TSTP Solution File: SEU280+2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU280+2 : 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.fl50i9cRPG true

% Computer : n009.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 19:11:48 EDT 2023

% Result   : Theorem 150.62s 22.43s
% Output   : Refutation 150.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   54
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  268 (  14 unt;  17 typ;   0 def)
%            Number of atoms       :  804 ( 219 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives : 2851 ( 455   ~; 529   |;  12   &;1843   @)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :  434 (   0   ^; 428   !;   6   ?; 434   :)

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

thf(zip_tseitin_3_type,type,
    zip_tseitin_3: $i > $i > $i > $o ).

thf(sk__4_type,type,
    sk__4: $i > $i ).

thf(zip_tseitin_1_type,type,
    zip_tseitin_1: $i > $i > $i > $o ).

thf(zip_tseitin_0_type,type,
    zip_tseitin_0: $i > $i > $i > $o ).

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

thf(zip_tseitin_2_type,type,
    zip_tseitin_2: $i > $i > $i > $o ).

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

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

thf(ordinal_type,type,
    ordinal: $i > $o ).

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

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

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

thf(s1_tarski__e6_22__wellord2__1,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i,D: $i] :
          ( ( ( ordinal @ D )
            & ( B = D )
            & ( ordinal @ C )
            & ( B = C ) )
         => ( C = D ) )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( in @ C @ B )
        <=> ? [D: $i] :
              ( ( in @ D @ A )
              & ( D = C )
              & ( ordinal @ C ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [D: $i,C: $i,B: $i] :
      ( ( ( zip_tseitin_0 @ D @ C @ B )
       => ( C = D ) )
     => ( zip_tseitin_1 @ D @ C @ B ) ) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zf_stmt_1,type,
    zip_tseitin_3: $i > $i > $i > $o ).

thf(zf_stmt_2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( zip_tseitin_3 @ C @ B @ A )
     => ( ( in @ C @ B )
      <=> ? [D: $i] : ( zip_tseitin_2 @ D @ C @ A ) ) ) ).

thf(zf_stmt_3,type,
    zip_tseitin_2: $i > $i > $i > $o ).

thf(zf_stmt_4,axiom,
    ! [D: $i,C: $i,A: $i] :
      ( ( zip_tseitin_2 @ D @ C @ A )
    <=> ( ( ordinal @ C )
        & ( D = C )
        & ( in @ D @ A ) ) ) ).

thf(zf_stmt_5,type,
    zip_tseitin_1: $i > $i > $i > $o ).

thf(zf_stmt_6,type,
    zip_tseitin_0: $i > $i > $i > $o ).

thf(zf_stmt_7,axiom,
    ! [D: $i,C: $i,B: $i] :
      ( ( zip_tseitin_0 @ D @ C @ B )
     => ( ( B = C )
        & ( ordinal @ C )
        & ( B = D )
        & ( ordinal @ D ) ) ) ).

thf(zf_stmt_8,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i,D: $i] : ( zip_tseitin_1 @ D @ C @ B )
     => ? [B: $i] :
        ! [C: $i] : ( zip_tseitin_3 @ C @ B @ A ) ) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X0 @ ( sk__4 @ X1 ) @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl54,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl13]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X0 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl360,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( sk__1 = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_2 @ X0 @ X1 @ X2 )
      | ~ ( in @ X0 @ X2 )
      | ( X0 != X1 )
      | ~ ( ordinal @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( zip_tseitin_2 @ X0 @ X1 @ X2 )
      | ( in @ X1 @ X3 )
      | ~ ( zip_tseitin_3 @ X1 @ X3 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl96,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ordinal @ X1 )
      | ( X2 != X1 )
      | ~ ( in @ X2 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X3 @ X0 )
      | ( in @ X1 @ X3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl11]) ).

thf(zip_derived_cl161,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X1 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X0 @ X2 )
      | ~ ( in @ X1 @ X2 )
      | ~ ( ordinal @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl543,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__1 = sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl360,zip_derived_cl161]) ).

thf(zip_derived_cl6_001,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(s1_xboole_0__e6_22__wellord2,conjecture,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
      ( ( in @ C @ B )
    <=> ( ( in @ C @ A )
        & ( ordinal @ C ) ) ) ).

thf(zf_stmt_9,negated_conjecture,
    ~ ! [A: $i] :
      ? [B: $i] :
      ! [C: $i] :
        ( ( in @ C @ B )
      <=> ( ( in @ C @ A )
          & ( ordinal @ C ) ) ),
    inference('cnf.neg',[status(esa)],[s1_xboole_0__e6_22__wellord2]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl54_002,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl13]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl358,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( sk__1 = sk__2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl1]) ).

