TSTP Solution File: SEU315+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.x1hAdyyswq true

% Computer : n006.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 19:12:04 EDT 2023

% Result   : Theorem 16.38s 2.92s
% Output   : Refutation 16.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  206 (  57 unt;  18 typ;   0 def)
%            Number of atoms       :  504 (  57 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 2301 ( 251   ~; 280   |;  21   &;1734   @)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;   4 con; 0-2 aty)
%            Number of variables   :  177 (   0   ^; 170   !;   7   ?; 177   :)

% Comments : 
%------------------------------------------------------------------------------
thf(element_type,type,
    element: $i > $i > $o ).

thf(sk__1_type,type,
    sk__1: $i ).

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

thf(closed_subset_type,type,
    closed_subset: $i > $i > $o ).

thf(sk__6_type,type,
    sk__6: $i > $i ).

thf(sk__9_type,type,
    sk__9: $i > $i > $i ).

thf(topological_space_type,type,
    topological_space: $i > $o ).

thf(top_str_type,type,
    top_str: $i > $o ).

thf(the_carrier_type,type,
    the_carrier: $i > $i ).

thf(empty_type,type,
    empty: $i > $o ).

thf(sk__2_type,type,
    sk__2: $i > $i ).

thf(sk__3_type,type,
    sk__3: $i > $i ).

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

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

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

thf(empty_set_type,type,
    empty_set: $i ).

thf(sk__11_type,type,
    sk__11: $i > $i > $i ).

thf(sk__8_type,type,
    sk__8: $i > $i > $i ).

thf(d2_subset_1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( empty @ A )
       => ( ( element @ B @ A )
        <=> ( empty @ B ) ) )
      & ( ~ ( empty @ A )
       => ( ( element @ B @ A )
        <=> ( in @ B @ A ) ) ) ) ).

thf(zip_derived_cl75,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ X1 )
      | ( in @ X0 @ X1 )
      | ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[d2_subset_1]) ).

thf(s3_subset_1__e1_40__pre_topc,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( topological_space @ A )
        & ( top_str @ A )
        & ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
     => ? [C: $i] :
          ( ! [D: $i] :
              ( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
             => ( ( in @ D @ C )
              <=> ? [E: $i] :
                    ( ( subset @ B @ D )
                    & ( closed_subset @ E @ A )
                    & ( E = D )
                    & ( element @ E @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
          & ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( ( topological_space @ A )
          & ( top_str @ A )
          & ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
       => ? [C: $i] :
            ( ! [D: $i] :
                ( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
               => ( ( in @ D @ C )
                <=> ? [E: $i] :
                      ( ( subset @ B @ D )
                      & ( closed_subset @ E @ A )
                      & ( E = D )
                      & ( element @ E @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
            & ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[s3_subset_1__e1_40__pre_topc]) ).

thf(zip_derived_cl6,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8,plain,
    top_str @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7,plain,
    topological_space @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(s1_xboole_0__e1_40__pre_topc__1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( topological_space @ A )
        & ( top_str @ A )
        & ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
     => ? [C: $i] :
        ! [D: $i] :
          ( ( in @ D @ C )
        <=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
            & ? [E: $i] :
                ( ( subset @ B @ D )
                & ( closed_subset @ E @ A )
                & ( E = D )
                & ( element @ E @ ( powerset @ ( the_carrier @ A ) ) ) ) ) ) ) ).

thf(zip_derived_cl68,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( in @ X2 @ ( sk__8 @ X1 @ X0 ) )
      | ~ ( element @ X3 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( X3 != X2 )
      | ~ ( closed_subset @ X3 @ X0 )
      | ~ ( subset @ X1 @ X2 )
      | ~ ( in @ X2 @ ( powerset @ ( the_carrier @ X0 ) ) ) ),
    inference(cnf,[status(esa)],[s1_xboole_0__e1_40__pre_topc__1]) ).

thf(zip_derived_cl342,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ X1 )
      | ~ ( closed_subset @ X2 @ sk_ )
      | ( X2 != X1 )
      | ~ ( element @ X2 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( top_str @ sk_ ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl7,zip_derived_cl68]) ).

thf(zip_derived_cl384,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sk_ != sk_ )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( in @ X0 @ ( sk__8 @ X1 @ sk_ ) )
      | ~ ( element @ X2 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( X2 != X0 )
      | ~ ( closed_subset @ X2 @ sk_ )
      | ~ ( subset @ X1 @ X0 )
      | ~ ( in @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl8,zip_derived_cl342]) ).

