TSTP Solution File: NUM503+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SfE14ezKWV true

% Computer : n020.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 12:41:56 EDT 2023

% Result   : Theorem 9.22s 1.95s
% Output   : Refutation 9.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  173 (  57 unt;  12 typ;   0 def)
%            Number of atoms       :  495 ( 222 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 1574 ( 256   ~; 283   |;  35   &; 984   @)
%                                         (   3 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   93 (   0   ^;  92   !;   1   ?;  93   :)

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

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

thf(sdtsldt0_type,type,
    sdtsldt0: $i > $i > $i ).

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

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

thf(isPrime0_type,type,
    isPrime0: $i > $o ).

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

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

thf(xk_type,type,
    xk: $i ).

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

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

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

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

thf(zip_derived_cl15,plain,
    ! [X0: $i] :
      ( ( sz00
        = ( sdtasdt0 @ sz00 @ X0 ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m_MulZero]) ).

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

thf(m__2306,axiom,
    ( xk
    = ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ) ).

thf(zip_derived_cl82,plain,
    ( xk
    = ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(mDefQuot,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( ( W0 != sz00 )
          & ( doDivides0 @ W0 @ W1 ) )
       => ! [W2: $i] :
            ( ( W2
              = ( sdtsldt0 @ W1 @ W0 ) )
          <=> ( ( aNaturalNumber0 @ W2 )
              & ( W1
                = ( sdtasdt0 @ W0 @ W2 ) ) ) ) ) ) ).

thf(zip_derived_cl53,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtsldt0 @ X1 @ X0 ) )
      | ( X1
        = ( sdtasdt0 @ X0 @ X2 ) )
      | ~ ( doDivides0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefQuot]) ).

thf(zip_derived_cl1397,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ xp )
      | ( xp = sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl53]) ).

thf(m__1860,axiom,
    ( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
    & ( isPrime0 @ xp ) ) ).

thf(zip_derived_cl74,plain,
    doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
    inference(cnf,[status(esa)],[m__1860]) ).

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

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

thf(zip_derived_cl1399,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( xp = sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl74,zip_derived_cl70]) ).

thf(zip_derived_cl75,plain,
    isPrime0 @ xp,
    inference(cnf,[status(esa)],[m__1860]) ).

thf(mDefPrime,axiom,
    ! [W0: $i] :
      ( ( aNaturalNumber0 @ W0 )
     => ( ( isPrime0 @ W0 )
      <=> ( ( W0 != sz00 )
          & ( W0 != sz10 )
          & ! [W1: $i] :
              ( ( ( aNaturalNumber0 @ W1 )
                & ( doDivides0 @ W1 @ W0 ) )
             => ( ( W1 = sz10 )
                | ( W1 = W0 ) ) ) ) ) ) ).

thf(zip_derived_cl66,plain,
    ! [X0: $i] :
      ( ~ ( isPrime0 @ X0 )
      | ( X0 != sz00 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[mDefPrime]) ).

thf(zip_derived_cl687,plain,
    ( ~ ( aNaturalNumber0 @ xp )
    | ( xp != sz00 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl75,zip_derived_cl66]) ).

thf(zip_derived_cl695,plain,
    ( ~ ( aNaturalNumber0 @ sz00 )
    | ( xp != sz00 ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl687]) ).

thf(mSortsC,axiom,
    aNaturalNumber0 @ sz00 ).

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

thf(zip_derived_cl696,plain,
    xp != sz00,
    inference(demod,[status(thm)],[zip_derived_cl695,zip_derived_cl1]) ).

thf(zip_derived_cl1400,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1399,zip_derived_cl696]) ).

thf(mLETotal,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( sdtlseqdt0 @ W0 @ W1 )
        | ( ( W1 != W0 )
          & ( sdtlseqdt0 @ W1 @ W0 ) ) ) ) ).

thf(zip_derived_cl34,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ( X1 != X0 ) ),
    inference(cnf,[status(esa)],[mLETotal]) ).

thf(mMulComm,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( ( sdtasdt0 @ W0 @ W1 )
        = ( sdtasdt0 @ W1 @ W0 ) ) ) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl34_001,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ( X1 != X0 ) ),
    inference(cnf,[status(esa)],[mLETotal]) ).

