TSTP Solution File: SEU734^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU734^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mBC5XPUCe3 true

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:16:50 EDT 2023

% Result   : Theorem 8.58s 1.74s
% Output   : Refutation 8.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   94 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :  463 (   4 equ;  64 cnn)
%            Maximal formula atoms :   15 (   6 avg)
%            Number of connectives : 2012 (  89   ~;  77   |;   0   &;1608   @)
%                                         (   4 <=>; 149  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  18 usr;  11 con; 0-6 aty)
%                                         (  85  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  152 (  29   ^; 111   !;   0   ?; 152   :)
%                                         (  12  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk4_type',type,
    '#sk4': $i > $i > $i > $i ).

thf(setminus_type,type,
    setminus: $i > $i > $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(complementT_lem_type,type,
    complementT_lem: $o ).

thf('#sk3_type',type,
    '#sk3': $i ).

thf(binintersectT_lem_type,type,
    binintersectT_lem: $o ).

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf('#sk1_type',type,
    '#sk1': $i ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf('#sk2_type',type,
    '#sk2': $i ).

thf(complementImpComplementIntersect_type,type,
    complementImpComplementIntersect: $o ).

thf(subsetTI_type,type,
    subsetTI: $o ).

thf(s_comb_type,type,
    '#S': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).

thf(c_comb_type,type,
    '#C': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).

thf(b_comb_type,type,
    '#B': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).

thf(k_comb_type,type,
    '#K': 
      !>[A: $tType,B: $tType] : ( B > A > B ) ).

thf(i_comb_type,type,
    '#I': 
      !>[A: $tType] : ( A > A ) ).

thf(complementSubsetComplementIntersect,conjecture,
    ( binintersectT_lem
   => ( complementT_lem
     => ( subsetTI
       => ( complementImpComplementIntersect
         => ! [A: $i,X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ! [Y: $i] :
                  ( ( in @ Y @ ( powerset @ A ) )
                 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( binintersectT_lem
     => ( complementT_lem
       => ( subsetTI
         => ( complementImpComplementIntersect
           => ! [A: $i,X: $i] :
                ( ( in @ X @ ( powerset @ A ) )
               => ! [Y: $i] :
                    ( ( in @ Y @ ( powerset @ A ) )
                   => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[complementSubsetComplementIntersect]) ).

thf(zip_derived_cl0,plain,
    ~ ( binintersectT_lem
     => ( complementT_lem
       => ( subsetTI
         => ( complementImpComplementIntersect
           => ( !!
              @ ^ [Y0: $i] :
                  ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ ( powerset @ Y0 ) )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( in @ Y2 @ ( powerset @ Y0 ) )
                           => ( subset @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( binintersectT_lem
     => ( complementT_lem
       => ( subsetTI
         => ( complementImpComplementIntersect
           => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ subset ) @ setminus ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    binintersectT_lem,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(binintersectT_lem,axiom,
    ( binintersectT_lem
   => ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( powerset @ Y0 ) )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ ( powerset @ Y0 ) )
                     => ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
      = $true ) ) ).

thf('0',plain,
    ( binintersectT_lem
  <=> ! [X5: $i,X7: $i] :
        ( ( in @ X7 @ ( powerset @ X5 ) )
       => ! [X9: $i] :
            ( ( in @ X9 @ ( powerset @ X5 ) )
           => ( in @ ( binintersect @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ),
    inference('rw.lit',[status(esa)],[binintersectT_lem]) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( powerset @ Y0 ) )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ ( powerset @ Y0 ) )
                 => ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
    inference(rw_clause,[status(thm)],[zip_derived_cl2,'0']) ).

