TSTP Solution File: SYO500^1.004 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SYO500^1.004 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AtW5B3XUDf true

% Computer : n004.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 : Fri Sep  1 05:51:44 EDT 2023

% Result   : Theorem 34.01s 5.00s
% Output   : Refutation 34.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    6
% Syntax   : Number of formulae    :  692 (   9 unt;   5 typ;   0 def)
%            Number of atoms       : 10253 ( 299 equ;   0 cnn)
%            Maximal formula atoms :   28 (  14 avg)
%            Number of connectives : 9728 ( 760   ~; 416   |; 514   &;7464   @)
%                                         (   0 <=>;   0  =>; 574  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f3_type,type,
    f3: $o > $o ).

thf(x_type,type,
    x: $o ).

thf(f1_type,type,
    f1: $o > $o ).

thf(f2_type,type,
    f2: $o > $o ).

thf(f0_type,type,
    f0: $o > $o ).

thf(kaminski4,conjecture,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[kaminski4]) ).

thf(zip_derived_cl0,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ( x
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl9,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl0_001,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2]) ).

thf(zip_derived_cl12,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl4]) ).

thf(zip_derived_cl28,plain,
    ( ( ( f3 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl30,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl9_002,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl0_003,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl6,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1]) ).

thf(zip_derived_cl16,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl6]) ).

thf(zip_derived_cl55,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl16]) ).

thf(zip_derived_cl30_004,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl30_005,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl60,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl62,plain,
    ( ( ( f2 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl64,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_006,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl9_007,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl0_008,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) ) )
   <= x ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl0]) ).

thf(zip_derived_cl9_009,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl11,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) ) )
   <= x ),
    inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl9]) ).

thf(zip_derived_cl82,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl11]) ).

thf(zip_derived_cl30_010,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl30_011,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl30_012,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl93,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl30,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl567,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl93]) ).

thf(zip_derived_cl64_013,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_014,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_015,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl578,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl567,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1797,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl578]) ).

thf(zip_derived_cl1803,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1797]) ).

thf(zip_derived_cl4316,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1803]) ).

thf('0',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl4316]) ).

thf(zip_derived_cl578_016,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl567,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1798,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl578]) ).

thf(zip_derived_cl1801,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1798]) ).

thf(zip_derived_cl4103,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1801]) ).

thf('1',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl4103]) ).

thf(zip_derived_cl578_017,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl567,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1799,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl578]) ).

thf(zip_derived_cl1805,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1799]) ).

thf(zip_derived_cl4411,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl1805]) ).

thf('2',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      = ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4411]) ).

thf(zip_derived_cl29,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl31,plain,
    ( ( ( f3 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl32,plain,
    ( ( ( f3 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl34,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl8,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl50,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl8]) ).

thf(zip_derived_cl34_018,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl53,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl34]) ).

thf(zip_derived_cl363,plain,
    ( ( ( f3 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl34_019,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl369,plain,
    ( ( ( f3 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl363,zip_derived_cl34]) ).

thf(zip_derived_cl370,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl369]) ).

thf(zip_derived_cl1220,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl370]) ).

thf('3',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl1220]) ).

thf(zip_derived_cl63,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl67,plain,
    ( ( ( f1 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl68,plain,
    ( ( ( f1 @ $false )
      | ( f0 @ $false ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl70,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl63_020,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl71,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl63]) ).

thf(zip_derived_cl101,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f1 @ $false ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl70_021,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl102,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ $true ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl101,zip_derived_cl70]) ).

thf(zip_derived_cl104,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl71_022,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl63]) ).

thf(zip_derived_cl105,plain,
    ( ( f0 @ ( f1 @ $true ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl71]) ).

thf(zip_derived_cl104_023,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl107,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl104]) ).

thf(zip_derived_cl70_024,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl8_025,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl37,plain,
    ( ( ( f3 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl38,plain,
    ( ( ( f3 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl43,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl38]) ).

thf(zip_derived_cl312,plain,
    ( ( ( f2 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl313,plain,
    ( ( ( f2 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl312]) ).

thf(zip_derived_cl319,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl313]) ).

thf(zip_derived_cl382,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl319]) ).

thf(zip_derived_cl386,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl382]) ).

thf(zip_derived_cl502,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl386]) ).

thf(zip_derived_cl510,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl502]) ).

thf(zip_derived_cl107_026,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl104]) ).

thf(zip_derived_cl107_027,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl104]) ).

thf('4',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $true )
    | ~ ( f1 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl510,zip_derived_cl107,zip_derived_cl107]) ).

thf(zip_derived_cl33,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl73,plain,
    ( ( ( f2 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl75,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl9_028,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1]) ).

thf(zip_derived_cl24,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl7]) ).

thf(zip_derived_cl202,plain,
    ( ( ( f3 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl204,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl202]) ).

thf(zip_derived_cl930,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl204]) ).

thf(zip_derived_cl2364,plain,
    ( ( ( f2 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl930]) ).

thf(zip_derived_cl75_029,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl2366,plain,
    ( ( ( f2 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) )
   <= ( ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2364,zip_derived_cl75]) ).

thf('5',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ~ ( f2 @ $false )
    | ( f2 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2366]) ).

thf(zip_derived_cl75_030,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl9_031,plain,
    ( x
   <= x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2]) ).

thf(zip_derived_cl20,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl5]) ).

thf(zip_derived_cl161,plain,
    ( ( ( f3 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl163,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl161]) ).

thf(zip_derived_cl799,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl163]) ).

thf(zip_derived_cl2209,plain,
    ( ( ( f2 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl799]) ).

thf(zip_derived_cl75_032,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl2211,plain,
    ( ( ( f2 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2209,zip_derived_cl75]) ).

thf('6',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ( f2 @ $true )
    | ~ ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl2211]) ).

thf(zip_derived_cl104_033,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl75_034,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl6_035,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1]) ).

thf(zip_derived_cl17,plain,
    ( ( x
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl18,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl17]) ).

thf(zip_derived_cl140,plain,
    ( ( ( f3 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl141,plain,
    ( ( ( f3 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl140]) ).

thf(zip_derived_cl143,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl141]) ).

