TSTP Solution File: NUM503+3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM503+3 : 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.e9u3ll1165 true

% Computer : n013.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 14.75s 2.71s
% Output   : Refutation 14.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  199 (  65 unt;  16 typ;   0 def)
%            Number of atoms       :  534 ( 188 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 1776 ( 271   ~; 272   |;  58   &;1154   @)
%                                         (   2 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :  147 (   0   ^; 136   !;  11   ?; 147   :)

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

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

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

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

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

thf(sk__10_type,type,
    sk__10: $i ).

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

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

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

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

thf(sk__14_type,type,
    sk__14: $i ).

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

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_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(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(m__2306,axiom,
    ( ( xk
      = ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) )
    & ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xk ) )
    & ( aNaturalNumber0 @ xk ) ) ).

thf(zip_derived_cl115,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_cl2322,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) )
      | ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl115,zip_derived_cl53]) ).

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_cl116,plain,
    ( ( sdtasdt0 @ xn @ xm )
    = ( sdtasdt0 @ xp @ xk ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

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_cl929,plain,
    ( ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xk )
    | ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl116,zip_derived_cl5]) ).

thf(zip_derived_cl70_001,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl930,plain,
    ( ~ ( aNaturalNumber0 @ xk )
    | ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl929,zip_derived_cl70]) ).

thf(zip_derived_cl117,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl935,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl117]) ).

thf(m__1860,axiom,
    ( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
    & ? [W0: $i] :
        ( ( ( sdtasdt0 @ xn @ xm )
          = ( sdtasdt0 @ xp @ W0 ) )
        & ( aNaturalNumber0 @ W0 ) )
    & ( isPrime0 @ xp )
    & ! [W0: $i] :
        ( ( ( aNaturalNumber0 @ W0 )
          & ( ? [W1: $i] :
                ( ( xp
                  = ( sdtasdt0 @ W0 @ W1 ) )
                & ( aNaturalNumber0 @ W1 ) )
            | ( doDivides0 @ W0 @ xp ) ) )
       => ( ( W0 = sz10 )
          | ( W0 = xp ) ) )
    & ( xp != sz10 )
    & ( xp != sz00 ) ) ).

thf(zip_derived_cl102,plain,
    doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl2324,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2322,zip_derived_cl70,zip_derived_cl935,zip_derived_cl102]) ).

thf(zip_derived_cl95,plain,
    xp != sz00,
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl2325,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ X0 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2324,zip_derived_cl95]) ).

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(zip_derived_cl2327,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2325,zip_derived_cl10]) ).

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

thf(zip_derived_cl2355,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2327,zip_derived_cl70]) ).

thf(zip_derived_cl115_004,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_cl2283,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ( X0 != xk )
      | ( aNaturalNumber0 @ X0 )
      | ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl115,zip_derived_cl52]) ).

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

thf(zip_derived_cl935_006,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl117]) ).

thf(zip_derived_cl102_007,plain,
    doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl2285,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ( X0 != xk )
      | ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2283,zip_derived_cl70,zip_derived_cl935,zip_derived_cl102]) ).

thf(zip_derived_cl95_008,plain,
    xp != sz00,
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl2286,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ( aNaturalNumber0 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2285,zip_derived_cl95]) ).

thf(zip_derived_cl2463,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ X0 @ xp ) )
      | ( X0 != xk ) ),
    inference(clc,[status(thm)],[zip_derived_cl2355,zip_derived_cl2286]) ).

thf(zip_derived_cl5_009,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(m__2287,axiom,
    ( ( sdtlseqdt0 @ xm @ xp )
    & ? [W0: $i] :
        ( ( ( sdtpldt0 @ xm @ W0 )
          = xp )
        & ( aNaturalNumber0 @ W0 ) )
    & ( xm != xp )
    & ( sdtlseqdt0 @ xn @ xp )
    & ? [W0: $i] :
        ( ( ( sdtpldt0 @ xn @ W0 )
          = xp )
        & ( aNaturalNumber0 @ W0 ) )
    & ( xn != xp ) ) ).