thf(zip_derived_cl10_002,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(m__,conjecture,
    ( ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xp @ xm ) )
    & ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    & ( ( sdtasdt0 @ xp @ xm )
     != ( sdtasdt0 @ xp @ xk ) )
    & ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      & ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      & ( ( sdtasdt0 @ xp @ xm )
       != ( sdtasdt0 @ xp @ xk ) )
      & ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) ) ),
    inference('cnf.neg',[status(esa)],[m__]) ).

thf(zip_derived_cl93,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl763,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xp @ xk ) )
    | ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xm )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl93]) ).

thf(zip_derived_cl70_003,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl71,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl791,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xp @ xk ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl763,zip_derived_cl70,zip_derived_cl71]) ).

thf(zip_derived_cl865,plain,
    ( ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xk ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl791]) ).

thf(zip_derived_cl866,plain,
    ( ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xm @ xp ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl865]) ).

thf(zip_derived_cl930,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xp )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl866]) ).

thf(zip_derived_cl71_004,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_005,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl933,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl71,zip_derived_cl70]) ).

thf(zip_derived_cl937,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xm @ xp ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl933]) ).

thf(zip_derived_cl938,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xm @ xp ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
    | ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl937]) ).

thf(zip_derived_cl939,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl938]) ).

thf(zip_derived_cl940,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xp @ xk )
     != ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl939]) ).

thf(zip_derived_cl1420,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( xk != xk )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl940]) ).

thf(zip_derived_cl1445,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1420]) ).

thf(zip_derived_cl54,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( X1
       != ( sdtasdt0 @ X0 @ X2 ) )
      | ( X2
        = ( sdtsldt0 @ X1 @ X0 ) )
      | ~ ( doDivides0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefQuot]) ).

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_cl1733,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2
        = ( sdtsldt0 @ X1 @ X0 ) )
      | ( X1
       != ( sdtasdt0 @ X0 @ X2 ) )
      | ~ ( aNaturalNumber0 @ X2 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( X0 = sz00 ) ),
    inference(clc,[status(thm)],[zip_derived_cl54,zip_derived_cl51]) ).

thf(zip_derived_cl1745,plain,
    ! [X0: $i] :
      ( ( X0
       != ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtasdt0 @ xm @ xp )
       != ( sdtasdt0 @ xn @ xm ) )
      | ( xp = sz00 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xm )
      | ( xm
        = ( sdtsldt0 @ X0 @ xp ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1445,zip_derived_cl1733]) ).

thf(zip_derived_cl70_006,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl71_007,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1764,plain,
    ! [X0: $i] :
      ( ( X0
       != ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtasdt0 @ xm @ xp )
       != ( sdtasdt0 @ xn @ xm ) )
      | ( xp = sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( xm
        = ( sdtsldt0 @ X0 @ xp ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1745,zip_derived_cl70,zip_derived_cl71]) ).

thf(zip_derived_cl696_008,plain,
    xp != sz00,
    inference(demod,[status(thm)],[zip_derived_cl695,zip_derived_cl1]) ).

thf(zip_derived_cl1765,plain,
    ! [X0: $i] :
      ( ( X0
       != ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtasdt0 @ xm @ xp )
       != ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( xm
        = ( sdtsldt0 @ X0 @ xp ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1764,zip_derived_cl696]) ).

thf(zip_derived_cl82_009,plain,
    ( xk
    = ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl1768,plain,
    ( ( xk = xm )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xn @ xm ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1765,zip_derived_cl82]) ).

thf(zip_derived_cl1775,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( xk = xm ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1768]) ).

thf(mSortsB_02,axiom,
    ! [W0: $i,W1: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 ) )
     => ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl1400_010,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1399,zip_derived_cl696]) ).

thf(zip_derived_cl10_011,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl1402,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( X0 != xk )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1400,zip_derived_cl10]) ).

thf(zip_derived_cl70_012,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1422,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( X0 != xk )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1402,zip_derived_cl70]) ).