thf(zip_derived_cl161_003,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X1 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X0 @ X2 )
      | ~ ( in @ X1 @ X2 )
      | ~ ( ordinal @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl524,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__1 = sk__2 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl358,zip_derived_cl161]) ).

thf(zip_derived_cl537,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ X0 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ~ ( ordinal @ ( sk__9 @ X0 ) )
      | ( sk__1 = sk__2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl524]) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ X0 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl22991,plain,
    ! [X0: $i] :
      ( ( sk__1 = sk__2 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl537,zip_derived_cl24]) ).

thf(zip_derived_cl23138,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__1 = sk__2 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl22991]) ).

thf(zip_derived_cl13_004,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X0 @ ( sk__4 @ X1 ) @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( zip_tseitin_2 @ ( sk_ @ X2 @ X0 ) @ X0 @ X2 )
      | ~ ( zip_tseitin_3 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl51,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl12]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl302,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl8]) ).

thf(zip_derived_cl6_005,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl573,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X1 @ X0 )
        = X0 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl302,zip_derived_cl6]) ).

thf(zip_derived_cl23179,plain,
    ( ( sk__1 = sk__2 )
    | ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
    | ( ( sk_ @ sk__8 @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23138,zip_derived_cl573]) ).

thf(zip_derived_cl1_006,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl28604,plain,
    ( ( ( sk_ @ sk__8 @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( sk__1 = sk__2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl23179,zip_derived_cl1]) ).

thf(zip_derived_cl51_007,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl12]) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X0 @ X1 )
      | ~ ( zip_tseitin_2 @ X0 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl303,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl9]) ).

thf(zip_derived_cl28609,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( sk__1 = sk__2 )
    | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl28604,zip_derived_cl303]) ).

thf(zip_derived_cl23138_008,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__1 = sk__2 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl22991]) ).

thf(zip_derived_cl28639,plain,
    ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
    | ( sk__1 = sk__2 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28609,zip_derived_cl23138]) ).

thf(zip_derived_cl28641,plain,
    ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( sk__1 = sk__2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl28639]) ).

thf(zip_derived_cl1_009,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl28642,plain,
    ( ( sk__1 = sk__2 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28641,zip_derived_cl1]) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i] :
      ( ~ ( ordinal @ ( sk__9 @ X0 ) )
      | ~ ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ~ ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl28664,plain,
    ( ( sk__1 = sk__2 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl28642,zip_derived_cl25]) ).

thf(zip_derived_cl23138_010,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__1 = sk__2 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl22991]) ).

thf(zip_derived_cl28672,plain,
    ( ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( sk__1 = sk__2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28664,zip_derived_cl23138]) ).

thf(zip_derived_cl24_011,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ X0 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl6_012,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl51_013,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl12]) ).

thf(zip_derived_cl7,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ordinal @ X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl301,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl7]) ).

thf(zip_derived_cl327,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( ordinal @ X0 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl301]) ).

thf(zip_derived_cl336,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl327]) ).

thf(zip_derived_cl337,plain,
    ! [X0: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl1_014,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl494,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( sk__1 = sk__2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl337,zip_derived_cl1]) ).

thf(zip_derived_cl28673,plain,
    sk__1 = sk__2,
    inference(clc,[status(thm)],[zip_derived_cl28672,zip_derived_cl494]) ).

thf(zip_derived_cl28704,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 = sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl543,zip_derived_cl28673]) ).

thf(zip_derived_cl13_015,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X0 @ ( sk__4 @ X1 ) @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( X1 != X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl50,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl5]) ).

thf(zip_derived_cl161_016,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X1 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X0 @ X2 )
      | ~ ( in @ X1 @ X2 )
      | ~ ( ordinal @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl163,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl31347,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( in @ X1 @ X0 )
      | ~ ( ordinal @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28704,zip_derived_cl163]) ).

thf(zip_derived_cl360_017,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( sk__1 = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl3]) ).

thf(zip_derived_cl12_018,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( zip_tseitin_2 @ ( sk_ @ X2 @ X0 ) @ X0 @ X2 )
      | ~ ( zip_tseitin_3 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl542,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__1 = sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl360,zip_derived_cl12]) ).

thf(zip_derived_cl28673_019,plain,
    sk__1 = sk__2,
    inference(clc,[status(thm)],[zip_derived_cl28672,zip_derived_cl494]) ).