thf(zip_derived_cl108,plain,
    ( ( sdtpldt0 @ xn @ sk__10 )
    = xp ),
    inference(cnf,[status(esa)],[m__2287]) ).

thf(zip_derived_cl5_010,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

thf(mAMDistr,axiom,
    ! [W0: $i,W1: $i,W2: $i] :
      ( ( ( aNaturalNumber0 @ W0 )
        & ( aNaturalNumber0 @ W1 )
        & ( aNaturalNumber0 @ W2 ) )
     => ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
          = ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
        & ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
          = ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ X0 @ X2 ) @ X1 )
        = ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[mAMDistr]) ).

thf(zip_derived_cl5_011,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB_02]) ).

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

thf(zip_derived_cl35,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ( sdtlseqdt0 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[mLETotal]) ).

thf(m__,conjecture,
    ( ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xp @ xm ) )
    & ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ? [W0: $i] :
          ( ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ W0 )
            = ( sdtasdt0 @ xp @ xm ) )
          & ( aNaturalNumber0 @ W0 ) ) )
    & ( ( sdtasdt0 @ xp @ xm )
     != ( sdtasdt0 @ xp @ xk ) )
    & ( ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) )
      | ? [W0: $i] :
          ( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ W0 )
            = ( sdtasdt0 @ xp @ xk ) )
          & ( aNaturalNumber0 @ W0 ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      & ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
        | ? [W0: $i] :
            ( ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ W0 )
              = ( sdtasdt0 @ xp @ xm ) )
            & ( aNaturalNumber0 @ W0 ) ) )
      & ( ( sdtasdt0 @ xp @ xm )
       != ( sdtasdt0 @ xp @ xk ) )
      & ( ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xp @ xk ) )
        | ? [W0: $i] :
            ( ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ W0 )
              = ( sdtasdt0 @ xp @ xk ) )
            & ( aNaturalNumber0 @ W0 ) ) ) ),
    inference('cnf.neg',[status(esa)],[m__]) ).

thf(zip_derived_cl139,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( 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_cl116_012,plain,
    ( ( sdtasdt0 @ xn @ xm )
    = ( sdtasdt0 @ xp @ xk ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl116_013,plain,
    ( ( sdtasdt0 @ xn @ xm )
    = ( sdtasdt0 @ xp @ xk ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl2796,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ xp @ xm )
        = ( sdtasdt0 @ xn @ xm ) )
      | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl139,zip_derived_cl116,zip_derived_cl116]) ).

thf(zip_derived_cl2797,plain,
    ! [X0: $i] :
      ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2796]) ).

thf(zip_derived_cl2798,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl2797]) ).

thf(zip_derived_cl935_014,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl117]) ).

thf(zip_derived_cl2805,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2798,zip_derived_cl935]) ).

thf(zip_derived_cl3197,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xp )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl2805]) ).

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

thf(zip_derived_cl70_015,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl3201,plain,
    ! [X0: $i] :
      ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtpldt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3197,zip_derived_cl71,zip_derived_cl70]) ).

thf(zip_derived_cl3213,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ xn )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ xn @ X0 ) @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl3201]) ).

thf(zip_derived_cl71_016,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_cl3222,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ xn @ X0 ) @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3213,zip_derived_cl71,zip_derived_cl72]) ).

thf(zip_derived_cl3685,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ xm )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ xn @ X0 ) @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl3222]) ).

thf(zip_derived_cl71_017,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl3694,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ xn @ X0 ) @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3685,zip_derived_cl71]) ).

thf(zip_derived_cl3695,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
        = ( sdtasdt0 @ xp @ xm ) )
      | ( ( sdtasdt0 @ ( sdtpldt0 @ xn @ X0 ) @ xm )
       != ( sdtasdt0 @ xp @ xm ) )
      | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3694]) ).

thf(zip_derived_cl5112,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
     != ( sdtasdt0 @ xp @ xm ) )
    | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ sk__10 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl108,zip_derived_cl3695]) ).

thf(zip_derived_cl109,plain,
    aNaturalNumber0 @ sk__10,
    inference(cnf,[status(esa)],[m__2287]) ).

thf(zip_derived_cl5121,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
     != ( sdtasdt0 @ xp @ xm ) )
    | ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5112,zip_derived_cl109]) ).

thf(zip_derived_cl5122,plain,
    ( ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5121]) ).