thf(zip_derived_cl7,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binintersect ) ) ) @ powerset ) ) ) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binintersect ) ) @ ( powerset @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( powerset @ X2 ) )
     => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binintersect @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binintersect @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( in @ X6 @ ( powerset @ X2 ) )
       => ( in @ ( binintersect @ X4 @ X6 ) @ ( powerset @ X2 ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ( in @ ( binintersect @ X4 @ X6 ) @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl3,plain,
    ~ ( complementT_lem
     => ( subsetTI
       => ( complementImpComplementIntersect
         => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ subset ) @ setminus ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ~ ( subsetTI
     => ( complementImpComplementIntersect
       => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ subset ) @ setminus ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl11,plain,
    ~ ( complementImpComplementIntersect
     => ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ subset ) @ setminus ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl17,plain,
    ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ subset ) @ setminus ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl23,plain,
    ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ subset @ ( setminus @ '#sk1' ) ) ) @ ( '#B' @ ( '#B' @ ( setminus @ '#sk1' ) ) @ binintersect ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl29,plain,
    ~ ( ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
     => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#B' @ ( subset @ ( setminus @ '#sk1' @ '#sk2' ) ) @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binintersect @ '#sk2' ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl34,plain,
    ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#B' @ ( subset @ ( setminus @ '#sk1' @ '#sk2' ) ) @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binintersect @ '#sk2' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl37,plain,
    ~ ( ( in @ '#sk3' @ ( powerset @ '#sk1' ) )
     => ( subset @ ( setminus @ '#sk1' @ '#sk2' ) @ ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl41,plain,
    ~ ( subset @ ( setminus @ '#sk1' @ '#sk2' ) @ ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl10,plain,
    subsetTI,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(subsetTI,axiom,
    ( subsetTI
   => ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( powerset @ Y0 ) )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ ( powerset @ Y0 ) )
                     => ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( in @ Y3 @ Y0 )
                             => ( ( in @ Y3 @ Y1 )
                               => ( in @ Y3 @ Y2 ) ) ) )
                       => ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
      = $true ) ) ).

thf('1',plain,
    ( subsetTI
  <=> ! [X5: $i,X7: $i] :
        ( ( in @ X7 @ ( powerset @ X5 ) )
       => ! [X9: $i] :
            ( ( in @ X9 @ ( powerset @ X5 ) )
           => ( ! [X11: $i] :
                  ( ( in @ X11 @ X5 )
                 => ( ( in @ X11 @ X7 )
                   => ( in @ X11 @ X9 ) ) )
             => ( subset @ X7 @ X9 ) ) ) ) ),
    inference('rw.lit',[status(esa)],[subsetTI]) ).

thf(zip_derived_cl15,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( powerset @ Y0 ) )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ ( powerset @ Y0 ) )
                 => ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y3 @ Y0 )
                         => ( ( in @ Y3 @ Y1 )
                           => ( in @ Y3 @ Y2 ) ) ) )
                   => ( subset @ Y1 @ Y2 ) ) ) ) ) ) ),
    inference(rw_clause,[status(thm)],[zip_derived_cl10,'1']) ).

thf(zip_derived_cl20,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) ) @ subset ) ) ) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) @ subset ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( powerset @ X2 ) )
     => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( subset @ X4 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( subset @ X4 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl35,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( in @ X6 @ ( powerset @ X2 ) )
       => ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
         => ( subset @ X4 @ X6 ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
       => ( subset @ X4 @ X6 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
      | ( subset @ X4 @ X6 )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
         => ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
           => ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( subset @ X4 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl46,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
      | ( subset @ X4 @ X6 )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl47,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
         => ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) )
      | ( subset @ X4 @ X6 )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl49,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
      | ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( subset @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl16,plain,
    complementImpComplementIntersect,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(complementImpComplementIntersect,axiom,
    ( complementImpComplementIntersect
   => ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( powerset @ Y0 ) )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ ( powerset @ Y0 ) )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) )
                             => ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
      = $true ) ) ).

thf('2',plain,
    ( complementImpComplementIntersect
  <=> ! [X5: $i,X7: $i] :
        ( ( in @ X7 @ ( powerset @ X5 ) )
       => ! [X9: $i] :
            ( ( in @ X9 @ ( powerset @ X5 ) )
           => ! [X11: $i] :
                ( ( in @ X11 @ X5 )
               => ( ( in @ X11 @ ( setminus @ X5 @ X7 ) )
                 => ( in @ X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) ) ) ) ) ),
    inference('rw.lit',[status(esa)],[complementImpComplementIntersect]) ).

thf(zip_derived_cl22,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( powerset @ Y0 ) )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ ( powerset @ Y0 ) )
                 => ( !!
                    @ ^ [Y3: $i] :
                        ( ( in @ Y3 @ Y0 )
                       => ( ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) )
                         => ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
    inference(rw_clause,[status(thm)],[zip_derived_cl16,'2']) ).

