TSTP Solution File: RNG050+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 02:37:34 EDT 2024

% Result   : Theorem 5.20s 2.71s
% Output   : Refutation 5.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   96 (  12 unt;  16 typ;   0 def)
%            Number of atoms       :  308 (  86 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  893 (  15   ~;   2   |; 121   &; 650   @)
%                                         (   1 <=>; 104  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   5 con; 0-2 aty)
%            Number of variables   :  132 (   0   ^ 130   !;   2   ?; 132   :)

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

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

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

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

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

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

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

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

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

thf(101,plain,
    aScalar0 @ sz0z00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

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

thf(56,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).

thf(57,plain,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(30,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(132,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)],[30]) ).

thf(12,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(70,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)],[12]) ).

thf(33,axiom,
    aVector0 @ xs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).

thf(156,plain,
    aVector0 @ xs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).

thf(59,plain,
    ! [A: $i,B: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( ( ( szszuzczcdt0 @ A )
          = ( szszuzczcdt0 @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(22,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(98,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)],[22]) ).

thf(25,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(103,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)],[25]) ).

thf(14,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(80,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)],[14]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

thf(123,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(21,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(95,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)],[21]) ).

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

thf(67,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(18,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(87,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)],[18]) ).

thf(13,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(75,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)],[13]) ).

thf(40,axiom,
    aNaturalNumber0 @ sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).

thf(170,plain,
    aNaturalNumber0 @ sz00,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(26,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(120,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)],[26]) ).

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

thf(125,plain,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
        & ( ( szszuzczcdt0 @ A )
         != sz00 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(34,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(157,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)],[34]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).

thf(85,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
       => $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).

thf(102,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(20,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(92,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)],[20]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

thf(65,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( aScalar0 @ ( smndt0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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(129,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(1,conjecture,
    ( ( ( ( aDimensionOf0 @ xs )
       != sz00 )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
   => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(41,plain,
    ~ ( ( ( ( aDimensionOf0 @ xs )
         != sz00 )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
     => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).

thf(166,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( ( sdtlseqdt0 @ A @ B )
        | ( sdtlseqdt0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

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(45,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(36,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(161,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)],[36]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1516) ).

thf(149,plain,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
       => ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

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

thf(54,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( aNaturalNumber0 @ A )
     => $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).

thf(86,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

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

thf(159,plain,
    ! [A: $i] :
      ( ( aVector0 @ A )
     => ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( A != sz00 ) )
     => ? [B: $i] :
          ( ( aNaturalNumber0 @ B )
          & ( A
            = ( szszuzczcdt0 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).

thf(151,plain,
    ! [A: $i] :
      ( ( ( aNaturalNumber0 @ A )
        & ( A != sz00 ) )
     => ? [B: $i] :
          ( ( aNaturalNumber0 @ B )
          & ( A
            = ( szszuzczcdt0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

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

thf(168,plain,
    ! [A: $i] :
      ( ( aScalar0 @ A )
     => ( sdtlseqdt0 @ A @ 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(163,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(11,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).

thf(68,plain,
    ! [A: $i,B: $i] :
      ( ( ( aVector0 @ A )
        & ( aNaturalNumber0 @ B ) )
     => ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,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(62,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)],[8]) ).

thf(19,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(90,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)],[19]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

thf(83,plain,
    ! [A: $i,B: $i] :
      ( ( ( aScalar0 @ A )
        & ( aScalar0 @ B ) )
     => ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(173,plain,
    $false,
    inference(cvc4,[status(thm)],[101,56,57,132,70,156,59,98,103,80,123,95,67,87,75,170,120,125,157,85,102,92,65,129,41,166,45,161,149,54,86,159,151,168,163,68,62,90,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n018.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.15/0.31  % WCLimit  : 300
% 0.15/0.31  % DateTime : Sat May 18 12:30:24 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.92/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.11  % [INFO] 	 Parsing done (194ms). 
% 1.32/1.12  % [INFO] 	 Running in sequential loop mode. 
% 2.00/1.47  % [INFO] 	 eprover registered as external prover. 
% 2.00/1.47  % [INFO] 	 cvc4 registered as external prover. 
% 2.02/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.15/1.56  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.15/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ... 
% 2.32/1.66  % [INFO] 	 Axiom selection finished. Selected 38 axioms (removed 0 axioms). 
% 2.59/1.72  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.59/1.74  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.59/1.75  % [INFO] 	 Type checking passed. 
% 2.59/1.76  % [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 ... 
% 5.20/2.70  % External prover 'cvc4' found a proof!
% 5.20/2.70  % [INFO] 	 Killing All external provers ... 
% 5.20/2.70  % Time passed: 2246ms (effective reasoning time: 1574ms)
% 5.20/2.70  % 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)>
% 5.20/2.71  % Axioms used in derivation (38): mLERef, mMulSc, mMNeg, mScSort, mLETrn, mDefSPZ, m__1516, mSqrt, mZeroNat, mIH, mElmSc, mNatSort, mSuccEqu, mNatExtr, mArith, mDefSPN, mDimNat, mLEMonM, mPosMon, mDefInit, mMDNeg, mLETot, mDistr, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, mLess, m__1542, mDistr2, mSqPos, mIHOrd, mNegSc, mSuccNat
% 5.20/2.71  % No. of inferences in proof: 80
% 5.20/2.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2246 ms resp. 1574 ms w/o parsing
% 5.20/2.78  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/2.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------