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

thf(zip_derived_cl32,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( X0 = X1 )
      | ~ ( sdtlseqdt0 @ X1 @ X0 )
      | ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[mLEAsym]) ).

thf(zip_derived_cl5124,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5122,zip_derived_cl32]) ).

thf(zip_derived_cl935_018,plain,
    aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
    inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl117]) ).

thf(zip_derived_cl5133,plain,
    ( ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xp @ xm )
      = ( sdtasdt0 @ xn @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5124,zip_derived_cl935]) ).

thf(zip_derived_cl5134,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5133]) ).

thf(zip_derived_cl5142,plain,
    ( ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xp )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl5134]) ).

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

thf(zip_derived_cl70_020,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl5146,plain,
    ( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
    | ( ( sdtasdt0 @ xn @ xm )
      = ( sdtasdt0 @ xp @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5142,zip_derived_cl71,zip_derived_cl70]) ).

thf(zip_derived_cl5185,plain,
    ! [X0: $i] :
      ( ( X0 != xk )
      | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ X0 @ xp ) )
      | ( ( sdtasdt0 @ X0 @ xp )
        = ( sdtasdt0 @ xp @ xm ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2463,zip_derived_cl5146]) ).

thf(zip_derived_cl5288,plain,
    ( ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xp @ xm ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xk @ xp ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl5185]) ).

thf(zip_derived_cl5292,plain,
    ( ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xp )
    | ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xm @ xp ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xk @ xp ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl5288]) ).

thf(zip_derived_cl71_021,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl70_022,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl5298,plain,
    ( ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xm @ xp ) )
    | ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xk @ xp ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5292,zip_derived_cl71,zip_derived_cl70]) ).

thf(zip_derived_cl5312,plain,
    ( ( xm = xk )
    | ~ ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ xp )
    | ~ ( aNaturalNumber0 @ xm )
    | ( xp = sz00 )
    | ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xm @ xp ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl5298]) ).

thf(zip_derived_cl117_023,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl70_024,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl71_025,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl5317,plain,
    ( ( xm = xk )
    | ~ ( sdtlseqdt0 @ xm @ xk )
    | ( xp = sz00 )
    | ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xm @ xp ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5312,zip_derived_cl117,zip_derived_cl70,zip_derived_cl71]) ).

thf(zip_derived_cl95_026,plain,
    xp != sz00,
    inference(cnf,[status(esa)],[m__1860]) ).

thf(m__2389,axiom,
    ( ( sdtlseqdt0 @ xp @ xk )
    & ? [W0: $i] :
        ( ( ( sdtpldt0 @ xp @ W0 )
          = xk )
        & ( aNaturalNumber0 @ W0 ) ) ) ).

thf(zip_derived_cl136,plain,
    ( ( sdtpldt0 @ xp @ sk__14 )
    = xk ),
    inference(cnf,[status(esa)],[m__2389]) ).

thf(m__2075,axiom,
    ~ ( ? [W0: $i] :
          ( ( ( sdtpldt0 @ xp @ W0 )
            = xm )
          & ( aNaturalNumber0 @ W0 ) )
      | ( sdtlseqdt0 @ xp @ xm ) ) ).

thf(zip_derived_cl106,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ xp @ X0 )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m__2075]) ).

thf(zip_derived_cl1074,plain,
    ( ( xk != xm )
    | ~ ( aNaturalNumber0 @ sk__14 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl106]) ).

thf(zip_derived_cl137,plain,
    aNaturalNumber0 @ sk__14,
    inference(cnf,[status(esa)],[m__2389]) ).

thf(zip_derived_cl1201,plain,
    xk != xm,
    inference(demod,[status(thm)],[zip_derived_cl1074,zip_derived_cl137]) ).

thf(zip_derived_cl5318,plain,
    ( ~ ( sdtlseqdt0 @ xm @ xk )
    | ( ( sdtasdt0 @ xk @ xp )
      = ( sdtasdt0 @ xm @ xp ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl5317,zip_derived_cl95,zip_derived_cl1201]) ).

thf(zip_derived_cl35_027,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ( sdtlseqdt0 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[mLETotal]) ).

