TSTP Solution File: NUM496+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM496+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Q2BzYLweYi true

% 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 : Thu Aug 31 12:41:53 EDT 2023

% Result   : Theorem 1.38s 1.44s
% Output   : Refutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  182 (  67 unt;  13 typ;   0 def)
%            Number of atoms       :  438 ( 108 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 1116 ( 229   ~; 230   |;  21   &; 618   @)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :  140 (   0   ^; 138   !;   2   ?; 140   :)

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

thf(xp_type,type,
    xp: $i ).

thf(sz10_type,type,
    sz10: $i ).

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

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

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

thf(doDivides0_type,type,
    doDivides0: $i > $i > $o ).

thf(xr_type,type,
    xr: $i ).

thf(sdtmndt0_type,type,
    sdtmndt0: $i > $i > $i ).

thf(xn_type,type,
    xn: $i ).

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

thf(xm_type,type,
    xm: $i ).

thf(sk__type,type,
    sk_: $i > $i > $i ).

thf(m__2027,axiom,
    ( ( doDivides0 @ xp @ xr )
    | ( doDivides0 @ xp @ xm ) ) ).

thf(zip_derived_cl81,plain,
    ( ( doDivides0 @ xp @ xr )
    | ( doDivides0 @ xp @ xm ) ),
    inference(cnf,[status(esa)],[m__2027]) ).

thf(m__,conjecture,
    ( ( doDivides0 @ xp @ xn )
    | ( doDivides0 @ xp @ xm ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( doDivides0 @ xp @ xn )
      | ( doDivides0 @ xp @ xm ) ),
    inference('cnf.neg',[status(esa)],[m__]) ).

thf(zip_derived_cl82,plain,
    ~ ( doDivides0 @ xp @ xm ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl88,plain,
    doDivides0 @ xp @ xr,
    inference(clc,[status(thm)],[zip_derived_cl81,zip_derived_cl82]) ).

thf(m_AddZero,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( ( ( sdtpldt0 @ W0 @ sz00 )
          = W0 )
        & ( W0
          = ( sdtpldt0 @ sz00 @ W0 ) ) ) ) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i] :
      ( ( X0
        = ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m_AddZero]) ).

thf(m_MulUnit,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( ( ( sdtasdt0 @ W0 @ sz10 )
          = W0 )
        & ( W0
          = ( sdtasdt0 @ sz10 @ W0 ) ) ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz10 )
        = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m_MulUnit]) ).

thf(mDefDiv,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( doDivides0 @ W0 @ W1 )
      <=> ? [W2: $i] :
            ( ( W1
              = ( sdtasdt0 @ W0 @ W2 ) )
            & ( aNaturalNumber0 @ W2 ) ) ) ) ).

thf(zip_derived_cl51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( X1
       != ( sdtasdt0 @ X0 @ X2 ) ) ),
    inference(cnf,[status(esa)],[mDefDiv]) ).

thf(zip_derived_cl329,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ sz10 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl51]) ).

thf(mSortsC_01,axiom,
    ( ( sz10 != sz00 )
    & ( aNaturalNumber0 @ sz10 ) ) ).

thf(zip_derived_cl3,plain,
    aNaturalNumber0 @ sz10,
    inference(cnf,[status(esa)],[mSortsC_01]) ).

thf(zip_derived_cl335,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl329,zip_derived_cl3]) ).

thf(zip_derived_cl336,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X1 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( X1 != X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl335]) ).

thf(zip_derived_cl618,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( doDivides0 @ X0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl619,plain,
    ! [X0: $i] :
      ( ( doDivides0 @ X0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl618]) ).

thf(m_MulZero,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( ( ( sdtasdt0 @ W0 @ sz00 )
          = sz00 )
        & ( sz00
          = ( sdtasdt0 @ sz00 @ W0 ) ) ) ) ).

thf(zip_derived_cl14,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ X0 @ sz00 )
        = sz00 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m_MulZero]) ).

thf(zip_derived_cl51_001,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( X1
       != ( sdtasdt0 @ X0 @ X2 ) ) ),
    inference(cnf,[status(esa)],[mDefDiv]) ).