thf(zip_derived_cl622,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X1 @ X0 )
      | ~ ( closed_subset @ X2 @ sk_ )
      | ( X2 != X0 )
      | ~ ( element @ X2 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( in @ X0 @ ( sk__8 @ X1 @ sk_ ) )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl384]) ).

thf(zip_derived_cl623,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( closed_subset @ X1 @ sk_ )
      | ~ ( subset @ X0 @ X1 )
      | ~ ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl622]) ).

thf(zip_derived_cl74,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( element @ X0 @ X1 )
      | ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[d2_subset_1]) ).

thf(t7_boole,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ) ).

thf(zip_derived_cl86,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl472,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ X1 )
      | ~ ( in @ X0 @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl86]) ).

thf(zip_derived_cl624,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ X1 )
      | ~ ( closed_subset @ X1 @ sk_ )
      | ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl623,zip_derived_cl472]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ ( sk__2 @ X0 ) @ X0 )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( closed_subset @ X1 @ sk_ )
      | ( X1
       != ( sk__2 @ X0 ) )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl437,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ~ ( element @ ( sk__2 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( in @ ( sk__2 @ X0 ) @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i] :
      ( ( element @ ( sk__2 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl466,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( sk__2 @ X0 ) @ X0 )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl437,zip_derived_cl5]) ).

thf(zip_derived_cl629,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ sk_ )
      | ~ ( subset @ X0 @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) )
      | ~ ( in @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) )
      | ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ sk_ )
      | ~ ( element @ ( sk__8 @ X0 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl624,zip_derived_cl466]) ).

thf(zip_derived_cl633,plain,
    ! [X0: $i] :
      ( ~ ( element @ ( sk__8 @ X0 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) )
      | ~ ( in @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) )
      | ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl629]) ).

thf(zip_derived_cl1868,plain,
    ( ~ ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl633]) ).

thf(zip_derived_cl1885,plain,
    ( ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ~ ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1868]) ).

thf(l71_subset_1,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) )
     => ( element @ A @ ( powerset @ B ) ) ) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ( in @ ( sk__11 @ X1 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl6_001,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8_002,plain,
    top_str @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7_003,plain,
    topological_space @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl73,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( in @ X2 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ~ ( in @ X2 @ ( sk__8 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[s1_xboole_0__e1_40__pre_topc__1]) ).

thf(zip_derived_cl347,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( top_str @ sk_ ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl7,zip_derived_cl73]) ).

thf(zip_derived_cl399,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk_ != sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl8,zip_derived_cl347]) ).

thf(zip_derived_cl735,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl399]) ).

thf(zip_derived_cl741,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ ( sk__8 @ sk__1 @ sk_ ) )
      | ( in @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl735]) ).

thf(zip_derived_cl1044,plain,
    ! [X0: $i] :
      ( ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ X0 ) )
      | ( in @ ( sk__11 @ X0 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl741]) ).

thf(zip_derived_cl81,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ~ ( in @ ( sk__11 @ X1 @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl4248,plain,
    ( ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
    | ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1044,zip_derived_cl81]) ).

thf(zip_derived_cl4263,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( closed_subset @ ( sk__3 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4267,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( closed_subset @ ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4263,zip_derived_cl0]) ).

thf(zip_derived_cl4263_004,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl472_005,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ X1 )
      | ~ ( in @ X0 @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl74,zip_derived_cl86]) ).

thf(zip_derived_cl473,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ( element @ ( sk__2 @ X0 ) @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl472]) ).

thf(zip_derived_cl4270,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( element @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4263,zip_derived_cl473]) ).

thf(zip_derived_cl75_006,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ X1 )
      | ( in @ X0 @ X1 )
      | ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[d2_subset_1]) ).

thf(zip_derived_cl8_007,plain,
    top_str @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7_008,plain,
    topological_space @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl71,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( ( sk__9 @ X2 @ X0 )
        = X2 )
      | ~ ( in @ X2 @ ( sk__8 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[s1_xboole_0__e1_40__pre_topc__1]) ).

thf(zip_derived_cl345,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( ( sk__9 @ X1 @ sk_ )
        = X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( top_str @ sk_ ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl7,zip_derived_cl71]) ).

thf(zip_derived_cl393,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk_ != sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( ( sk__9 @ X1 @ sk_ )
        = X1 )
      | ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl8,zip_derived_cl345]) ).