thf(zip_derived_cl5_013,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl82_014,plain,
    ( xk
    = ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X2
       != ( sdtsldt0 @ X1 @ X0 ) )
      | ( aNaturalNumber0 @ X2 )
      | ~ ( doDivides0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mDefQuot]) ).

thf(zip_derived_cl1190,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ xp )
      | ( xp = sz00 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl52]) ).

thf(zip_derived_cl74_015,plain,
    doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl70_016,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1192,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( xp = sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1190,zip_derived_cl74,zip_derived_cl70]) ).

thf(zip_derived_cl696_017,plain,
    xp != sz00,
    inference(demod,[status(thm)],[zip_derived_cl695,zip_derived_cl1]) ).

thf(zip_derived_cl1193,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1192,zip_derived_cl696]) ).

thf(zip_derived_cl1221,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xn )
      | ( aNaturalNumber0 @ X0 )
      | ( X0 != xk ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl1193]) ).

thf(zip_derived_cl71_018,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

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

thf(zip_derived_cl1224,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ X0 )
      | ( X0 != xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl1221,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl2689,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1422,zip_derived_cl1224]) ).

thf(zip_derived_cl2691,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xn )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk ) ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl2689]) ).

thf(zip_derived_cl71_019,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl72_020,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl2693,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl2691,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl2693_021,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl2691,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl5_022,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(zip_derived_cl2793,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk )
      | ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2693,zip_derived_cl5]) ).

thf(zip_derived_cl71_023,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

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

thf(zip_derived_cl2884,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl2793,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl3033,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( X0 != xk )
      | ( X0 != xk ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2693,zip_derived_cl2884]) ).

thf(zip_derived_cl3041,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3033]) ).

thf(zip_derived_cl3151,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(eq_res,[status(thm)],[zip_derived_cl3041]) ).

thf(zip_derived_cl3244,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ( xk = xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl1775,zip_derived_cl3151]) ).

thf(zip_derived_cl1224_025,plain,
    ! [X0: $i] :
      ( ( aNaturalNumber0 @ X0 )
      | ( X0 != xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl1221,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl93_026,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(mMonMul,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 )
        & ( aNaturalNumber0 @ W2 ) )
     => ( ( ( W0 != sz00 )
          & ( W1 != W2 )
          & ( sdtlseqdt0 @ W1 @ W2 ) )
       => ( ( ( sdtasdt0 @ W0 @ W1 )
           != ( sdtasdt0 @ W0 @ W2 ) )
          & ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) )
          & ( ( sdtasdt0 @ W1 @ W0 )
           != ( sdtasdt0 @ W2 @ W0 ) )
          & ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) ).

thf(zip_derived_cl41,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X0 @ X2 ) )
      | ~ ( sdtlseqdt0 @ X1 @ X2 )
      | ( X1 = X2 ) ),
    inference(cnf,[status(esa)],[mMonMul]) ).

thf(zip_derived_cl1666,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( xm = xk )
    | ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xm )
    | ( xp = sz00 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl93,zip_derived_cl41]) ).

thf(zip_derived_cl70_027,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl71_028,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1691,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( xm = xk )
    | ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ( xp = sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1666,zip_derived_cl70,zip_derived_cl71]) ).

thf(zip_derived_cl696_029,plain,
    xp != sz00,
    inference(demod,[status(thm)],[zip_derived_cl695,zip_derived_cl1]) ).

thf(zip_derived_cl1692,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( xm = xk )
    | ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1691,zip_derived_cl696]) ).

thf(zip_derived_cl1778,plain,
    ( ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( sdtlseqdt0 @ xm @ xk ) ),
    inference(condensation,[status(thm)],[zip_derived_cl1692]) ).

thf(zip_derived_cl43,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X2 @ X0 ) )
      | ~ ( sdtlseqdt0 @ X1 @ X2 )
      | ( X1 = X2 ) ),
    inference(cnf,[status(esa)],[mMonMul]) ).

thf(zip_derived_cl1800,plain,
    ( ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ( xn = xp )
    | ~ ( sdtlseqdt0 @ xn @ xp )
    | ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xn )
    | ( xm = sz00 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1778,zip_derived_cl43]) ).