thf(zip_derived_cl328,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ sz00 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl51]) ).

thf(mSortsC,axiom,
    aNaturalNumber0 @ sz00 ).

thf(zip_derived_cl1,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl333,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl328,zip_derived_cl1]) ).

thf(zip_derived_cl334,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X1 )
      | ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( X1 != sz00 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl333]) ).

thf(mLERefl,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( sdtlseqdt0 @ W0 @ W0 ) ) ).

thf(zip_derived_cl31,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ X0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[mLERefl]) ).

thf(mDefLE,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( sdtlseqdt0 @ W0 @ W1 )
      <=> ? [W2: $i] :
            ( ( ( sdtpldt0 @ W0 @ W2 )
              = W1 )
            & ( aNaturalNumber0 @ W2 ) ) ) ) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sk_ @ X1 @ X0 ) )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefLE]) ).

thf(zip_derived_cl209,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( aNaturalNumber0 @ ( sk_ @ X0 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl26]) ).

thf(zip_derived_cl213,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ ( sk_ @ X0 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl209]) ).

thf(zip_derived_cl31_002,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ X0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[mLERefl]) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ ( sk_ @ X1 @ X0 ) )
        = X1 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefLE]) ).

thf(zip_derived_cl654,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X0 @ ( sk_ @ X0 @ X0 ) )
        = X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl25]) ).

thf(zip_derived_cl659,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( sk_ @ X0 @ X0 ) )
        = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl654]) ).

thf(mAddComm,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( sdtpldt0 @ W0 @ W1 )
        = ( sdtpldt0 @ W1 @ W0 ) ) ) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

thf(zip_derived_cl6_003,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

thf(m__1837,axiom,
    ( ( aNaturalNumber0 @ xp )
    & ( aNaturalNumber0 @ xm )
    & ( aNaturalNumber0 @ xn ) ) ).

thf(zip_derived_cl72,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl145,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ xn @ X0 )
        = ( sdtpldt0 @ X0 @ xn ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl6,zip_derived_cl72]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ sz00 )
        = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m_AddZero]) ).

thf(zip_derived_cl285,plain,
    ( ( ( sdtpldt0 @ sz00 @ xn )
      = xn )
    | ~ ( aNaturalNumber0 @ sz00 )
    | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup+',[status(thm)],[zip_derived_cl145,zip_derived_cl8]) ).

thf(zip_derived_cl1_004,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl72_005,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl303,plain,
    ( ( sdtpldt0 @ sz00 @ xn )
    = xn ),
    inference(demod,[status(thm)],[zip_derived_cl285,zip_derived_cl1,zip_derived_cl72]) ).

thf(mAddCanc,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 )
        & ( aNaturalNumber0 @ W2 ) )
     => ( ( ( ( sdtpldt0 @ W0 @ W1 )
            = ( sdtpldt0 @ W0 @ W2 ) )
          | ( ( sdtpldt0 @ W1 @ W0 )
            = ( sdtpldt0 @ W2 @ W0 ) ) )
       => ( W1 = W2 ) ) ) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( X0 = X2 )
      | ( ( sdtpldt0 @ X0 @ X1 )
       != ( sdtpldt0 @ X2 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mAddCanc]) ).

thf(zip_derived_cl857,plain,
    ! [X0: $i] :
      ( ( xn
       != ( sdtpldt0 @ X0 @ xn ) )
      | ( sz00 = X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl303,zip_derived_cl18]) ).

thf(zip_derived_cl72_006,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1_007,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl890,plain,
    ! [X0: $i] :
      ( ( xn
       != ( sdtpldt0 @ X0 @ xn ) )
      | ( sz00 = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl857,zip_derived_cl72,zip_derived_cl1]) ).

thf(zip_derived_cl1107,plain,
    ! [X0: $i] :
      ( ( xn
       != ( sdtpldt0 @ xn @ X0 ) )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( sz00 = X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl890]) ).

thf(zip_derived_cl72_008,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1114,plain,
    ! [X0: $i] :
      ( ( xn
       != ( sdtpldt0 @ xn @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( sz00 = X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1107,zip_derived_cl72]) ).