thf(zip_derived_cl277,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl143]) ).

thf(zip_derived_cl282,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl277]) ).

thf(zip_derived_cl104_036,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_037,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl287,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl282,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl104_038,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1801_039,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1798]) ).

thf(zip_derived_cl4102,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1801]) ).

thf(zip_derived_cl4154,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl4102]) ).

thf(zip_derived_cl287_040,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl282,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl287_041,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl282,zip_derived_cl104,zip_derived_cl104]) ).

thf('7',plain,
    ( ~ ( f1 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ~ ( f2 @ $false )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4154,zip_derived_cl287,zip_derived_cl287]) ).

thf(zip_derived_cl104_042,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1803_043,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1797]) ).

thf(zip_derived_cl4315,plain,
    ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ( f1 @ $true )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl1803]) ).

thf(zip_derived_cl4330,plain,
    ( ( ( f0 @ $true )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( ( f1 @ $true )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl4315]) ).

thf('8',plain,
    ( ( f0 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
    | ( f0 @ ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4330]) ).

thf(zip_derived_cl104_044,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl75_045,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl43_046,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl38]) ).

thf(zip_derived_cl309,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl43]) ).

thf(zip_derived_cl75_047,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl321,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl309,zip_derived_cl75]) ).

thf(zip_derived_cl1083,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $false ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl321]) ).

thf(zip_derived_cl75_048,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl1089,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1083,zip_derived_cl75]) ).

thf(zip_derived_cl1090,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1089]) ).

thf(zip_derived_cl2740,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1090]) ).

thf(zip_derived_cl104_049,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_050,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_051,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl2751,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2740,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl2751_052,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2740,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl2780,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2751]) ).

thf(zip_derived_cl2783,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl2780]) ).

thf(zip_derived_cl2783_053,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl2780]) ).

thf(zip_derived_cl2817,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2751,zip_derived_cl2783,zip_derived_cl2783]) ).

thf(zip_derived_cl2817_054,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2751,zip_derived_cl2783,zip_derived_cl2783]) ).

thf(zip_derived_cl2858,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl2817]) ).

thf(zip_derived_cl2859,plain,
    ( ( f0 @ $false )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2858]) ).

thf(zip_derived_cl2783_055,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl2780]) ).

thf('9',plain,
    ( ~ ( f1 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2817,zip_derived_cl2859,zip_derived_cl2783]) ).

thf(zip_derived_cl1805_056,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1799]) ).

thf(zip_derived_cl4412,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl1805]) ).

thf('10',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      = ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4412]) ).

thf(zip_derived_cl1090_057,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1089]) ).

thf(zip_derived_cl2743,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1090]) ).

thf('11',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl2743]) ).

thf('12',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
    | ~ ( f2 @ $false )
    | ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1089]) ).

thf(zip_derived_cl30_058,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl53_059,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl34]) ).

thf(zip_derived_cl360,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl53]) ).

thf(zip_derived_cl30_060,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl372,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl360,zip_derived_cl30]) ).

thf(zip_derived_cl1233,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl372]) ).

thf('13',plain,
    ( ~ ( f3 @ $false )
    | ~ ( f3 @ $true )
    | ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1233]) ).

thf(zip_derived_cl93_061,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl30,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl570,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl93]) ).

thf('14',plain,
    ( ~ ( f3 @ $true )
    | ~ x
    | ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl570]) ).

thf(zip_derived_cl64_062,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl370_063,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl369]) ).

thf(zip_derived_cl1217,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl370]) ).

thf(zip_derived_cl64_064,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_065,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_066,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl1228,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1217,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl3244,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1228]) ).

thf('15',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ~ ( f2 @ $true )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl3244]) ).

thf(zip_derived_cl64_067,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl93_068,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl30,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl568,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl575,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl568]) ).

thf(zip_derived_cl1779,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f2 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl575]) ).

thf(zip_derived_cl4200,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f2 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1779]) ).

thf('16',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ~ ( f2 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl4200]) ).

thf(zip_derived_cl34_069,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl18_070,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl17]) ).

thf(zip_derived_cl139,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl18]) ).

thf(zip_derived_cl653,plain,
    ( ( ( f3 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl139]) ).

thf(zip_derived_cl34_071,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl655,plain,
    ( ( ( f3 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl653,zip_derived_cl34]) ).

thf('17',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f3 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl655]) ).

thf(zip_derived_cl64_072,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl372_073,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl360,zip_derived_cl30]) ).

thf(zip_derived_cl1230,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl372]) ).

thf(zip_derived_cl64_074,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_075,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_076,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl1241,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1230,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl3468,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1241]) ).

thf('18',plain,
    ( ~ ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ~ ( f3 @ $true )
    | ~ ( f3 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl3468]) ).

thf(zip_derived_cl4_077,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2]) ).

thf(zip_derived_cl13,plain,
    ( ( x
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl14,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl13]) ).

thf(zip_derived_cl126,plain,
    ( ( ( f3 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl127,plain,
    ( ( ( f3 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl126]) ).

thf('19',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f3 @ $false )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl127]) ).

thf(zip_derived_cl64_078,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_079,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl34_080,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl14_081,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl13]) ).

thf(zip_derived_cl125,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl14]) ).

thf(zip_derived_cl600,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl125]) ).

thf(zip_derived_cl30_082,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl606,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl600,zip_derived_cl30]) ).

thf(zip_derived_cl1957,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl606]) ).

thf(zip_derived_cl4364,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1957]) ).

thf('20',plain,
    ( ~ ( f2 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f3 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ~ ( f3 @ $false )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl4364]) ).

thf(zip_derived_cl7_083,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1]) ).

thf(zip_derived_cl25,plain,
    ( ( x
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl7]) ).

thf('21',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | x ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf('22',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | x ),
    inference(split,[status(esa)],[zip_derived_cl13]) ).

thf(zip_derived_cl64_084,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_085,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl139_086,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl18]) ).

thf(zip_derived_cl652,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl139]) ).

thf(zip_derived_cl30_087,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl658,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl652,zip_derived_cl30]) ).

thf(zip_derived_cl1991,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl658]) ).

thf(zip_derived_cl4426,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1991]) ).