thf(m__2287,axiom,
    ( ( sdtlseqdt0 @ xm @ xp )
    & ( xm != xp )
    & ( sdtlseqdt0 @ xn @ xp )
    & ( xn != xp ) ) ).

thf(zip_derived_cl80,plain,
    sdtlseqdt0 @ xn @ xp,
    inference(cnf,[status(esa)],[m__2287]) ).

thf(zip_derived_cl70_030,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl71_031,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl72_032,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1828,plain,
    ( ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ( xn = xp )
    | ( xm = sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1800,zip_derived_cl80,zip_derived_cl70,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl81,plain,
    xn != xp,
    inference(cnf,[status(esa)],[m__2287]) ).

thf(zip_derived_cl1829,plain,
    ( ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ( xm = sz00 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1828,zip_derived_cl81]) ).

thf(zip_derived_cl78,plain,
    sdtlseqdt0 @ xm @ xp,
    inference(cnf,[status(esa)],[m__2287]) ).

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

thf(zip_derived_cl33,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( sdtlseqdt0 @ X0 @ X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( sdtlseqdt0 @ X0 @ X2 )
      | ~ ( sdtlseqdt0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[mLETran]) ).

thf(zip_derived_cl901,plain,
    ! [X0: $i] :
      ( ~ ( sdtlseqdt0 @ xp @ X0 )
      | ( sdtlseqdt0 @ xm @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup-',[status(thm)],[zip_derived_cl78,zip_derived_cl33]) ).

thf(zip_derived_cl71_033,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_034,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl913,plain,
    ! [X0: $i] :
      ( ~ ( sdtlseqdt0 @ xp @ X0 )
      | ( sdtlseqdt0 @ xm @ X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl901,zip_derived_cl71,zip_derived_cl70]) ).

thf(m__2389,axiom,
    sdtlseqdt0 @ xp @ xk ).

thf(zip_derived_cl92,plain,
    sdtlseqdt0 @ xp @ xk,
    inference(cnf,[status(esa)],[m__2389]) ).

thf(zip_derived_cl7035,plain,
    ( ~ ( aNaturalNumber0 @ xk )
    | ( sdtlseqdt0 @ xm @ xk ) ),
    inference('sup+',[status(thm)],[zip_derived_cl913,zip_derived_cl92]) ).

thf(zip_derived_cl7190,plain,
    ( ( xm = sz00 )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ xk ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1829,zip_derived_cl7035]) ).

thf(zip_derived_cl7191,plain,
    ( ~ ( aNaturalNumber0 @ xk )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    | ( xm = sz00 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7190]) ).

thf(zip_derived_cl1400_035,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1399,zip_derived_cl696]) ).

thf(zip_derived_cl3151_036,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(eq_res,[status(thm)],[zip_derived_cl3041]) ).

thf(zip_derived_cl3232,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1400,zip_derived_cl3151]) ).

thf(zip_derived_cl8061,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( xm = sz00 )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ xk )
    | ( xk != xk ) ),
    inference('sup+',[status(thm)],[zip_derived_cl7191,zip_derived_cl3232]) ).

thf(zip_derived_cl8145,plain,
    ( ~ ( aNaturalNumber0 @ xk )
    | ( xm = sz00 )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8061]) ).

thf(zip_derived_cl10_037,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl8175,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xm @ xp ) )
    | ( xm = sz00 )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup+',[status(thm)],[zip_derived_cl8145,zip_derived_cl10]) ).

thf(zip_derived_cl71_038,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_039,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl8221,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xm @ xp ) )
    | ( xm = sz00 )
    | ~ ( aNaturalNumber0 @ xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl8175,zip_derived_cl71,zip_derived_cl70]) ).

thf(zip_derived_cl3244_040,plain,
    ( ( ( sdtasdt0 @ xm @ xp )
     != ( sdtasdt0 @ xn @ xm ) )
    | ( xk = xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl1775,zip_derived_cl3151]) ).

thf(zip_derived_cl8360,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ xk )
    | ( xm = sz00 )
    | ( xk = xm ) ),
    inference('sup-',[status(thm)],[zip_derived_cl8221,zip_derived_cl3244]) ).

thf(zip_derived_cl8456,plain,
    ( ( xk = xm )
    | ( xm = sz00 )
    | ~ ( aNaturalNumber0 @ xk ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8360]) ).