thf(zip_derived_cl1115,plain,
    ! [X0: $i] :
      ( ( sz00 = X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( xn
       != ( sdtpldt0 @ xn @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1114]) ).

thf(zip_derived_cl1992,plain,
    ( ( xn != xn )
    | ~ ( aNaturalNumber0 @ xn )
    | ~ ( aNaturalNumber0 @ ( sk_ @ xn @ xn ) )
    | ( sz00
      = ( sk_ @ xn @ xn ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl659,zip_derived_cl1115]) ).

thf(zip_derived_cl72_009,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2009,plain,
    ( ( xn != xn )
    | ~ ( aNaturalNumber0 @ ( sk_ @ xn @ xn ) )
    | ( sz00
      = ( sk_ @ xn @ xn ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1992,zip_derived_cl72]) ).

thf(zip_derived_cl2010,plain,
    ( ( sz00
      = ( sk_ @ xn @ xn ) )
    | ~ ( aNaturalNumber0 @ ( sk_ @ xn @ xn ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2009]) ).

thf(zip_derived_cl2048,plain,
    ( ~ ( aNaturalNumber0 @ xn )
    | ( sz00
      = ( sk_ @ xn @ xn ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl213,zip_derived_cl2010]) ).

thf(zip_derived_cl72_010,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2049,plain,
    ( sz00
    = ( sk_ @ xn @ xn ) ),
    inference(demod,[status(thm)],[zip_derived_cl2048,zip_derived_cl72]) ).

thf(zip_derived_cl659_011,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ ( sk_ @ X0 @ X0 ) )
        = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl654]) ).

thf(zip_derived_cl2051,plain,
    ( ( ( sdtpldt0 @ xn @ sz00 )
      = xn )
    | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2049,zip_derived_cl659]) ).

thf(zip_derived_cl72_012,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2053,plain,
    ( ( sdtpldt0 @ xn @ sz00 )
    = xn ),
    inference(demod,[status(thm)],[zip_derived_cl2051,zip_derived_cl72]) ).

thf(mDefDiff,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( sdtlseqdt0 @ W0 @ W1 )
       => ! [W2: $i] :
            ( ( W2
              = ( sdtmndt0 @ W1 @ W0 ) )
          <=> ( ( aNaturalNumber0 @ W2 )
              & ( ( sdtpldt0 @ W0 @ W2 )
                = W1 ) ) ) ) ) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 )
      | ( X2
        = ( sdtmndt0 @ X1 @ X0 ) )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefDiff]) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 ) ),
    inference(cnf,[status(esa)],[mDefLE]) ).

thf(zip_derived_cl1285,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2
        = ( sdtmndt0 @ X1 @ X0 ) )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28,zip_derived_cl27]) ).

thf(zip_derived_cl2063,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ sz00 )
      | ( sz00
        = ( sdtmndt0 @ X0 @ xn ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2053,zip_derived_cl1285]) ).

thf(zip_derived_cl72_013,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1_014,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2080,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( sz00
        = ( sdtmndt0 @ X0 @ xn ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2063,zip_derived_cl72,zip_derived_cl1]) ).

thf(zip_derived_cl303_015,plain,
    ( ( sdtpldt0 @ sz00 @ xn )
    = xn ),
    inference(demod,[status(thm)],[zip_derived_cl285,zip_derived_cl1,zip_derived_cl72]) ).

thf(zip_derived_cl1285_016,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2
        = ( sdtmndt0 @ X1 @ X0 ) )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28,zip_derived_cl27]) ).

thf(zip_derived_cl1291,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ( xn
        = ( sdtmndt0 @ X0 @ sz00 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl303,zip_derived_cl1285]) ).

thf(zip_derived_cl1_017,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl72_018,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1309,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( xn
        = ( sdtmndt0 @ X0 @ sz00 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1291,zip_derived_cl1,zip_derived_cl72]) ).

thf(zip_derived_cl1330,plain,
    ( ( xn
      = ( sdtmndt0 @ xn @ sz00 ) )
    | ~ ( aNaturalNumber0 @ xn ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1309]) ).

thf(zip_derived_cl72_019,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1331,plain,
    ( xn
    = ( sdtmndt0 @ xn @ sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1330,zip_derived_cl72]) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtmndt0 @ X1 @ X0 ) )
      | ( aNaturalNumber0 @ X2 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefDiff]) ).