thf('23',plain,
    ( ~ ( f2 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f3 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f1 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl4426]) ).

thf(zip_derived_cl64_088,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl34_089,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl5_090,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2]) ).

thf(zip_derived_cl21,plain,
    ( ( x
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl22,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf(zip_derived_cl184,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl22]) ).

thf(zip_derived_cl805,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl184]) ).

thf(zip_derived_cl64_091,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_092,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl810,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl805,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1049,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl810]) ).

thf('24',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f2 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f1 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl1049]) ).

thf(zip_derived_cl22_093,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf(zip_derived_cl185,plain,
    ( ( ( f3 @ $false )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl22]) ).

thf('25',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f3 @ $false )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl185]) ).

thf('26',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | x ),
    inference(split,[status(esa)],[zip_derived_cl21]) ).

thf('27',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | x ),
    inference(split,[status(esa)],[zip_derived_cl17]) ).

thf('28',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f3 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl141]) ).

thf(zip_derived_cl26,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf(zip_derived_cl224,plain,
    ( ( ( f3 @ $false )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl26]) ).

thf('29',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f3 @ $false )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl224]) ).

thf(zip_derived_cl70_094,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl319_095,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl313]) ).

thf(zip_derived_cl381,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl319]) ).

thf(zip_derived_cl388,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl381]) ).

thf(zip_derived_cl812,plain,
    ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ( f1 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl388]) ).

thf(zip_derived_cl822,plain,
    ( ( ( f0 @ $true )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( ( f1 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl812]) ).

thf(zip_derived_cl828,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl822]) ).

thf(zip_derived_cl828_096,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl822]) ).

thf(zip_derived_cl841,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl828]) ).

thf(zip_derived_cl842,plain,
    ( ( f0 @ $false )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl841]) ).

thf(zip_derived_cl895,plain,
    ( ( f0 @ $true )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl828,zip_derived_cl842]) ).

thf(zip_derived_cl70_097,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl74,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl76,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl74]) ).

thf(zip_derived_cl110,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f1 @ $false ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl70_098,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl112,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl110,zip_derived_cl70]) ).

thf(zip_derived_cl113,plain,
    ( ~ ( f0 @ $true )
   <= ~ ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl112]) ).

thf('30',plain,
    ( ~ ( f0 @ ( f0 @ $false ) )
    | ( f0 @ $true ) ),
    inference('sup-',[status(thm)],[zip_derived_cl895,zip_derived_cl113]) ).

thf('31',plain,
    ( ~ ( f0 @ $true )
    | ~ ( f1 @ $false )
    | ( f1 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl112]) ).

thf(zip_derived_cl103,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl502_099,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl386]) ).

thf(zip_derived_cl511,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f0 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl103,zip_derived_cl502]) ).

thf(zip_derived_cl103_100,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl103_101,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf('32',plain,
    ( ~ ( f0 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl511,zip_derived_cl103,zip_derived_cl103]) ).

thf('33',plain,
    ( ( f0 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $true )
    | ~ ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl64_102,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl321_103,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl309,zip_derived_cl75]) ).

thf(zip_derived_cl1080,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $true ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl321]) ).

thf(zip_derived_cl64_104,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl1092,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl64]) ).

thf(zip_derived_cl2756,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1092]) ).

thf('34',plain,
    ( ~ ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
    | ( f1 @ $true )
    | ~ ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl2756]) ).

thf(zip_derived_cl1805_105,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1799]) ).

thf(zip_derived_cl4413,plain,
    ( ( ( f1 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1805]) ).

thf(zip_derived_cl4414,plain,
    ( ( ( f1 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ $false ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl4413]) ).

thf('35',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      = ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4414]) ).

thf(zip_derived_cl75_106,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl33_107,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl99,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl33]) ).

thf(zip_derived_cl146,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl99]) ).

thf('36',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f2 @ $false )
    | ( f1 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl146]) ).

thf(zip_derived_cl64_108,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl930_109,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl204]) ).

thf(zip_derived_cl2363,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl930]) ).

thf(zip_derived_cl64_110,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl2369,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2363,zip_derived_cl64]) ).

thf(zip_derived_cl4601,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl2369]) ).

thf('37',plain,
    ( ~ ( f2 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ~ ( f2 @ $false )
    | ( f1 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4601]) ).

thf(zip_derived_cl277_111,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl75,zip_derived_cl143]) ).

thf(zip_derived_cl283,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl277]) ).

thf('38',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $true )
    | ~ ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl283]) ).

thf(zip_derived_cl64_112,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl799_113,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl163]) ).

thf(zip_derived_cl2208,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl799]) ).

thf(zip_derived_cl64_114,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl2214,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2208,zip_derived_cl64]) ).

thf(zip_derived_cl4544,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl2214]) ).

thf('39',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f2 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ( f1 @ $true )
    | ~ ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl4544]) ).

thf('40',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
    | ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl74_115,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl77,plain,
    ( ( ( f1 @ $false )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl78,plain,
    ( ( ( f1 @ $false )
      | ~ ( f0 @ $false ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl77]) ).

thf('41',plain,
    ( ~ ( f0 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl78]) ).

thf(zip_derived_cl388_116,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl381]) ).

thf(zip_derived_cl813,plain,
    ( ( ( f1 @ $false )
      | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl388]) ).

thf('42',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl813]) ).

thf(zip_derived_cl104_117,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl76_118,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl74]) ).

thf(zip_derived_cl109,plain,
    ( ~ ( f0 @ ( f1 @ $true ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl76]) ).

thf(zip_derived_cl104_119,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl115,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl104]) ).

thf(zip_derived_cl103_120,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf('43',plain,
    ( ~ ( f0 @ $true )
    | ~ ( f1 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $true ) ),
    inference('sup+',[status(thm)],[zip_derived_cl115,zip_derived_cl103]) ).

thf(zip_derived_cl895_121,plain,
    ( ( f0 @ $true )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl828,zip_derived_cl842]) ).

thf(zip_derived_cl115_122,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl104]) ).

thf('44',plain,
    ( ~ ( f0 @ ( f0 @ $false ) )
    | ~ ( f1 @ $true )
    | ~ ( f1 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl895,zip_derived_cl115]) ).