thf(zip_derived_cl8468,plain,
    ( ( xk != xk )
    | ( xm = sz00 )
    | ( xk = xm ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1224,zip_derived_cl8456]) ).

thf(zip_derived_cl8470,plain,
    ( ( xk = xm )
    | ( xm = sz00 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8468]) ).

thf(zip_derived_cl92_041,plain,
    sdtlseqdt0 @ xp @ xk,
    inference(cnf,[status(esa)],[m__2389]) ).

thf(zip_derived_cl8481,plain,
    ( ( sdtlseqdt0 @ xp @ xm )
    | ( xm = sz00 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl8470,zip_derived_cl92]) ).

thf(m__2075,axiom,
    ~ ( sdtlseqdt0 @ xp @ xm ) ).

thf(zip_derived_cl77,plain,
    ~ ( sdtlseqdt0 @ xp @ xm ),
    inference(cnf,[status(esa)],[m__2075]) ).

thf(zip_derived_cl8515,plain,
    xm = sz00,
    inference(clc,[status(thm)],[zip_derived_cl8481,zip_derived_cl77]) ).

thf(zip_derived_cl8515_042,plain,
    xm = sz00,
    inference(clc,[status(thm)],[zip_derived_cl8481,zip_derived_cl77]) ).

thf(zip_derived_cl8515_043,plain,
    xm = sz00,
    inference(clc,[status(thm)],[zip_derived_cl8481,zip_derived_cl77]) ).

thf(zip_derived_cl8593,plain,
    ( ( ( sdtasdt0 @ sz00 @ xp )
     != ( sdtasdt0 @ xn @ sz00 ) )
    | ( xk = sz00 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3244,zip_derived_cl8515,zip_derived_cl8515,zip_derived_cl8515]) ).

thf(m__2315,axiom,
    ~ ( ( xk = sz00 )
      | ( xk = sz10 ) ) ).

thf(zip_derived_cl84,plain,
    xk != sz00,
    inference(cnf,[status(esa)],[m__2315]) ).

thf(zip_derived_cl8594,plain,
    ( ( sdtasdt0 @ sz00 @ xp )
   != ( sdtasdt0 @ xn @ sz00 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8593,zip_derived_cl84]) ).

thf(zip_derived_cl8876,plain,
    ( ( ( sdtasdt0 @ sz00 @ xp )
     != sz00 )
    | ~ ( aNaturalNumber0 @ xn ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl8594]) ).

thf(zip_derived_cl72_044,plain,
    aNaturalNumber0 @ xn,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl8880,plain,
    ( ( sdtasdt0 @ sz00 @ xp )
   != sz00 ),
    inference(demod,[status(thm)],[zip_derived_cl8876,zip_derived_cl72]) ).

thf(zip_derived_cl8881,plain,
    ( ( sz00 != sz00 )
    | ~ ( aNaturalNumber0 @ xp ) ),
    inference('sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl8880]) ).

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

thf(zip_derived_cl8882,plain,
    sz00 != sz00,
    inference(demod,[status(thm)],[zip_derived_cl8881,zip_derived_cl70]) ).

thf(zip_derived_cl8883,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl8882]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM503+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SfE14ezKWV true
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug 25 09:52:00 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in FO mode
% 0.22/0.69  % Total configuration time : 435
% 0.22/0.69  % Estimated wc time : 1092
% 0.22/0.69  % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.76  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.29/0.79  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.29/0.81  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 9.22/1.95  % Solved by fo/fo3_bce.sh.
% 9.22/1.95  % BCE start: 94
% 9.22/1.95  % BCE eliminated: 1
% 9.22/1.95  % PE start: 93
% 9.22/1.95  logic: eq
% 9.22/1.95  % PE eliminated: -8
% 9.22/1.95  % done 959 iterations in 1.138s
% 9.22/1.95  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.22/1.95  % SZS output start Refutation
% See solution above
% 9.22/1.95  
% 9.22/1.95  
% 9.22/1.95  % Terminating...
% 9.22/1.99  % Runner terminated.
% 9.22/2.01  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------