thf(zip_derived_cl1332,plain,
    ! [X0: $i] :
      ( ( X0 != xn )
      | ~ ( sdtlseqdt0 @ sz00 @ xn )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1331,zip_derived_cl30]) ).

thf(zip_derived_cl303_020,plain,
    ( ( sdtpldt0 @ sz00 @ xn )
    = xn ),
    inference(demod,[status(thm)],[zip_derived_cl285,zip_derived_cl1,zip_derived_cl72]) ).

thf(zip_derived_cl27_021,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 ) ),
    inference(cnf,[status(esa)],[mDefLE]) ).

thf(zip_derived_cl637,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ( sdtlseqdt0 @ sz00 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl303,zip_derived_cl27]) ).

thf(zip_derived_cl72_022,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1_023,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl650,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ( sdtlseqdt0 @ sz00 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl637,zip_derived_cl72,zip_derived_cl1]) ).

thf(zip_derived_cl749,plain,
    ( ~ ( aNaturalNumber0 @ xn )
    | ( sdtlseqdt0 @ sz00 @ xn ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl650]) ).

thf(zip_derived_cl72_024,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl750,plain,
    sdtlseqdt0 @ sz00 @ xn,
    inference(demod,[status(thm)],[zip_derived_cl749,zip_derived_cl72]) ).

thf(zip_derived_cl72_025,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1_026,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl1333,plain,
    ! [X0: $i] :
      ( ( X0 != xn )
      | ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1332,zip_derived_cl750,zip_derived_cl72,zip_derived_cl1]) ).

thf(zip_derived_cl2558,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtmndt0 @ X0 @ xn ) )
      | ( xn != X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2080,zip_derived_cl1333]) ).

thf(zip_derived_cl2559,plain,
    ( sz00
    = ( sdtmndt0 @ xn @ xn ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl2558]) ).

thf(zip_derived_cl30_027,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtmndt0 @ X1 @ X0 ) )
      | ( aNaturalNumber0 @ X2 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefDiff]) ).

thf(zip_derived_cl2561,plain,
    ! [X0: $i] :
      ( ( X0 != sz00 )
      | ~ ( sdtlseqdt0 @ xn @ xn )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2559,zip_derived_cl30]) ).

thf(zip_derived_cl2053_028,plain,
    ( ( sdtpldt0 @ xn @ sz00 )
    = xn ),
    inference(demod,[status(thm)],[zip_derived_cl2051,zip_derived_cl72]) ).

thf(zip_derived_cl27_029,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtpldt0 @ X0 @ X2 )
       != X1 ) ),
    inference(cnf,[status(esa)],[mDefLE]) ).

thf(zip_derived_cl2062,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ~ ( aNaturalNumber0 @ sz00 )
      | ( sdtlseqdt0 @ xn @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2053,zip_derived_cl27]) ).

thf(zip_derived_cl1_030,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl72_031,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2079,plain,
    ! [X0: $i] :
      ( ( xn != X0 )
      | ( sdtlseqdt0 @ xn @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2062,zip_derived_cl1,zip_derived_cl72]) ).

thf(zip_derived_cl1333_032,plain,
    ! [X0: $i] :
      ( ( X0 != xn )
      | ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1332,zip_derived_cl750,zip_derived_cl72,zip_derived_cl1]) ).

thf(zip_derived_cl2090,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ xn @ X0 )
      | ( xn != X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2079,zip_derived_cl1333]) ).

thf(zip_derived_cl2091,plain,
    sdtlseqdt0 @ xn @ xn,
    inference(eq_res,[status(thm)],[zip_derived_cl2090]) ).

thf(zip_derived_cl72_033,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl72_034,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2563,plain,
    ! [X0: $i] :
      ( ( X0 != sz00 )
      | ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2561,zip_derived_cl2091,zip_derived_cl72,zip_derived_cl72]) ).

thf(zip_derived_cl2642,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( doDivides0 @ X0 @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl334,zip_derived_cl2563]) ).