thf(zip_derived_cl28703,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 = sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl542,zip_derived_cl28673]) ).

thf(zip_derived_cl50_020,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl5]) ).

thf(zip_derived_cl12_021,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( zip_tseitin_2 @ ( sk_ @ X2 @ X0 ) @ X0 @ X2 )
      | ~ ( zip_tseitin_3 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl53,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl12]) ).

thf(zip_derived_cl36427,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28703,zip_derived_cl53]) ).

thf(zip_derived_cl8_022,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl36429,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36427,zip_derived_cl8]) ).

thf(zip_derived_cl23_023,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl54_024,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl13]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ordinal @ X0 )
      | ~ ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl361,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_3 @ X1 @ ( sk__4 @ X0 ) @ X0 )
      | ( ordinal @ sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl4]) ).

thf(zip_derived_cl161_025,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X1 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X0 @ X2 )
      | ~ ( in @ X1 @ X2 )
      | ~ ( ordinal @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl390,plain,
    ! [X0: $i,X1: $i] :
      ( ( ordinal @ sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl361,zip_derived_cl161]) ).

thf(zip_derived_cl401,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ X0 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ~ ( ordinal @ ( sk__9 @ X0 ) )
      | ( ordinal @ sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl390]) ).

thf(zip_derived_cl24_026,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ X0 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl14214,plain,
    ! [X0: $i] :
      ( ( ordinal @ sk__3 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl401,zip_derived_cl24]) ).

thf(zip_derived_cl14354,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( ordinal @ sk__3 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl14214]) ).

thf(zip_derived_cl390_027,plain,
    ! [X0: $i,X1: $i] :
      ( ( ordinal @ sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl361,zip_derived_cl161]) ).

thf(zip_derived_cl14373,plain,
    ( ( ordinal @ sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( ordinal @ sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14354,zip_derived_cl390]) ).

thf(zip_derived_cl14404,plain,
    ( ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ( ordinal @ sk__3 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl14373]) ).

thf(zip_derived_cl337_028,plain,
    ! [X0: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl4_029,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ordinal @ X0 )
      | ~ ( zip_tseitin_0 @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl497,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( ordinal @ sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl337,zip_derived_cl4]) ).

thf(zip_derived_cl14630,plain,
    ( ( ordinal @ sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl14404,zip_derived_cl497]) ).

thf(zip_derived_cl37005,plain,
    ( ( ( sk_ @ ( sk__4 @ sk__8 ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( ordinal @ sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl36429,zip_derived_cl14630]) ).

thf(zip_derived_cl163_030,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl163_031,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl53_032,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl12]) ).

thf(zip_derived_cl8_033,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl72,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl8]) ).

thf(zip_derived_cl163_034,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl176,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl72,zip_derived_cl163]) ).

thf(zip_derived_cl183,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl176]) ).

thf(zip_derived_cl206,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl183]) ).

thf(zip_derived_cl214,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl72_035,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl8]) ).

thf(zip_derived_cl53_036,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl12]) ).

thf(zip_derived_cl9_037,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X0 @ X1 )
      | ~ ( zip_tseitin_2 @ X0 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl73,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl9]) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl72,zip_derived_cl73]) ).

thf(zip_derived_cl91,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl1119,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X1 @ X0 )
        = ( sk_ @ ( sk__4 @ X1 ) @ X0 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl214,zip_derived_cl91]) ).

thf(zip_derived_cl1121,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( ( sk_ @ X1 @ X0 )
        = ( sk_ @ ( sk__4 @ X1 ) @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1119]) ).

thf(zip_derived_cl53_038,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl12]) ).

thf(zip_derived_cl7_039,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ordinal @ X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl71,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl5501,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X1 @ X0 )
        = ( sk_ @ ( sk__4 @ X1 ) @ X0 ) )
      | ~ ( in @ X0 @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1121,zip_derived_cl71]) ).

thf(zip_derived_cl5530,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl5501]) ).

thf(zip_derived_cl5560,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ~ ( in @ X1 @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5530]) ).

thf(zip_derived_cl71_040,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl5574,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl5560,zip_derived_cl71]) ).

thf(zip_derived_cl214_041,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl163_042,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl5574_043,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl5560,zip_derived_cl71]) ).

thf(zip_derived_cl5603,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ~ ( in @ X1 @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl5574]) ).

thf(zip_derived_cl5632,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5603]) ).

thf(zip_derived_cl13_044,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( zip_tseitin_3 @ X0 @ ( sk__4 @ X1 ) @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_8]) ).

