ D @ D ) )
                                            & ? [J: $i] :
                                                ( ( aScalar0 @ J )
                                                & ( J
                                                  = ( sdtasdt0 @ C @ D ) )
                                                & ? [K: $i] :
                                                    ( ( aScalar0 @ K )
                                                    & ( K
                                                      = ( sdtasdt0 @ E @ I ) )
                                                    & ? [L: $i] :
                                                        ( ( aScalar0 @ L )
                                                        & ( L
                                                          = ( sdtasdt0 @ G @ J ) )
                                                        & ? [M: $i] :
                                                            ( ( aScalar0 @ M )
                                                            & ( M
                                                              = ( sdtasdt0 @ H @ F ) )
                                                            & ? [N: $i] :
                                                                ( ( aScalar0 @ N )
                                                                & ( N
                                                                  = ( sdtasdt0 @ K @ M ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ G @ G ) @ ( sdtasdt0 @ E @ F ) )
                                                                & ( sdtlseqdt0 @ ( sdtpldt0 @ L @ L ) @ ( sdtpldt0 @ K @ M ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ G @ J ) @ ( sdtpldt0 @ G @ J ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ E @ H ) @ ( sdtpldt0 @ F @ I ) ) )
                                                                & ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
     => ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xt ) @ ( sdtasasdt0 @ xs @ xt ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ xs @ xs ) @ ( sdtasasdt0 @ xt @ xt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( ( ( aDimensionOf0 @ A )
         != sz00 )
       => ! [B: $i] :
            ( ( B
              = ( sziznziztdt0 @ A ) )
          <=> ( ( aVector0 @ B )
              & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                = ( aDimensionOf0 @ A ) )
              & ! [C: $i] :
                  ( ( aNaturalNumber0 @ C )
                 => ( ( sdtlbdtrb0 @ B @ C )
                    = ( sdtlbdtrb0 @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).

thf(152,plain,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( ( ( aDimensionOf0 @ A )
         != sz00 )
       => ! [B: $i] :
            ( ( ( B
                = ( sziznziztdt0 @ A ) )
             => ( ( aVector0 @ B )
                & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                  = ( aDimensionOf0 @ A ) )
                & ! [C: $i] :
                    ( ( aNaturalNumber0 @ C )
                   => ( ( sdtlbdtrb0 @ B @ C )
                      = ( sdtlbdtrb0 @ A @ C ) ) ) ) )
            & ( ( ( aVector0 @ B )
                & ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
                  = ( aDimensionOf0 @ A ) )
                & ! [C: $i] :
                    ( ( aNaturalNumber0 @ C )
                   => ( ( sdtlbdtrb0 @ B @ C )
                      = ( sdtlbdtrb0 @ A @ C ) ) ) )
             => ( B
                = ( sziznziztdt0 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( A != sz00 ) )
     => ? [B: $i] :
          ( ( aNaturalNumber0 @ B )
          & ( A
            = ( szszuzczcdt0 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).

thf(228,plain,
    ! [A: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( A != sz00 ) )
     => ? [B: $i] :
          ( ( aNaturalNumber0 @ B )
          & ( A
            = ( szszuzczcdt0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ C @ D ) )
       => ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).

thf(133,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ C @ D ) )
       => ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

thf(243,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).

thf(206,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).

thf(233,plain,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).

thf(248,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(24,axiom,
    ( ( aVector0 @ xs )
    & ( aVector0 @ xt ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).

thf(188,plain,
    ( ( aVector0 @ xs )
    & ( aVector0 @ xt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ sz0z00 @ C )
          & ( sdtlseqdt0 @ C @ D ) )
       => ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).

thf(169,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ sz0z00 @ C )
          & ( sdtlseqdt0 @ C @ D ) )
       => ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).

thf(141,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(13,axiom,
    aScalar0 @ sz0z00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

thf(148,plain,
    aScalar0 @ sz0z00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).

thf(149,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).

thf(176,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
        = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).

thf(191,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C )
        & ( aScalar0 @ D ) )
     => ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
        = ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
        & ( ( sdtpldt0 @ A @ B )
          = ( sdtpldt0 @ B @ A ) )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
          = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
        & ( ( sdtasdt0 @ A @ B )
          = ( sdtasdt0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

thf(118,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
        & ( ( sdtpldt0 @ A @ B )
          = ( sdtpldt0 @ B @ A ) )
        & ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
          = ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
        & ( ( sdtasdt0 @ A @ B )
          = ( sdtasdt0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
            = sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).

thf(130,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
            = sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = sz0z00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
           != sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).