thf(zip_derived_cl2643,plain,
    ! [X0: $i] :
      ( ( doDivides0 @ X0 @ sz00 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl2642]) ).

thf(zip_derived_cl88_035,plain,
    doDivides0 @ xp @ xr,
    inference(clc,[status(thm)],[zip_derived_cl81,zip_derived_cl82]) ).

thf(mDivTrans,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 )
        & ( aNaturalNumber0 @ W2 ) )
     => ( ( ( doDivides0 @ W0 @ W1 )
          & ( doDivides0 @ W1 @ W2 ) )
       => ( doDivides0 @ W0 @ W2 ) ) ) ).

thf(zip_derived_cl55,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( doDivides0 @ X0 @ X2 )
      | ~ ( doDivides0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[mDivTrans]) ).

thf(zip_derived_cl346,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xr @ X0 )
      | ( doDivides0 @ xp @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ xr ) ),
    inference('sup-',[status(thm)],[zip_derived_cl88,zip_derived_cl55]) ).

thf(zip_derived_cl70,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl354,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xr @ X0 )
      | ( doDivides0 @ xp @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xr ) ),
    inference(demod,[status(thm)],[zip_derived_cl346,zip_derived_cl70]) ).

thf(m__1883,axiom,
    ( xr
    = ( sdtmndt0 @ xn @ xp ) ) ).

thf(zip_derived_cl77,plain,
    ( xr
    = ( sdtmndt0 @ xn @ xp ) ),
    inference(cnf,[status(esa)],[m__1883]) ).

thf(zip_derived_cl30_036,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtmndt0 @ X1 @ X0 ) )
      | ( aNaturalNumber0 @ X2 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefDiff]) ).

thf(zip_derived_cl341,plain,
    ! [X0: $i] :
      ( ( X0 != xr )
      | ~ ( sdtlseqdt0 @ xp @ xn )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl30]) ).

thf(m__1870,axiom,
    sdtlseqdt0 @ xp @ xn ).

thf(zip_derived_cl76,plain,
    sdtlseqdt0 @ xp @ xn,
    inference(cnf,[status(esa)],[m__1870]) ).

thf(zip_derived_cl72_037,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_038,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl343,plain,
    ! [X0: $i] :
      ( ( X0 != xr )
      | ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl341,zip_derived_cl76,zip_derived_cl72,zip_derived_cl70]) ).

thf(zip_derived_cl428,plain,
    aNaturalNumber0 @ xr,
    inference(eq_res,[status(thm)],[zip_derived_cl343]) ).

thf(zip_derived_cl435,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xr @ X0 )
      | ( doDivides0 @ xp @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl354,zip_derived_cl428]) ).

thf(zip_derived_cl2649,plain,
    ( ~ ( aNaturalNumber0 @ xr )
    | ~ ( aNaturalNumber0 @ sz00 )
    | ( doDivides0 @ xp @ sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2643,zip_derived_cl435]) ).

thf(zip_derived_cl428_039,plain,
    aNaturalNumber0 @ xr,
    inference(eq_res,[status(thm)],[zip_derived_cl343]) ).

thf(zip_derived_cl1_040,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2661,plain,
    doDivides0 @ xp @ sz00,
    inference(demod,[status(thm)],[zip_derived_cl2649,zip_derived_cl428,zip_derived_cl1]) ).

thf(mDivSum,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 )
        & ( aNaturalNumber0 @ W2 ) )
     => ( ( ( doDivides0 @ W0 @ W1 )
          & ( doDivides0 @ W0 @ W2 ) )
       => ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) ) ) ).

thf(zip_derived_cl56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( doDivides0 @ X0 @ ( sdtpldt0 @ X1 @ X2 ) )
      | ~ ( doDivides0 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[mDivSum]) ).

thf(zip_derived_cl2898,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xp @ X0 )
      | ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2661,zip_derived_cl56]) ).

thf(zip_derived_cl70_041,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1_042,plain,
    aNaturalNumber0 @ sz00,
    inference(cnf,[status(esa)],[mSortsC]) ).

thf(zip_derived_cl2910,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xp @ X0 )
      | ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2898,zip_derived_cl70,zip_derived_cl1]) ).