thf('45',plain,
    ( ( f0 @ $true )
    | ( f0 @ ( f0 @ $false ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl822]) ).

thf(zip_derived_cl204_123,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl202]) ).

thf(zip_derived_cl931,plain,
    ( ( ( f2 @ $false )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl204]) ).

thf(zip_derived_cl932,plain,
    ( ( ( f2 @ $false )
      | ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl931]) ).

thf('46',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl932]) ).

thf('47',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl895_124,plain,
    ( ( f0 @ $true )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl828,zip_derived_cl842]) ).

thf(zip_derived_cl104_125,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl99_126,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl33]) ).

thf(zip_derived_cl145,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl99]) ).

thf(zip_derived_cl104_127,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_128,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl150,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl145,zip_derived_cl104,zip_derived_cl104]) ).

thf('48',plain,
    ( ~ ( f0 @ ( f0 @ $false ) )
    | ~ ( f1 @ $true )
    | ~ ( f2 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl895,zip_derived_cl150]) ).

thf(zip_derived_cl150_129,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl145,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl103_130,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf('49',plain,
    ( ~ ( f0 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f2 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl150,zip_derived_cl103]) ).

thf(zip_derived_cl104_131,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl2369_132,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2363,zip_derived_cl64]) ).

thf(zip_derived_cl4600,plain,
    ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl2369]) ).

thf(zip_derived_cl4668,plain,
    ( ( ( f0 @ $true )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl4600]) ).

thf('50',plain,
    ( ( f0 @ $true )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f2 @ $false )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ( f0 @ ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl4668]) ).

thf(zip_derived_cl34_133,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl29_134,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl49,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl29]) ).

thf(zip_derived_cl324,plain,
    ( ( ( f3 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl49]) ).

thf('51',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
    | ( f3 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl324]) ).

thf('52',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ x
    | ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl202]) ).

thf('53',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ( f3 @ $true )
    | ~ x ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl11_135,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) ) )
   <= x ),
    inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl9]) ).

thf(zip_derived_cl85,plain,
    ( ( ( f3 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
   <= x ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl91,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl85]) ).

thf(zip_derived_cl533,plain,
    ( ( ( f3 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl534,plain,
    ( ( ( f3 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl533]) ).

thf('54',plain,
    ( ( f3 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl534]) ).

thf('55',plain,
    ( ( f0 @ $false )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl386_136,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl382]) ).

thf(zip_derived_cl503,plain,
    ( ( ( f1 @ $false )
      | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl386]) ).

thf('56',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl503]) ).

thf(zip_derived_cl104_137,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl64_138,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl93_139,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl30,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl569,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( x
      & ( f3 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl573,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl569]) ).

thf(zip_derived_cl1741,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl573]) ).

thf(zip_derived_cl2598,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1741]) ).

thf(zip_derived_cl104_140,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_141,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl2603,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2598,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl287_142,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl282,zip_derived_cl104,zip_derived_cl104]) ).

thf('57',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ~ ( f2 @ $false ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2603,zip_derived_cl287]) ).

thf(zip_derived_cl104_143,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl70_144,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl148,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl146]) ).

thf(zip_derived_cl195,plain,
    ( ~ ( f0 @ ( f1 @ $true ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl148]) ).

thf(zip_derived_cl206,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl195]) ).

thf(zip_derived_cl107_145,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl104]) ).

thf('58',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f1 @ $false ) ),
    inference('sup+',[status(thm)],[zip_derived_cl206,zip_derived_cl107]) ).

thf(zip_derived_cl287_146,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl282,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl206_147,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl195]) ).

thf('59',plain,
    ( ~ ( f1 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f2 @ $false )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ~ ( f1 @ $false ) ),
    inference('sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl206]) ).

thf(zip_derived_cl104_148,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1779_149,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f2 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl575]) ).

thf(zip_derived_cl4199,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ( f2 @ $true )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl1779]) ).

thf(zip_derived_cl104_150,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_151,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl4204,plain,
    ( ( f0 @ $true )
   <= ( ( f2 @ $true )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4199,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl104_152,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl2214_153,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2208,zip_derived_cl64]) ).

thf(zip_derived_cl4543,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl2214]) ).

thf(zip_derived_cl4549,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4204,zip_derived_cl4543]) ).

thf(zip_derived_cl4204_154,plain,
    ( ( f0 @ $true )
   <= ( ( f2 @ $true )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4199,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl4204_155,plain,
    ( ( f0 @ $true )
   <= ( ( f2 @ $true )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4199,zip_derived_cl104,zip_derived_cl104]) ).

thf('60',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ~ ( f2 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl4549,zip_derived_cl4204,zip_derived_cl4204]) ).

thf(zip_derived_cl104_156,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl70_157,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl64_158,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl60_159,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl65,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl60]) ).

thf(zip_derived_cl166,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl168,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $false ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl166]) ).

thf(zip_derived_cl189,plain,
    ( ( f0 @ ( f1 @ $true ) )
   <= ( ( f1 @ $false )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl168]) ).

thf(zip_derived_cl228,plain,
    ( ( f0 @ $true )
   <= ( ( f1 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl189]) ).

thf(zip_derived_cl502_160,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl386]) ).

thf(zip_derived_cl508,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl228,zip_derived_cl502]) ).

thf(zip_derived_cl228_161,plain,
    ( ( f0 @ $true )
   <= ( ( f1 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl189]) ).

thf(zip_derived_cl228_162,plain,
    ( ( f0 @ $true )
   <= ( ( f1 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl189]) ).

thf('61',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ~ ( f1 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f1 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl508,zip_derived_cl228,zip_derived_cl228]) ).

thf(zip_derived_cl2603_163,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2598,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl228_164,plain,
    ( ( f0 @ $true )
   <= ( ( f1 @ $false )
      & ( f1 @ $true )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl189]) ).

thf('62',plain,
    ( ~ ( f2 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ~ ( f1 @ $true )
    | ~ ( f1 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2603,zip_derived_cl228]) ).

thf(zip_derived_cl163_165,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl161]) ).

thf(zip_derived_cl800,plain,
    ( ( ( f2 @ $false )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl163]) ).