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_cl35_028,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( sdtlseqdt0 @ X0 @ X1 )
      | ( sdtlseqdt0 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[mLETotal]) ).

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(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_cl136_029,plain,
    ( ( sdtpldt0 @ xp @ sk__14 )
    = xk ),
    inference(cnf,[status(esa)],[m__2389]) ).

thf(zip_derived_cl6_030,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

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

thf(zip_derived_cl7,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ( ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
        = ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) ) ) ),
    inference(cnf,[status(esa)],[mAddAsso]) ).

thf(zip_derived_cl6_031,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X0 @ X1 )
        = ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mAddComm]) ).

thf(zip_derived_cl106_032,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ xp @ X0 )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[m__2075]) ).

thf(zip_derived_cl1071,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp )
      | ( ( sdtpldt0 @ X0 @ xp )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl106]) ).

thf(zip_derived_cl70_033,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1075,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X0 @ xp )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1071,zip_derived_cl70]) ).

thf(zip_derived_cl1076,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ X0 @ xp )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1075]) ).

thf(zip_derived_cl1143,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ xp ) )
       != xm )
      | ~ ( aNaturalNumber0 @ ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl1076]) ).

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

thf(zip_derived_cl1149,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ xp ) )
       != xm )
      | ~ ( aNaturalNumber0 @ ( sdtpldt0 @ X1 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1143,zip_derived_cl70]) ).

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

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( aNaturalNumber0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
    inference(cnf,[status(esa)],[mSortsB]) ).

thf(zip_derived_cl5656,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ xp ) )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1149,zip_derived_cl4]) ).

thf(zip_derived_cl5663,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ xp )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ xp @ X0 ) )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl5656]) ).

thf(zip_derived_cl70_035,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl5673,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ xp @ X0 ) )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5663,zip_derived_cl70]) ).

thf(zip_derived_cl5674,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ xp @ X0 ) )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5673]) ).

thf(zip_derived_cl5695,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X0 @ xk )
       != xm )
      | ~ ( aNaturalNumber0 @ sk__14 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl5674]) ).

thf(zip_derived_cl137_036,plain,
    aNaturalNumber0 @ sk__14,
    inference(cnf,[status(esa)],[m__2389]) ).

thf(zip_derived_cl5706,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ X0 @ xk )
       != xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl5695,zip_derived_cl137]) ).

thf(zip_derived_cl5919,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ xk )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ xk @ X0 )
       != xm ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl5706]) ).

thf(zip_derived_cl117_037,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl5924,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtpldt0 @ xk @ X0 )
       != xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl5919,zip_derived_cl117]) ).

thf(zip_derived_cl5925,plain,
    ! [X0: $i] :
      ( ( ( sdtpldt0 @ xk @ X0 )
       != xm )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5924]) ).

thf(zip_derived_cl5934,plain,
    ! [X0: $i] :
      ( ~ ( sdtlseqdt0 @ xk @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xk )
      | ( X0 != xm )
      | ~ ( aNaturalNumber0 @ ( sk_ @ X0 @ xk ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl5925]) ).

thf(zip_derived_cl117_038,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl5941,plain,
    ! [X0: $i] :
      ( ~ ( sdtlseqdt0 @ xk @ X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ( X0 != xm )
      | ~ ( aNaturalNumber0 @ ( sk_ @ X0 @ xk ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5934,zip_derived_cl117]) ).