thf(zip_derived_cl673,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( ( sk__9 @ X1 @ sk_ )
        = X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl393]) ).

thf(zip_derived_cl674,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty @ ( sk__8 @ X0 @ sk_ ) )
      | ~ ( element @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( ( sk__9 @ X1 @ sk_ )
        = X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl673]) ).

thf(zip_derived_cl4538,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( empty @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4270,zip_derived_cl674]) ).

thf(zip_derived_cl82_009,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ( in @ ( sk__11 @ X1 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl86_010,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl511,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ~ ( empty @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl86]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl523,plain,
    ! [X0: $i] :
      ( ~ ( empty @ X0 )
      | ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( subset @ sk__1 @ ( sk__2 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl511,zip_derived_cl3]) ).

thf(zip_derived_cl86_011,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl1310,plain,
    ! [X0: $i] :
      ( ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( empty @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl523,zip_derived_cl86]) ).

thf(zip_derived_cl75_012,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ X1 )
      | ( in @ X0 @ X1 )
      | ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[d2_subset_1]) ).

thf(zip_derived_cl1_013,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl86_014,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl428,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( empty @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl86]) ).

thf(rc2_subset_1,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( empty @ B )
      & ( element @ B @ ( powerset @ A ) ) ) ).

thf(zip_derived_cl52,plain,
    ! [X0: $i] : ( element @ ( sk__6 @ X0 ) @ ( powerset @ X0 ) ),
    inference(cnf,[status(esa)],[rc2_subset_1]) ).

thf(zip_derived_cl53,plain,
    ! [X0: $i] : ( empty @ ( sk__6 @ X0 ) ),
    inference(cnf,[status(esa)],[rc2_subset_1]) ).

thf(t6_boole,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ) ).

thf(zip_derived_cl85,plain,
    ! [X0: $i] :
      ( ( X0 = empty_set )
      | ~ ( empty @ X0 ) ),
    inference(cnf,[status(esa)],[t6_boole]) ).

thf(zip_derived_cl439,plain,
    ! [X0: $i] :
      ( ( sk__6 @ X0 )
      = empty_set ),
    inference('s_sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl85]) ).

thf(zip_derived_cl445,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl439]) ).

thf(zip_derived_cl0_015,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( closed_subset @ ( sk__3 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl446,plain,
    ( ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ( closed_subset @ ( sk__3 @ empty_set ) @ sk_ ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl445,zip_derived_cl0]) ).

thf(zip_derived_cl470,plain,
    ( ~ ( empty @ empty_set )
    | ~ ( element @ empty_set @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
    | ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ( closed_subset @ ( sk__2 @ empty_set ) @ sk_ ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl428,zip_derived_cl446]) ).

thf(fc1_xboole_0,axiom,
    empty @ empty_set ).

thf(zip_derived_cl80,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(zip_derived_cl445_016,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl439]) ).

thf(zip_derived_cl471,plain,
    ( ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ( closed_subset @ ( sk__2 @ empty_set ) @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl470,zip_derived_cl80,zip_derived_cl445]) ).

thf(zip_derived_cl1_017,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl466_018,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( sk__2 @ X0 ) @ X0 )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl437,zip_derived_cl5]) ).

thf(zip_derived_cl467,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl466]) ).

thf(zip_derived_cl468,plain,
    ! [X0: $i] :
      ( ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl467]) ).

thf(zip_derived_cl1127,plain,
    ( ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ~ ( subset @ sk__1 @ ( sk__2 @ empty_set ) )
    | ( ( sk__3 @ empty_set )
      = ( sk__2 @ empty_set ) )
    | ~ ( element @ empty_set @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl471,zip_derived_cl468]) ).

thf(zip_derived_cl445_019,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl439]) ).

thf(zip_derived_cl1130,plain,
    ( ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ~ ( subset @ sk__1 @ ( sk__2 @ empty_set ) )
    | ( ( sk__3 @ empty_set )
      = ( sk__2 @ empty_set ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1127,zip_derived_cl445]) ).

thf(zip_derived_cl445_020,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl439]) ).

thf(zip_derived_cl3_021,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl448,plain,
    ( ( in @ ( sk__2 @ empty_set ) @ empty_set )
    | ( subset @ sk__1 @ ( sk__2 @ empty_set ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl445,zip_derived_cl3]) ).