thf(zip_derived_cl801,plain,
    ( ( ( f2 @ $false )
      | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl800]) ).

thf('63',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
    | ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl801]) ).

thf(zip_derived_cl143_166,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl141]) ).

thf(zip_derived_cl278,plain,
    ( ( ( f2 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl143]) ).

thf('64',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) )
    | ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl278]) ).

thf(zip_derived_cl16_167,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl6]) ).

thf(zip_derived_cl56,plain,
    ( ( ( f3 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl58,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl56]) ).

thf(zip_derived_cl375,plain,
    ( ( ( f3 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl376,plain,
    ( ( ( f3 @ $false )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl375]) ).

thf('65',plain,
    ( ( f3 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl376]) ).

thf(zip_derived_cl34_168,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl58_169,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl56]) ).

thf(zip_derived_cl374,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl58]) ).

thf(zip_derived_cl1282,plain,
    ( ( ( f3 @ $true )
      | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl374]) ).

thf('66',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) )
    | ( f3 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl1282]) ).

thf('67',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
    | ( f3 @ $true )
    | ~ x ),
    inference(split,[status(esa)],[zip_derived_cl161]) ).

thf('68',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) )
    | ( f3 @ $true )
    | ~ x ),
    inference(split,[status(esa)],[zip_derived_cl56]) ).

thf('69',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ~ x
    | ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl85]) ).

thf(zip_derived_cl104_170,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1241_171,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1230,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl3465,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1241]) ).

thf(zip_derived_cl104_172,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_173,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_174,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl3476,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3465,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl3476_175,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3465,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl3703,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3476]) ).

thf(zip_derived_cl3706,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3703]) ).

thf(zip_derived_cl3706_176,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3703]) ).

thf(zip_derived_cl3736,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3476,zip_derived_cl3706,zip_derived_cl3706]) ).

thf(zip_derived_cl3736_177,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3476,zip_derived_cl3706,zip_derived_cl3706]) ).

thf(zip_derived_cl3778,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl3736]) ).

thf(zip_derived_cl3779,plain,
    ( ( f0 @ $false )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3778]) ).

thf(zip_derived_cl3706_178,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
      & ( f3 @ $true )
      & ( f3 @ $false )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3703]) ).

thf('70',plain,
    ( ~ ( f2 @ $true )
    | ~ ( f3 @ $false )
    | ~ ( f1 @ $true )
    | ~ ( f3 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3736,zip_derived_cl3779,zip_derived_cl3706]) ).

thf(zip_derived_cl64_179,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_180,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl12_181,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl4]) ).

thf(zip_derived_cl45,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl12]) ).

thf(zip_derived_cl30_182,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl30_183,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl47,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl30,zip_derived_cl30]) ).

thf(zip_derived_cl249,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl47]) ).

thf(zip_derived_cl255,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl249]) ).

thf('71',plain,
    ( ~ ( f3 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $true )
    | ~ x
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl255]) ).

thf(zip_derived_cl64_184,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_185,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl24_186,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl7]) ).

thf(zip_derived_cl201,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl24]) ).

thf(zip_derived_cl888,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl201]) ).

thf(zip_derived_cl64_187,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_188,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl893,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl888,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1154,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl893]) ).

thf('72',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f3 @ $true )
    | ( f1 @ $true )
    | ~ x
    | ~ ( f2 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1154]) ).

thf(zip_derived_cl895_189,plain,
    ( ( f0 @ $true )
   <= ( f0 @ ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl828,zip_derived_cl842]) ).

thf(zip_derived_cl104_190,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl249_191,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl47]) ).

thf(zip_derived_cl254,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl249]) ).

thf(zip_derived_cl104_192,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_193,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl259,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl254,zip_derived_cl104,zip_derived_cl104]) ).

thf('73',plain,
    ( ~ ( f0 @ ( f0 @ $false ) )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f3 @ $true )
    | ~ x
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl895,zip_derived_cl259]) ).

thf(zip_derived_cl259_194,plain,
    ( ~ ( f0 @ $true )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl254,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl103_195,plain,
    ( ( f0 @ $true )
   <= ( f0 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf('74',plain,
    ( ~ ( f0 @ $true )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ ( f3 @ $true )
    | ~ x
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl259,zip_derived_cl103]) ).

thf(zip_derived_cl104_196,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl893_197,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl888,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl1153,plain,
    ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl893]) ).

thf(zip_derived_cl1164,plain,
    ( ( ( f0 @ $true )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1153]) ).

thf('75',plain,
    ( ( f0 @ $true )
    | ~ ( f3 @ $true )
    | ~ x
    | ( f0 @ ( f0 @ $false ) )
    | ~ ( f2 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl1164]) ).

thf('76',plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1]) ).

thf('77',plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl2]) ).

thf(zip_derived_cl168_198,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $false ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl166]) ).

thf(zip_derived_cl190,plain,
    ( ( ( f1 @ $false )
      | ( f0 @ ( f1 @ $false ) ) )
   <= ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl168]) ).

thf(zip_derived_cl191,plain,
    ( ( ( f1 @ $false )
      | ( f0 @ $false ) )
   <= ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl190]) ).

thf('78',plain,
    ( ( f0 @ $false )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl191]) ).

thf(zip_derived_cl69,plain,
    ( ( f0 @ $false )
   <= ( f0 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl505,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
   <= ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl503]) ).

thf(zip_derived_cl701,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      & ( f0 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl505]) ).

thf(zip_derived_cl701_199,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      & ( f0 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl505]) ).

thf(zip_derived_cl717,plain,
    ( ( ( f0 @ $true )
      | ~ ( f0 @ $false ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      & ( f0 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl701]) ).

thf(zip_derived_cl69_200,plain,
    ( ( f0 @ $false )
   <= ( f0 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl723,plain,
    ( ( f0 @ $true )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      & ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl717,zip_derived_cl69]) ).

thf(zip_derived_cl723_201,plain,
    ( ( f0 @ $true )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
      & ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl717,zip_derived_cl69]) ).

thf('79',plain,
    ( ~ ( f0 @ $false )
    | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl701,zip_derived_cl723,zip_derived_cl723]) ).