thf(zip_derived_cl6823,plain,
    ( ~ ( aNaturalNumber0 @ ( sk_ @ xm @ xk ) )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( sdtlseqdt0 @ xk @ xm ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl5941]) ).

thf(zip_derived_cl71_039,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl6824,plain,
    ( ~ ( aNaturalNumber0 @ ( sk_ @ xm @ xk ) )
    | ~ ( sdtlseqdt0 @ xk @ xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl6823,zip_derived_cl71]) ).

thf(zip_derived_cl6825,plain,
    ( ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ ( sk_ @ xm @ xk ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl6824]) ).

thf(zip_derived_cl71_040,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl117_041,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl6827,plain,
    ( ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ ( sk_ @ xm @ xk ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl6825,zip_derived_cl71,zip_derived_cl117]) ).

thf(zip_derived_cl6833,plain,
    ( ~ ( sdtlseqdt0 @ xk @ xm )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xk )
    | ( sdtlseqdt0 @ xm @ xk ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl6827]) ).

thf(zip_derived_cl71_042,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl117_043,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl6834,plain,
    ( ~ ( sdtlseqdt0 @ xk @ xm )
    | ( sdtlseqdt0 @ xm @ xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl6833,zip_derived_cl71,zip_derived_cl117]) ).

thf(zip_derived_cl6835,plain,
    ( ( sdtlseqdt0 @ xm @ xk )
    | ~ ( aNaturalNumber0 @ xm )
    | ~ ( aNaturalNumber0 @ xk )
    | ( sdtlseqdt0 @ xm @ xk ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl6834]) ).

thf(zip_derived_cl71_044,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl117_045,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl6837,plain,
    ( ( sdtlseqdt0 @ xm @ xk )
    | ( sdtlseqdt0 @ xm @ xk ) ),
    inference(demod,[status(thm)],[zip_derived_cl6835,zip_derived_cl71,zip_derived_cl117]) ).

thf(zip_derived_cl6838,plain,
    sdtlseqdt0 @ xm @ xk,
    inference(simplify,[status(thm)],[zip_derived_cl6837]) ).

thf(zip_derived_cl6841,plain,
    ( ( sdtasdt0 @ xk @ xp )
    = ( sdtasdt0 @ xm @ xp ) ),
    inference(demod,[status(thm)],[zip_derived_cl5318,zip_derived_cl6838]) ).

thf(zip_derived_cl10_046,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl6877,plain,
    ( ~ ( aNaturalNumber0 @ xk )
    | ~ ( aNaturalNumber0 @ xp )
    | ( ( sdtasdt0 @ xm @ xp )
      = ( sdtasdt0 @ xp @ xk ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl6841,zip_derived_cl10]) ).

thf(zip_derived_cl117_047,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

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

thf(zip_derived_cl116_049,plain,
    ( ( sdtasdt0 @ xn @ xm )
    = ( sdtasdt0 @ xp @ xk ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

thf(zip_derived_cl6906,plain,
    ( ( sdtasdt0 @ xm @ xp )
    = ( sdtasdt0 @ xn @ xm ) ),
    inference(demod,[status(thm)],[zip_derived_cl6877,zip_derived_cl117,zip_derived_cl70,zip_derived_cl116]) ).

thf(zip_derived_cl10_050,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ( ( sdtasdt0 @ X0 @ X1 )
        = ( sdtasdt0 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[mMulComm]) ).

thf(zip_derived_cl116_051,plain,
    ( ( sdtasdt0 @ xn @ xm )
    = ( sdtasdt0 @ xp @ xk ) ),
    inference(cnf,[status(esa)],[m__2306]) ).

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

thf(zip_derived_cl21,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sz00 )
      | ( ( sdtasdt0 @ X0 @ X2 )
       != ( sdtasdt0 @ X0 @ X1 ) )
      | ( X2 = X1 )
      | ~ ( aNaturalNumber0 @ X1 )
      | ~ ( aNaturalNumber0 @ X2 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(cnf,[status(esa)],[mMulCanc]) ).

thf(zip_derived_cl1384,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ xp @ X0 ) )
      | ( xk = X0 )
      | ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xk )
      | ~ ( aNaturalNumber0 @ xp ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl21]) ).

thf(zip_derived_cl117_052,plain,
    aNaturalNumber0 @ xk,
    inference(cnf,[status(esa)],[m__2306]) ).