thf(zip_derived_cl161_045,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X1 @ X0 )
      | ~ ( zip_tseitin_3 @ X1 @ X0 @ X2 )
      | ~ ( in @ X1 @ X2 )
      | ~ ( ordinal @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl162,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl161]) ).

thf(zip_derived_cl5632_046,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5603]) ).

thf(zip_derived_cl91_047,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ( sk__2 != sk__3 )
      | ( ( sk_ @ X0 @ ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl73_048,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl9]) ).

thf(zip_derived_cl1115,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl91,zip_derived_cl73]) ).

thf(zip_derived_cl1123,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1115]) ).

thf(zip_derived_cl73_049,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl9]) ).

thf(zip_derived_cl7380,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1123,zip_derived_cl73]) ).

thf(zip_derived_cl7462,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ X1 )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5632,zip_derived_cl7380]) ).

thf(zip_derived_cl7485,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ ( sk_ @ X1 @ X0 ) @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7462]) ).

thf(zip_derived_cl71_050,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl7566,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ X1 )
      | ~ ( in @ X0 @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl7485,zip_derived_cl71]) ).

thf(zip_derived_cl7686,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( ordinal @ X1 )
      | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl162,zip_derived_cl7566]) ).

thf(zip_derived_cl163_051,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl10661,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X0 @ X1 ) @ X0 )
      | ~ ( in @ X1 @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( zip_tseitin_1 @ sk__3 @ sk__2 @ sk__1 )
      | ~ ( ordinal @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl7686,zip_derived_cl163]) ).

thf(zip_derived_cl5_052,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X0 @ X1 @ X2 )
      | ( X1 != X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10662,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl10661,zip_derived_cl5]) ).

thf(zip_derived_cl10756,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5632,zip_derived_cl10662]) ).

thf(zip_derived_cl10784,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl10756]) ).

thf(zip_derived_cl163_053,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl11066,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl10784,zip_derived_cl163]) ).

thf(zip_derived_cl11132,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl214,zip_derived_cl11066]) ).

thf(zip_derived_cl11160,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl11132]) ).

thf(zip_derived_cl163_054,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl11334,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl11160,zip_derived_cl163]) ).

thf(zip_derived_cl214_055,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl5632_056,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5603]) ).

thf(zip_derived_cl73_057,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl9]) ).

thf(zip_derived_cl5960,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5632,zip_derived_cl73]) ).

thf(zip_derived_cl5983,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5960]) ).

thf(zip_derived_cl71_058,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl6164,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl5983,zip_derived_cl71]) ).

thf(zip_derived_cl6216,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl214,zip_derived_cl6164]) ).

thf(zip_derived_cl6239,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl6216]) ).

thf(zip_derived_cl163_059,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl6613,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl6239,zip_derived_cl163]) ).

thf(zip_derived_cl71_060,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl6614,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl6613,zip_derived_cl71]) ).

thf(zip_derived_cl11373,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ~ ( in @ X1 @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11334,zip_derived_cl6614]) ).

thf(zip_derived_cl11536,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl11373]) ).

thf(zip_derived_cl163_061,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl11847,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl11536,zip_derived_cl163]) ).

thf(zip_derived_cl71_062,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl11848,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl11847,zip_derived_cl71]) ).

thf(zip_derived_cl11958,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = ( sk_ @ ( sk__4 @ ( sk__4 @ X0 ) ) @ X1 ) )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5574,zip_derived_cl11848]) ).

thf(zip_derived_cl12000,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = ( sk_ @ ( sk__4 @ ( sk__4 @ X0 ) ) @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl11958]) ).

thf(zip_derived_cl214_063,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ ( sk__4 @ X0 ) @ X1 )
        = X1 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl7566_064,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ X1 )
      | ~ ( in @ X0 @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl7485,zip_derived_cl71]) ).

thf(zip_derived_cl5632_065,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ X0 @ X1 )
        = ( sk_ @ ( sk__4 @ X0 ) @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5603]) ).

thf(zip_derived_cl11066_066,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl10784,zip_derived_cl163]) ).

thf(zip_derived_cl11134,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5632,zip_derived_cl11066]) ).

thf(zip_derived_cl11162,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl11134]) ).

thf(zip_derived_cl163_067,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl18943,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ X1 @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl11162,zip_derived_cl163]) ).

thf(zip_derived_cl18993,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( in @ ( sk_ @ X0 @ X1 ) @ X0 )
      | ( in @ ( sk_ @ X0 @ ( sk_ @ X0 @ X1 ) ) @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl7566,zip_derived_cl18943]) ).