thf('80',plain,
    ( ~ ( f3 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $true )
    | ~ x
    | ~ ( f2 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl166]) ).

thf(zip_derived_cl64_202,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl30_203,plain,
    ( ( f3 @ $true )
   <= ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl28]) ).

thf(zip_derived_cl20_204,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $true ) ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl5]) ).

thf(zip_derived_cl160,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl20]) ).

thf(zip_derived_cl705,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl160]) ).

thf(zip_derived_cl64_205,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_206,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl710,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl705,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl772,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl710]) ).

thf('81',plain,
    ( ~ ( f3 @ $true )
    | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ( f1 @ $true )
    | ~ x
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl772]) ).

thf(zip_derived_cl104_207,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl65_208,plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl60]) ).

thf(zip_derived_cl165,plain,
    ( ( f0 @ ( f1 @ ( f1 @ $true ) ) )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl65]) ).

thf(zip_derived_cl104_209,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_210,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl170,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl104_211,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl710_212,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl705,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl771,plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl710]) ).

thf(zip_derived_cl778,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
      & ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl170,zip_derived_cl771]) ).

thf(zip_derived_cl170_213,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl170_214,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
      & x
      & ( f3 @ $true )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl104,zip_derived_cl104]) ).

thf('82',plain,
    ( ~ ( f3 @ $true )
    | ~ x
    | ~ ( f2 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
    | ~ ( f1 @ $true ) ),
    inference(demod,[status(thm)],[zip_derived_cl778,zip_derived_cl170,zip_derived_cl170]) ).

thf(zip_derived_cl189_215,plain,
    ( ( f0 @ ( f1 @ $true ) )
   <= ( ( f1 @ $false )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl168]) ).

thf(zip_derived_cl229,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ $false ) )
   <= ( ( f1 @ $false )
      & ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl189]) ).

thf('83',plain,
    ( ( f0 @ $false )
    | ~ ( f1 @ $false )
    | ( f1 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl229]) ).

thf(zip_derived_cl148_216,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl146]) ).

thf(zip_derived_cl196,plain,
    ( ( ( f1 @ $false )
      | ~ ( f0 @ ( f1 @ $false ) ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl197,plain,
    ( ( ( f1 @ $false )
      | ~ ( f0 @ $false ) )
   <= ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl196]) ).

thf('84',plain,
    ( ~ ( f0 @ $false )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl197]) ).

thf('85',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
    | ( f2 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl313]) ).

thf(zip_derived_cl70_217,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl319_218,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl313]) ).

thf(zip_derived_cl380,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl319]) ).

thf(zip_derived_cl70_219,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl392,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl380,zip_derived_cl70]) ).

thf(zip_derived_cl1289,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
       != ( f0 @ ( f1 @ $false ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl392]) ).

thf(zip_derived_cl70_220,plain,
    ( ( f1 @ $false )
   <= ( f1 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl68]) ).

thf(zip_derived_cl1295,plain,
    ( ( ( f1 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
       != ( f0 @ $true ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1289,zip_derived_cl70]) ).

thf(zip_derived_cl1296,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1295]) ).

thf(zip_derived_cl1296_221,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1295]) ).

thf(zip_derived_cl1540,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl1296]) ).

thf(zip_derived_cl1543,plain,
    ( ~ ( f0 @ $true )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1540]) ).

thf(zip_derived_cl1543_222,plain,
    ( ~ ( f0 @ $true )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1540]) ).

thf(zip_derived_cl1581,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1296,zip_derived_cl1543,zip_derived_cl1543]) ).

thf(zip_derived_cl1581_223,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1296,zip_derived_cl1543,zip_derived_cl1543]) ).

thf(zip_derived_cl2374,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1581]) ).

thf(zip_derived_cl2375,plain,
    ( ( f0 @ $false )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2374]) ).

thf(zip_derived_cl1543_224,plain,
    ( ~ ( f0 @ $true )
   <= ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1540]) ).

thf('86',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
    = ( f0 @ $true ) ),
    inference(demod,[status(thm)],[zip_derived_cl1581,zip_derived_cl2375,zip_derived_cl1543]) ).

thf(zip_derived_cl104_225,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl392_226,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl380,zip_derived_cl70]) ).

thf(zip_derived_cl1290,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ ( f1 @ $true ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl392]) ).

thf(zip_derived_cl104_227,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1299,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1290,zip_derived_cl104]) ).

thf(zip_derived_cl104_228,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl392_229,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl380,zip_derived_cl70]) ).

thf(zip_derived_cl1286,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ ( f1 @ $true ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl392]) ).

thf(zip_derived_cl104_230,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1298,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1286,zip_derived_cl104]) ).

thf(zip_derived_cl1709,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl1298]) ).

thf(zip_derived_cl1712,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1709]) ).

thf(zip_derived_cl1712_231,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1709]) ).

thf(zip_derived_cl1809,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1299,zip_derived_cl1712,zip_derived_cl1712]) ).

thf(zip_derived_cl1809_232,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1299,zip_derived_cl1712,zip_derived_cl1712]) ).

thf(zip_derived_cl1813,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1809]) ).

thf(zip_derived_cl1814,plain,
    ( ( f0 @ $false )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1813]) ).

thf(zip_derived_cl1712_233,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f1 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1709]) ).

thf('87',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ~ ( f1 @ $false )
    | ~ ( f1 @ $true ) ),
    inference(demod,[status(thm)],[zip_derived_cl1809,zip_derived_cl1814,zip_derived_cl1712]) ).

thf(zip_derived_cl319_234,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl313]) ).

thf(zip_derived_cl383,plain,
    ( ( ( f1 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl319]) ).

thf(zip_derived_cl384,plain,
    ( ( ( f1 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
       != ( f0 @ $false ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl383]) ).

thf('88',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ( f1 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl384]) ).

thf(zip_derived_cl390,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl384]) ).

thf(zip_derived_cl390_235,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(split,[status(esa)],[zip_derived_cl384]) ).

thf(zip_derived_cl397,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl390]) ).

thf(zip_derived_cl398,plain,
    ( ( f0 @ $false )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl397]) ).