thf(zip_derived_cl2954,plain,
    ( ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xp )
    | ( doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ xp ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl619,zip_derived_cl2910]) ).

thf(zip_derived_cl70_043,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_044,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2961,plain,
    doDivides0 @ xp @ ( sdtpldt0 @ sz00 @ xp ),
    inference(demod,[status(thm)],[zip_derived_cl2954,zip_derived_cl70,zip_derived_cl70]) ).

thf(zip_derived_cl2972,plain,
    ( ( doDivides0 @ xp @ xp )
    | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl2961]) ).

thf(zip_derived_cl70_045,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2973,plain,
    doDivides0 @ xp @ xp,
    inference(demod,[status(thm)],[zip_derived_cl2972,zip_derived_cl70]) ).

thf(zip_derived_cl56_046,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( doDivides0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( doDivides0 @ X0 @ ( sdtpldt0 @ X1 @ X2 ) )
      | ~ ( doDivides0 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[mDivSum]) ).

thf(zip_derived_cl2983,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xp @ X0 )
      | ( doDivides0 @ xp @ ( sdtpldt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2973,zip_derived_cl56]) ).

thf(zip_derived_cl70_047,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_048,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2990,plain,
    ! [X0: $i] :
      ( ~ ( doDivides0 @ xp @ X0 )
      | ( doDivides0 @ xp @ ( sdtpldt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2983,zip_derived_cl70,zip_derived_cl70]) ).

thf(zip_derived_cl3481,plain,
    ( ~ ( aNaturalNumber0 @ xr )
    | ( doDivides0 @ xp @ ( sdtpldt0 @ xp @ xr ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl88,zip_derived_cl2990]) ).

thf(zip_derived_cl428_049,plain,
    aNaturalNumber0 @ xr,
    inference(eq_res,[status(thm)],[zip_derived_cl343]) ).

thf(zip_derived_cl77_050,plain,
    ( xr
    = ( sdtmndt0 @ xn @ xp ) ),
    inference(cnf,[status(esa)],[m__1883]) ).

thf(zip_derived_cl29,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtmndt0 @ X1 @ X0 ) )
      | ( ( sdtpldt0 @ X0 @ X2 )
        = X1 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefDiff]) ).

thf(zip_derived_cl1354,plain,
    ! [X0: $i] :
      ( ( X0 != xr )
      | ~ ( sdtlseqdt0 @ xp @ xn )
      | ( ( sdtpldt0 @ xp @ X0 )
        = xn )
      | ~ ( aNaturalNumber0 @ xn )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl29]) ).

thf(zip_derived_cl76_051,plain,
    sdtlseqdt0 @ xp @ xn,
    inference(cnf,[status(esa)],[m__1870]) ).

thf(zip_derived_cl72_052,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_053,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1357,plain,
    ! [X0: $i] :
      ( ( X0 != xr )
      | ( ( sdtpldt0 @ xp @ X0 )
        = xn ) ),
    inference(demod,[status(thm)],[zip_derived_cl1354,zip_derived_cl76,zip_derived_cl72,zip_derived_cl70]) ).

thf(zip_derived_cl1359,plain,
    ( ( sdtpldt0 @ xp @ xr )
    = xn ),
    inference(eq_res,[status(thm)],[zip_derived_cl1357]) ).

thf(zip_derived_cl83,plain,
    ~ ( doDivides0 @ xp @ xn ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3486,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl3481,zip_derived_cl428,zip_derived_cl1359,zip_derived_cl83]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM496+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Q2BzYLweYi true
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug 25 16:56:59 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.37  % Python version: Python 3.6.8
% 0.14/0.37  % Running in FO mode
% 0.22/0.68  % Total configuration time : 435
% 0.22/0.68  % Estimated wc time : 1092
% 0.22/0.68  % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.38/1.44  % Solved by fo/fo5.sh.
% 1.38/1.44  % done 559 iterations in 0.627s
% 1.38/1.44  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.38/1.44  % SZS output start Refutation
% See solution above
% 1.38/1.44  
% 1.38/1.44  
% 1.38/1.44  % Terminating...
% 5.88/1.53  % Runner terminated.
% 5.88/1.55  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------