thf(zip_derived_cl1385,plain,
    ( ( ( sk__3 @ empty_set )
      = ( sk__2 @ empty_set ) )
    | ( in @ ( sk__2 @ empty_set ) @ empty_set ) ),
    inference(clc,[status(thm)],[zip_derived_cl1130,zip_derived_cl448]) ).

thf(zip_derived_cl86_022,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl1387,plain,
    ( ( ( sk__3 @ empty_set )
      = ( sk__2 @ empty_set ) )
    | ~ ( empty @ empty_set ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1385,zip_derived_cl86]) ).

thf(zip_derived_cl80_023,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(zip_derived_cl1392,plain,
    ( ( sk__3 @ empty_set )
    = ( sk__2 @ empty_set ) ),
    inference(demod,[status(thm)],[zip_derived_cl1387,zip_derived_cl80]) ).

thf(zip_derived_cl511_024,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ~ ( empty @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl86]) ).

thf(zip_derived_cl0_025,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( closed_subset @ ( sk__3 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl521,plain,
    ! [X0: $i] :
      ( ~ ( empty @ X0 )
      | ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( closed_subset @ ( sk__3 @ X0 ) @ sk_ ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl511,zip_derived_cl0]) ).

thf(zip_derived_cl86_026,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl1243,plain,
    ! [X0: $i] :
      ( ( closed_subset @ ( sk__3 @ X0 ) @ sk_ )
      | ~ ( empty @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl521,zip_derived_cl86]) ).

thf(zip_derived_cl1400,plain,
    ( ( closed_subset @ ( sk__2 @ empty_set ) @ sk_ )
    | ~ ( empty @ empty_set ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1392,zip_derived_cl1243]) ).

thf(zip_derived_cl80_027,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(zip_derived_cl1403,plain,
    closed_subset @ ( sk__2 @ empty_set ) @ sk_,
    inference(demod,[status(thm)],[zip_derived_cl1400,zip_derived_cl80]) ).

thf(zip_derived_cl624_028,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ X1 )
      | ~ ( closed_subset @ X1 @ sk_ )
      | ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl623,zip_derived_cl472]) ).

thf(zip_derived_cl86_029,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl626,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( closed_subset @ X1 @ sk_ )
      | ~ ( subset @ X0 @ X1 )
      | ~ ( in @ X1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( empty @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl624,zip_derived_cl86]) ).

thf(zip_derived_cl1407,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ ( sk__2 @ empty_set ) )
      | ~ ( in @ ( sk__2 @ empty_set ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( empty @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1403,zip_derived_cl626]) ).

thf(zip_derived_cl1889,plain,
    ! [X0: $i] :
      ( ( empty @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ ( sk__2 @ empty_set ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ ( sk__2 @ empty_set ) )
      | ~ ( empty @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl1407]) ).

thf(fc1_subset_1,axiom,
    ! [A: $i] :
      ~ ( empty @ ( powerset @ A ) ) ).

thf(zip_derived_cl67,plain,
    ! [X0: $i] :
      ~ ( empty @ ( powerset @ X0 ) ),
    inference(cnf,[status(esa)],[fc1_subset_1]) ).

thf(zip_derived_cl1392_030,plain,
    ( ( sk__3 @ empty_set )
    = ( sk__2 @ empty_set ) ),
    inference(demod,[status(thm)],[zip_derived_cl1387,zip_derived_cl80]) ).

thf(zip_derived_cl511_031,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ~ ( empty @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl86]) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( element @ ( sk__3 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl522,plain,
    ! [X0: $i] :
      ( ~ ( empty @ X0 )
      | ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( element @ ( sk__3 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl511,zip_derived_cl2]) ).

thf(zip_derived_cl86_032,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X1 ) ),
    inference(cnf,[status(esa)],[t7_boole]) ).

thf(zip_derived_cl1258,plain,
    ! [X0: $i] :
      ( ( element @ ( sk__3 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( empty @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl522,zip_derived_cl86]) ).

thf(zip_derived_cl1401,plain,
    ( ( element @ ( sk__2 @ empty_set ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( empty @ empty_set ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1392,zip_derived_cl1258]) ).

thf(zip_derived_cl80_033,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(zip_derived_cl1404,plain,
    element @ ( sk__2 @ empty_set ) @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl1401,zip_derived_cl80]) ).

thf(zip_derived_cl1896,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( subset @ X0 @ ( sk__2 @ empty_set ) )
      | ~ ( empty @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1889,zip_derived_cl67,zip_derived_cl1404]) ).