thf(zip_derived_cl398_236,plain,
    ( ( f0 @ $false )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl397]) ).

thf(zip_derived_cl468,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl390,zip_derived_cl398,zip_derived_cl398]) ).

thf(zip_derived_cl468_237,plain,
    ( ~ ( f0 @ ( f0 @ $true ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl390,zip_derived_cl398,zip_derived_cl398]) ).

thf(zip_derived_cl478,plain,
    ( ( ( f0 @ $true )
      | ~ ( f0 @ $false ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl468]) ).

thf(zip_derived_cl398_238,plain,
    ( ( f0 @ $false )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl397]) ).

thf(zip_derived_cl484,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl478,zip_derived_cl398]) ).

thf(zip_derived_cl484_239,plain,
    ( ( f0 @ $true )
   <= ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
     != ( f0 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl478,zip_derived_cl398]) ).

thf('89',plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    = ( f0 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl468,zip_derived_cl484,zip_derived_cl484]) ).

thf('90',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ~ ( f1 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl1295]) ).

thf(zip_derived_cl104_240,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1092_241,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl64]) ).

thf(zip_derived_cl2753,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1092]) ).

thf(zip_derived_cl104_242,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_243,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_244,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl2764,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2753,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl2764_245,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2753,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl3075,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2764]) ).

thf(zip_derived_cl3078,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3075]) ).

thf(zip_derived_cl3078_246,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3075]) ).

thf(zip_derived_cl3108,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2764,zip_derived_cl3078,zip_derived_cl3078]) ).

thf(zip_derived_cl3108_247,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2764,zip_derived_cl3078,zip_derived_cl3078]) ).

thf(zip_derived_cl3146,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl3108]) ).

thf(zip_derived_cl3147,plain,
    ( ( f0 @ $false )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3146]) ).

thf(zip_derived_cl3078_248,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f2 @ $false )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3075]) ).

thf('91',plain,
    ( ~ ( f2 @ $true )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) )
    | ~ ( f1 @ $true )
    | ~ ( f2 @ $false ) ),
    inference(demod,[status(thm)],[zip_derived_cl3108,zip_derived_cl3147,zip_derived_cl3078]) ).

thf(zip_derived_cl104_249,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl1228_250,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1217,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl3241,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1228]) ).

thf(zip_derived_cl104_251,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_252,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl104_253,plain,
    ( ( f1 @ $true )
   <= ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl102]) ).

thf(zip_derived_cl3252,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3241,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl3252_254,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ $true ) ) )
     != ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3241,zip_derived_cl104,zip_derived_cl104,zip_derived_cl104]) ).

thf(zip_derived_cl3400,plain,
    ( ( ~ ( f0 @ ( f0 @ ( f0 @ $true ) ) )
      | ~ ( f0 @ $true ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3252]) ).

thf(zip_derived_cl3403,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3400]) ).

thf(zip_derived_cl3403_255,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3400]) ).

thf(zip_derived_cl3432,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3252,zip_derived_cl3403,zip_derived_cl3403]) ).

thf(zip_derived_cl3432_256,plain,
    ( ( f0 @ ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3252,zip_derived_cl3403,zip_derived_cl3403]) ).

thf(zip_derived_cl3483,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ $false ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl3432]) ).

thf(zip_derived_cl3484,plain,
    ( ( f0 @ $false )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3483]) ).

thf(zip_derived_cl3403_257,plain,
    ( ~ ( f0 @ $true )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
      & ( f2 @ $true )
      & ( f1 @ $true ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3400]) ).

thf('92',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
    | ~ ( f1 @ $true )
    | ~ ( f2 @ $true ) ),
    inference(demod,[status(thm)],[zip_derived_cl3432,zip_derived_cl3484,zip_derived_cl3403]) ).

thf(zip_derived_cl1741_258,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ $true ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl573]) ).

thf(zip_derived_cl2599,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1741]) ).

thf('93',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ~ ( f2 @ $true )
    | ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
    | ( f1 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl2599]) ).

thf(zip_derived_cl125_259,plain,
    ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ $true ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl14]) ).

thf(zip_derived_cl601,plain,
    ( ( ( f3 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl125]) ).

thf(zip_derived_cl34_260,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl603,plain,
    ( ( ( f3 @ $true )
      | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl601,zip_derived_cl34]) ).

thf('94',plain,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ~ ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) )
    | ( f3 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl603]) ).

thf(zip_derived_cl64_261,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl34_262,plain,
    ( ( f3 @ $false )
   <= ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl32]) ).

thf(zip_derived_cl26_263,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl25]) ).

thf(zip_derived_cl223,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl26]) ).

thf(zip_derived_cl984,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $true ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl64,zip_derived_cl223]) ).

thf(zip_derived_cl64_264,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl64_265,plain,
    ( ( f2 @ $true )
   <= ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl62]) ).

thf(zip_derived_cl989,plain,
    ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $true ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl984,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl2544,plain,
    ( ( ( f1 @ $true )
      | ( f0 @ ( f0 @ ( f0 @ $false ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      & ( f3 @ $false )
      & ( f2 @ $true ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl989]) ).

thf('95',plain,
    ( ~ ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
    | ( f0 @ ( f0 @ ( f0 @ $false ) ) )
    | ~ ( f2 @ $true )
    | ( f1 @ $true )
    | ~ ( f3 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl2544]) ).

thf(zip_derived_cl195_266,plain,
    ( ~ ( f0 @ ( f1 @ $true ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
      & ( f1 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl148]) ).

thf(zip_derived_cl207,plain,
    ( ( ( f1 @ $true )
      | ~ ( f0 @ $false ) )
   <= ( ~ ( f0 @ ( f1 @ ( f1 @ $false ) ) )
      & ( f1 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl195]) ).

thf('96',plain,
    ( ~ ( f0 @ $false )
    | ~ ( f1 @ $false )
    | ( f1 @ $true )
    | ( f0 @ ( f1 @ ( f1 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl207]) ).

thf(zip_derived_cl75_267,plain,
    ( ( f2 @ $false )
   <= ( f2 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl73]) ).

thf(zip_derived_cl576,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl570]) ).