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

thf(zip_derived_cl1411,plain,
    ! [X0: $i] :
      ( ( xp = sz00 )
      | ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ xp @ X0 ) )
      | ( xk = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1384,zip_derived_cl117,zip_derived_cl70]) ).

thf(zip_derived_cl95_054,plain,
    xp != sz00,
    inference(cnf,[status(esa)],[m__1860]) ).

thf(zip_derived_cl1412,plain,
    ! [X0: $i] :
      ( ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ xp @ X0 ) )
      | ( xk = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1411,zip_derived_cl95]) ).

thf(zip_derived_cl1565,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ~ ( aNaturalNumber0 @ xp )
      | ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ X0 @ xp ) )
      | ( xk = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl1412]) ).

thf(zip_derived_cl70_055,plain,
    aNaturalNumber0 @ xp,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl1571,plain,
    ! [X0: $i] :
      ( ~ ( aNaturalNumber0 @ X0 )
      | ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ X0 @ xp ) )
      | ( xk = X0 )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1565,zip_derived_cl70]) ).

thf(zip_derived_cl1572,plain,
    ! [X0: $i] :
      ( ( xk = X0 )
      | ( ( sdtasdt0 @ xn @ xm )
       != ( sdtasdt0 @ X0 @ xp ) )
      | ~ ( aNaturalNumber0 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1571]) ).

thf(zip_derived_cl6999,plain,
    ( ( xk = xm )
    | ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xn @ xm ) )
    | ~ ( aNaturalNumber0 @ xm ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6906,zip_derived_cl1572]) ).

thf(zip_derived_cl71_056,plain,
    aNaturalNumber0 @ xm,
    inference(cnf,[status(esa)],[m__1837]) ).

thf(zip_derived_cl7031,plain,
    ( ( xk = xm )
    | ( ( sdtasdt0 @ xn @ xm )
     != ( sdtasdt0 @ xn @ xm ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl6999,zip_derived_cl71]) ).

thf(zip_derived_cl7032,plain,
    xk = xm,
    inference(simplify,[status(thm)],[zip_derived_cl7031]) ).

thf(zip_derived_cl1201_057,plain,
    xk != xm,
    inference(demod,[status(thm)],[zip_derived_cl1074,zip_derived_cl137]) ).

thf(zip_derived_cl7033,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl7032,zip_derived_cl1201]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM503+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.e9u3ll1165 true
% 0.11/0.33  % Computer : n013.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Aug 25 10:19:17 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  % Running portfolio for 300 s
% 0.11/0.33  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33  % Number of cores: 8
% 0.11/0.34  % Python version: Python 3.6.8
% 0.17/0.34  % Running in FO mode
% 0.17/0.55  % Total configuration time : 435
% 0.17/0.55  % Estimated wc time : 1092
% 0.17/0.55  % Estimated cpu time (7 cpus) : 156.0
% 0.17/0.67  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.17/0.67  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.17/0.68  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.17/0.68  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.17/0.69  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.17/0.69  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.17/0.70  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 14.75/2.71  % Solved by fo/fo6_bce.sh.
% 14.75/2.71  % BCE start: 143
% 14.75/2.71  % BCE eliminated: 1
% 14.75/2.71  % PE start: 142
% 14.75/2.71  logic: eq
% 14.75/2.71  % PE eliminated: 8
% 14.75/2.71  % done 1301 iterations in 1.997s
% 14.75/2.71  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 14.75/2.71  % SZS output start Refutation
% See solution above
% 14.75/2.71  
% 14.75/2.71  
% 14.75/2.71  % Terminating...
% 15.03/2.80  % Runner terminated.
% 15.03/2.80  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------