thf(zip_derived_cl1928,plain,
    ( ~ ( empty @ empty_set )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( empty @ ( sk__8 @ sk__1 @ sk_ ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1310,zip_derived_cl1896]) ).

thf(zip_derived_cl80_034,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(zip_derived_cl6_035,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1933,plain,
    ~ ( empty @ ( sk__8 @ sk__1 @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl1928,zip_derived_cl80,zip_derived_cl6]) ).

thf(zip_derived_cl6_036,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4553,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4538,zip_derived_cl1933,zip_derived_cl6]) ).

thf(zip_derived_cl1_037,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8_038,plain,
    top_str @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7_039,plain,
    topological_space @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl70,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( closed_subset @ ( sk__9 @ X2 @ X0 ) @ X0 )
      | ~ ( in @ X2 @ ( sk__8 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[s1_xboole_0__e1_40__pre_topc__1]) ).

thf(zip_derived_cl344,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( closed_subset @ ( sk__9 @ X1 @ sk_ ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( top_str @ sk_ ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl7,zip_derived_cl70]) ).

thf(zip_derived_cl390,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk_ != sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( closed_subset @ ( sk__9 @ X1 @ sk_ ) @ sk_ )
      | ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl8,zip_derived_cl344]) ).

thf(zip_derived_cl659,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( closed_subset @ ( sk__9 @ X1 @ sk_ ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl390]) ).

thf(zip_derived_cl662,plain,
    ! [X0: $i] :
      ( ~ ( element @ ( sk__8 @ X0 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
      | ( ( sk__3 @ ( sk__8 @ X0 @ sk_ ) )
        = ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) )
      | ( closed_subset @ ( sk__9 @ ( sk__2 @ ( sk__8 @ X0 @ sk_ ) ) @ sk_ ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl659]) ).

thf(zip_derived_cl4608,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl4553,zip_derived_cl662]) ).

thf(zip_derived_cl4263_040,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl6_041,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4617,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl4608,zip_derived_cl4263,zip_derived_cl6]) ).

thf(zip_derived_cl4618,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4617]) ).

thf(zip_derived_cl468_042,plain,
    ! [X0: $i] :
      ( ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ( ( sk__3 @ X0 )
        = ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl467]) ).

thf(zip_derived_cl4643,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4618,zip_derived_cl468]) ).

thf(zip_derived_cl4263_043,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl4651,plain,
    ( ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4643,zip_derived_cl4263]) ).

thf(zip_derived_cl4652,plain,
    ( ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4651]) ).

thf(zip_derived_cl4263_044,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl3_045,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4269,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4263,zip_derived_cl3]) ).

thf(zip_derived_cl8_046,plain,
    top_str @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7_047,plain,
    topological_space @ sk_,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl69,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( subset @ X1 @ X2 )
      | ~ ( in @ X2 @ ( sk__8 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[s1_xboole_0__e1_40__pre_topc__1]) ).

thf(zip_derived_cl343,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( subset @ X0 @ X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( top_str @ sk_ ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl7,zip_derived_cl69]) ).

thf(zip_derived_cl387,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk_ != sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ( subset @ X0 @ X1 )
      | ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl8,zip_derived_cl343]) ).

thf(zip_derived_cl637,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( subset @ X0 @ X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl387]) ).

thf(zip_derived_cl5485,plain,
    ( ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4269,zip_derived_cl637]) ).

thf(zip_derived_cl6_048,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5504,plain,
    ( ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5485,zip_derived_cl6]) ).

thf(zip_derived_cl5505,plain,
    subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5504]) ).

thf(zip_derived_cl5780,plain,
    ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
    = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4652,zip_derived_cl5505]) ).

thf(zip_derived_cl5781,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl4267,zip_derived_cl5780]) ).

thf(zip_derived_cl673_049,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( ( sk__9 @ X1 @ sk_ )
        = X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl393]) ).

thf(zip_derived_cl5833,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5781,zip_derived_cl673]) ).

thf(zip_derived_cl6_050,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5852,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
      = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5833,zip_derived_cl6]) ).

thf(zip_derived_cl5781_051,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl4267,zip_derived_cl5780]) ).

thf(zip_derived_cl659_052,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__8 @ X0 @ sk_ ) )
      | ( closed_subset @ ( sk__9 @ X1 @ sk_ ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl390]) ).

thf(zip_derived_cl5832,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( closed_subset @ ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) @ sk_ )
    | ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5781,zip_derived_cl659]) ).