thf(zip_derived_cl1784,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $true ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl576]) ).

thf(zip_derived_cl4307,plain,
    ( ( ( f2 @ $true )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
      & ( f2 @ $false ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl1784]) ).

thf('97',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ~ ( f2 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ( f2 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl4307]) ).

thf(zip_derived_cl576_268,plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl570]) ).

thf(zip_derived_cl1787,plain,
    ( ( ( f2 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ $false ) ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl576]) ).

thf(zip_derived_cl1788,plain,
    ( ( ( f2 @ $false )
      | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
       != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) )
   <= ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1787]) ).

thf('98',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ $false ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) )
    | ( f2 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ $false ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ $false ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl1788]) ).

thf(zip_derived_cl815,plain,
    ( ( f0 @ ( f0 @ ( f0 @ $false ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl813]) ).

thf(zip_derived_cl994,plain,
    ( ( ( f0 @ $false )
      | ( f0 @ ( f0 @ $false ) ) )
   <= ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl815]) ).

thf(zip_derived_cl995,plain,
    ( ( f0 @ $false )
   <= ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl994]) ).

thf(zip_derived_cl80,plain,
    ( ~ ( f0 @ $false )
   <= ~ ( f0 @ $false ) ),
    inference(split,[status(esa)],[zip_derived_cl78]) ).

thf('99',plain,
    ( ( f0 @ $false )
    | ~ ( f0 @ ( f0 @ ( f0 @ $false ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl995,zip_derived_cl80]) ).

thf('100',plain,
    ( ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
    | x ),
    inference(split,[status(esa)],[zip_derived_cl3]) ).

thf('101',plain,
    ( ( f3 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $false ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $false ) ) ) ) ) ) ),
    inference(split,[status(esa)],[zip_derived_cl38]) ).

thf('102',plain,
    ( ~ ( f3 @ $false )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ $false ) ) ) ) ) ) ) )
      = ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ $false ) ) ) ) ) ) ) ) )
    | ( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ $true ) ) ) ) ) ) )
     != ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ $true ) ) ) ) ) )
    | ( f3 @ $true ) ),
    inference(split,[status(esa)],[zip_derived_cl369]) ).

thf(zip_derived_cl4708,plain,
    $false,
    inference('sat_resolution*',[status(thm)],['0','1','2','3','4','5','6','7','8','9','10','11','12','13','14','15','16','17','18','19','20','21','22','23','24','25','26','27','28','29','30','31','32','33','34','35','36','37','38','39','40','41','42','43','44','45','46','47','48','49','50','51','52','53','54','55','56','57','58','59','60','61','62','63','64','65','66','67','68','69','70','71','72','73','74','75','76','77','78','79','80','81','82','83','84','85','86','87','88','89','90','91','92','93','94','95','96','97','98','99','100','101','102']) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO500^1.004 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.AtW5B3XUDf true
% 0.15/0.34  % Computer : n004.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Sat Aug 26 05:48:23 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.15/0.34  % Running portfolio for 300 s
% 0.15/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.34  % Number of cores: 8
% 0.15/0.35  % Python version: Python 3.6.8
% 0.15/0.35  % Running in HO mode
% 0.21/0.67  % Total configuration time : 828
% 0.21/0.67  % Estimated wc time : 1656
% 0.21/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.21/0.81  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.58/0.83  % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s
% 1.88/0.86  % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s
% 1.88/0.86  % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s
% 2.03/0.89  % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s
% 7.48/1.57  % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s
% 7.77/1.61  % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s
% 7.96/1.65  % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s
% 7.96/1.68  % /export/starexec/sandbox2/solver/bin/lams/8_add_var_l_av.sh running for 16s
% 7.96/1.71  % /export/starexec/sandbox2/solver/bin/lams/8_new_sh_or.sh running for 16s
% 8.66/1.74  % /export/starexec/sandbox2/solver/bin/lams/30_old_zip1.sh running for 36s
% 25.74/3.91  % /export/starexec/sandbox2/solver/bin/lams/10_shallow_lift.sh running for 30s
% 25.74/3.93  % /export/starexec/sandbox2/solver/bin/lams/15_lcnf_noform.sh running for 30s
% 25.74/3.96  % /export/starexec/sandbox2/solver/bin/lams/8_sh.eqenc2.sh running for 10s
% 25.74/3.98  % /export/starexec/sandbox2/solver/bin/lams/8_cmb.lcnf4.sh running for 10s
% 28.86/4.40  % /export/starexec/sandbox2/solver/bin/lams/8_new_l_av.sh running for 24s
% 29.69/4.45  % /export/starexec/sandbox2/solver/bin/lams/10_forms1.sh running for 20s
% 29.69/4.47  % /export/starexec/sandbox2/solver/bin/lams/10_forms4.sh running for 20s
% 29.69/4.49  % /export/starexec/sandbox2/solver/bin/lams/15_ch_av2.sh running for 26s
% 30.37/4.50  % /export/starexec/sandbox2/solver/bin/lams/15_sine_deep.sh running for 44s
% 30.37/4.51  % /export/starexec/sandbox2/solver/bin/lams/10_shallow_sine.sh running for 30s
% 30.37/4.53  % /export/starexec/sandbox2/solver/bin/lams/20_new_c.s3.sh running for 40s
% 30.37/4.54  % /export/starexec/sandbox2/solver/bin/lams/10_forms2.sh running for 20s
% 30.37/4.56  % /export/starexec/sandbox2/solver/bin/lams/8_sh.or.sh running for 24s
% 31.05/4.62  % /export/starexec/sandbox2/solver/bin/lams/15_combs_pe.sh running for 20s
% 34.01/5.00  % Solved by lams/15_combs_pe.sh.
% 34.01/5.00  % done 2170 iterations in 0.319s
% 34.01/5.00  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 34.01/5.00  % SZS output start Refutation
% See solution above
% 34.01/5.00  
% 34.01/5.00  
% 34.01/5.01  % Terminating...
% 34.01/5.01  % /export/starexec/sandbox2/solver/bin/lams/15_b.split.li.sh running for 44s
% 35.07/5.19  % Runner terminated.
% 35.07/5.20  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------