thf(zip_derived_cl27,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ setminus ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( setminus @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#B' @ ( '#B' @ ( setminus @ X2 ) ) @ binintersect ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( powerset @ X2 ) )
     => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( in @ X6 @ ( powerset @ X2 ) )
       => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl45,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( ( in @ X8 @ X2 )
       => ( ( in @ X8 @ ( setminus @ X2 @ X4 ) )
         => ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8 @ X2 )
      | ( ( in @ X8 @ ( setminus @ X2 @ X4 ) )
       => ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( in @ X8 @ ( setminus @ X2 @ X4 ) )
      | ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ~ ( in @ X8 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 )
      | ~ ( in @ X6 @ ( powerset @ X2 ) )
      | ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( subset @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
      | ~ ( in @ X0 @ ( powerset @ X2 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ ( setminus @ X2 @ X1 ) )
      | ( subset @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
      | ~ ( in @ X3 @ ( powerset @ X4 ) )
      | ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X4 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl50]) ).

thf(zip_derived_cl251,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( subset @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
      | ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
      | ~ ( in @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
      | ~ ( in @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
      | ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
      | ( subset @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
      | ~ ( in @ X0 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) )
      | ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl92]) ).

thf(zip_derived_cl254,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) @ X1 )
      | ~ ( in @ X2 @ ( powerset @ X1 ) )
      | ~ ( in @ X0 @ ( powerset @ X1 ) )
      | ~ ( in @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
      | ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
      | ( subset @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl251]) ).

thf(zip_derived_cl807,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
      | ~ ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) )
      | ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
      | ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
      | ~ ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) )
      | ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
      | ~ ( in @ X2 @ ( powerset @ X0 ) )
      | ~ ( in @ X1 @ ( powerset @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl254]) ).

thf(zip_derived_cl808,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X1 @ ( powerset @ X0 ) )
      | ~ ( in @ X2 @ ( powerset @ X0 ) )
      | ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
      | ~ ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) )
      | ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl807]) ).

thf(zip_derived_cl5,plain,
    complementT_lem,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(complementT_lem,axiom,
    ( complementT_lem
   => ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( powerset @ Y0 ) )
               => ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
      = $true ) ) ).

thf('3',plain,
    ( complementT_lem
  <=> ! [X5: $i,X7: $i] :
        ( ( in @ X7 @ ( powerset @ X5 ) )
       => ( in @ ( setminus @ X5 @ X7 ) @ ( powerset @ X5 ) ) ) ),
    inference('rw.lit',[status(esa)],[complementT_lem]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( powerset @ Y0 ) )
           => ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ),
    inference(rw_clause,[status(thm)],[zip_derived_cl5,'3']) ).

thf(zip_derived_cl13,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ setminus ) ) @ powerset ) ) ),
    inference('comb-normalize',[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( setminus @ X2 ) ) @ ( powerset @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( powerset @ X2 ) )
     => ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl810,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
      | ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
      | ~ ( in @ X2 @ ( powerset @ X0 ) )
      | ~ ( in @ X1 @ ( powerset @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl808,zip_derived_cl25]) ).

thf(zip_derived_cl812,plain,
    ( ~ ( in @ '#sk3' @ ( powerset @ '#sk1' ) )
    | ~ ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
    | ~ ( in @ ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) @ ( powerset @ '#sk1' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl810]) ).

thf(zip_derived_cl40,plain,
    in @ '#sk3' @ ( powerset @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl33,plain,
    in @ '#sk2' @ ( powerset @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl813,plain,
    ~ ( in @ ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) @ ( powerset @ '#sk1' ) ),
    inference(demod,[status(thm)],[zip_derived_cl812,zip_derived_cl40,zip_derived_cl33]) ).

thf(zip_derived_cl25_001,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl815,plain,
    ~ ( in @ ( binintersect @ '#sk2' @ '#sk3' ) @ ( powerset @ '#sk1' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl813,zip_derived_cl25]) ).

thf(zip_derived_cl818,plain,
    ( ~ ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
    | ~ ( in @ '#sk3' @ ( powerset @ '#sk1' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl815]) ).

thf(zip_derived_cl33_002,plain,
    in @ '#sk2' @ ( powerset @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl40_003,plain,
    in @ '#sk3' @ ( powerset @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl819,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl818,zip_derived_cl33,zip_derived_cl40]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU734^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.mBC5XPUCe3 true
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 01:19:00 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 8.58/1.74  % Solved by lams/40_b.comb.sh.
% 8.58/1.74  % done 347 iterations in 0.941s
% 8.58/1.74  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 8.58/1.74  % SZS output start Refutation
% See solution above
% 8.58/1.74  
% 8.58/1.74  
% 8.58/1.74  % Terminating...
% 8.58/1.78  % Runner terminated.
% 8.58/1.79  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------