thf(zip_derived_cl6_053,plain,
    element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5851,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( closed_subset @ ( sk__9 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl5832,zip_derived_cl6]) ).

thf(zip_derived_cl7117,plain,
    ( ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl5852,zip_derived_cl5851]) ).

thf(zip_derived_cl7127,plain,
    closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_,
    inference(simplify,[status(thm)],[zip_derived_cl7117]) ).

thf(zip_derived_cl5505_054,plain,
    subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5504]) ).

thf(zip_derived_cl4263_055,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl9117,plain,
    ~ ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1885,zip_derived_cl7127,zip_derived_cl5505,zip_derived_cl4263]) ).

thf(zip_derived_cl9118,plain,
    ( ( empty @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( element @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl9117]) ).

thf(zip_derived_cl67_056,plain,
    ! [X0: $i] :
      ~ ( empty @ ( powerset @ X0 ) ),
    inference(cnf,[status(esa)],[fc1_subset_1]) ).

thf(zip_derived_cl4263_057,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl2_058,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__2 @ X0 ) @ X0 )
      | ( element @ ( sk__3 @ X0 ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl4268,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( element @ ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl4263,zip_derived_cl2]) ).

thf(zip_derived_cl5780_059,plain,
    ( ( sk__3 @ ( sk__8 @ sk__1 @ sk_ ) )
    = ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4652,zip_derived_cl5505]) ).

thf(zip_derived_cl7670,plain,
    ( ( in @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( sk__8 @ sk__1 @ sk_ ) )
    | ( element @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4268,zip_derived_cl5780]) ).

thf(zip_derived_cl466_060,plain,
    ! [X0: $i] :
      ( ~ ( in @ ( sk__2 @ X0 ) @ X0 )
      | ~ ( subset @ sk__1 @ ( sk__2 @ X0 ) )
      | ~ ( closed_subset @ ( sk__2 @ X0 ) @ sk_ )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl437,zip_derived_cl5]) ).

thf(zip_derived_cl7680,plain,
    ( ( element @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ) )
    | ~ ( subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) )
    | ~ ( closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_ )
    | ~ ( element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl7670,zip_derived_cl466]) ).

thf(zip_derived_cl5505_061,plain,
    subset @ sk__1 @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5504]) ).

thf(zip_derived_cl7127_062,plain,
    closed_subset @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ sk_,
    inference(simplify,[status(thm)],[zip_derived_cl7117]) ).

thf(zip_derived_cl4263_063,plain,
    element @ ( sk__8 @ sk__1 @ sk_ ) @ ( powerset @ ( powerset @ ( the_carrier @ sk_ ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4248]) ).

thf(zip_derived_cl7697,plain,
    element @ ( sk__2 @ ( sk__8 @ sk__1 @ sk_ ) ) @ ( powerset @ ( the_carrier @ sk_ ) ),
    inference(demod,[status(thm)],[zip_derived_cl7680,zip_derived_cl5505,zip_derived_cl7127,zip_derived_cl4263]) ).

thf(zip_derived_cl9129,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl9118,zip_derived_cl67,zip_derived_cl7697]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.x1hAdyyswq true
% 0.11/0.31  % Computer : n006.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Wed Aug 23 14:40:38 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.11/0.31  % Running portfolio for 300 s
% 0.11/0.31  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.31  % Number of cores: 8
% 0.11/0.31  % Python version: Python 3.6.8
% 0.11/0.31  % Running in FO mode
% 0.17/0.60  % Total configuration time : 435
% 0.17/0.60  % Estimated wc time : 1092
% 0.17/0.60  % Estimated cpu time (7 cpus) : 156.0
% 0.17/0.67  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.17/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.17/0.72  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.17/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.17/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.17/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.17/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 16.38/2.92  % Solved by fo/fo6_bce.sh.
% 16.38/2.92  % BCE start: 88
% 16.38/2.92  % BCE eliminated: 45
% 16.38/2.92  % PE start: 43
% 16.38/2.92  logic: eq
% 16.38/2.92  % PE eliminated: 2
% 16.38/2.92  % done 1623 iterations in 2.215s
% 16.38/2.92  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 16.38/2.92  % SZS output start Refutation
% See solution above
% 16.38/2.92  
% 16.38/2.92  
% 16.38/2.92  % Terminating...
% 16.77/3.01  % Runner terminated.
% 16.77/3.03  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------