thf(135,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( ( aDimensionOf0 @ A )
            = ( aDimensionOf0 @ B ) )
          & ( ( aDimensionOf0 @ B )
           != sz00 ) )
       => ( ( sdtasasdt0 @ A @ B )
          = ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(33,axiom,
    ( ( aDimensionOf0 @ xs )
    = ( aDimensionOf0 @ xt ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).

thf(226,plain,
    ( ( aDimensionOf0 @ xs )
    = ( aDimensionOf0 @ xt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz0z00 )
          = A )
        & ( ( sdtpldt0 @ sz0z00 @ A )
          = A )
        & ( ( sdtasdt0 @ A @ sz0z00 )
          = sz0z00 )
        & ( ( sdtasdt0 @ sz0z00 @ A )
          = sz0z00 )
        & ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz0z00 )
        & ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
          = sz0z00 )
        & ( ( smndt0 @ ( smndt0 @ A ) )
          = A )
        & ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

thf(209,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( ( ( sdtpldt0 @ A @ sz0z00 )
          = A )
        & ( ( sdtpldt0 @ sz0z00 @ A )
          = A )
        & ( ( sdtasdt0 @ A @ sz0z00 )
          = sz0z00 )
        & ( ( sdtasdt0 @ sz0z00 @ A )
          = sz0z00 )
        & ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
          = sz0z00 )
        & ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
          = sz0z00 )
        & ( ( smndt0 @ ( smndt0 @ A ) )
          = A )
        & ( ( smndt0 @ sz0z00 )
          = sz0z00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
        = ( sdtasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).

thf(194,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
        = ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ A )
          & ( sdtlseqdt0 @ sz0z00 @ B )
          & ( ( sdtasdt0 @ A @ A )
            = ( sdtasdt0 @ B @ B ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).

thf(145,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtlseqdt0 @ sz0z00 @ A )
          & ( sdtlseqdt0 @ sz0z00 @ B )
          & ( ( sdtasdt0 @ A @ A )
            = ( sdtasdt0 @ B @ B ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

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

thf(199,plain,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
        & ( ( szszuzczcdt0 @ A )
         != sz00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

thf(127,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(42,axiom,
    aNaturalNumber0 @ sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).

thf(250,plain,
    aNaturalNumber0 @ sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( aDimensionOf0 @ A )
          = ( aDimensionOf0 @ B ) )
       => ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).

thf(203,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aVector0 @ B ) )
     => ( ( ( aDimensionOf0 @ A )
          = ( aDimensionOf0 @ B ) )
       => ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ C ) )
       => ( sdtlseqdt0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).

thf(186,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtlseqdt0 @ A @ B )
          & ( sdtlseqdt0 @ B @ C ) )
       => ( sdtlseqdt0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
          = ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
        & ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
          = ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

thf(171,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
          = ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
        & ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
          = ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).

thf(235,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B )
        & ( aScalar0 @ C ) )
     => ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
          = ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).

thf(207,plain,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).

thf(151,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).

thf(183,plain,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(253,plain,
    $false,
    inference(cvc4,[status(thm)],[138,247,142,179,197,129,181,245,240,43,152,228,133,243,206,233,248,188,169,141,148,149,176,191,118,130,135,226,209,194,145,199,127,250,203,186,171,235,207,151,183]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : RNG081+2 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat May 18 12:25:53 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.79/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.93  % [INFO] 	 Parsing done (148ms). 
% 1.22/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.75/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.26  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.09/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ... 
% 2.24/1.39  % [INFO] 	 Axiom selection finished. Selected 40 axioms (removed 0 axioms). 
% 2.24/1.42  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.24/1.44  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.24/1.45  % [INFO] 	 Type checking passed. 
% 2.47/1.45  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.94/2.44  % External prover 'cvc4' found a proof!
% 4.94/2.44  % [INFO] 	 Killing All external provers ... 
% 4.94/2.44  % Time passed: 1974ms (effective reasoning time: 1486ms)
% 4.94/2.44  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.94/2.44  % Axioms used in derivation (40): mLERef, mMulSc, mMNeg, mScSort, mLETrn, mDefSPZ, mSqrt, mZeroNat, mIH, mLess, mElmSc, m__1678, mSuccEqu, mScSqPos, mNatExtr, mArith, mDefSPN, mDimNat, mLEMonM, mPosMon, mDefInit, mMDNeg, mLETot, mDistr, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, m__1678_01, mDistr2, mSqPos, m__1652, mNatSort, mIHOrd, mNegSc, mSuccNat
% 4.94/2.44  % No. of inferences in proof: 84
% 4.94/2.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1974 ms resp. 1486 ms w/o parsing
% 5.29/2.49  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.29/2.49  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------