thf(zip_derived_cl19045,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ X0 )
      | ~ ( ordinal @ X1 )
      | ( in @ ( sk_ @ X0 @ ( sk_ @ X0 @ X1 ) ) @ X0 )
      | ~ ( in @ ( sk_ @ X0 @ X1 ) @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl18993]) ).

thf(zip_derived_cl10662_068,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ordinal @ X1 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ ( sk_ @ X0 @ X1 ) @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl10661,zip_derived_cl5]) ).

thf(zip_derived_cl19538,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ( in @ ( sk_ @ X0 @ ( sk_ @ X0 @ X1 ) ) @ X0 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl19045,zip_derived_cl10662]) ).

thf(zip_derived_cl19646,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl214,zip_derived_cl19538]) ).

thf(zip_derived_cl19698,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ X1 )
      | ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl19646]) ).

thf(zip_derived_cl163_069,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__2 != sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl161]) ).

thf(zip_derived_cl22635,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl19698,zip_derived_cl163]) ).

thf(zip_derived_cl22708,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 )
      | ( sk__2 != sk__3 )
      | ~ ( ordinal @ X0 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl12000,zip_derived_cl22635]) ).

thf(zip_derived_cl22753,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl22708]) ).

thf(zip_derived_cl71_070,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl7]) ).

thf(zip_derived_cl32834,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ ( sk__4 @ X1 ) ) )
      | ~ ( in @ X0 @ ( sk__4 @ X1 ) )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl22753,zip_derived_cl71]) ).

thf(zip_derived_cl41812,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ( ordinal @ sk__3 )
    | ( sk__2 != sk__3 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl37005,zip_derived_cl32834]) ).

thf(zip_derived_cl11848_071,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ X1 @ ( sk__4 @ ( sk__4 @ X0 ) ) )
      | ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl11847,zip_derived_cl71]) ).

thf(zip_derived_cl45967,plain,
    ( ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__2 != sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl41812,zip_derived_cl11848]) ).

thf(zip_derived_cl23_072,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl543_073,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__1 = sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl360,zip_derived_cl161]) ).

thf(zip_derived_cl556,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ X0 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ~ ( ordinal @ ( sk__9 @ X0 ) )
      | ( sk__1 = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl543]) ).

thf(zip_derived_cl24_074,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ X0 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl24240,plain,
    ! [X0: $i] :
      ( ( sk__1 = sk__3 )
      | ( in @ ( sk__9 @ X0 ) @ ( sk__4 @ sk__8 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl556,zip_derived_cl24]) ).

thf(zip_derived_cl24391,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__1 = sk__3 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl24240]) ).

thf(zip_derived_cl543_075,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__1 = sk__3 )
      | ~ ( ordinal @ X1 )
      | ~ ( in @ X1 @ X0 )
      | ( in @ X1 @ ( sk__4 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl360,zip_derived_cl161]) ).

thf(zip_derived_cl24414,plain,
    ( ( sk__1 = sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( sk__1 = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24391,zip_derived_cl543]) ).

thf(zip_derived_cl24445,plain,
    ( ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ( sk__1 = sk__3 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl24414]) ).

thf(zip_derived_cl337_076,plain,
    ! [X0: $i] :
      ( ( zip_tseitin_0 @ sk__3 @ sk__2 @ sk__1 )
      | ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl3_077,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X0 )
      | ~ ( zip_tseitin_0 @ X0 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl496,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( sk__1 = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl337,zip_derived_cl3]) ).

thf(zip_derived_cl24679,plain,
    ( ( sk__1 = sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl24445,zip_derived_cl496]) ).

thf(zip_derived_cl28673_078,plain,
    sk__1 = sk__2,
    inference(clc,[status(thm)],[zip_derived_cl28672,zip_derived_cl494]) ).

thf(zip_derived_cl29034,plain,
    ( ( sk__2 = sk__3 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl24679,zip_derived_cl28673]) ).

thf(zip_derived_cl45968,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ ( sk__4 @ sk__8 ) ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl45967,zip_derived_cl29034]) ).

thf(zip_derived_cl36429_079,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36427,zip_derived_cl8]) ).

thf(zip_derived_cl45982,plain,
    ( ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( ( sk_ @ ( sk__4 @ sk__8 ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl45968,zip_derived_cl36429]) ).

thf(zip_derived_cl51081,plain,
    ( ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( ( sk_ @ ( sk__4 @ sk__8 ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl31347,zip_derived_cl45982]) ).

thf(zip_derived_cl24_080,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ X0 ) )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl36427_081,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28703,zip_derived_cl53]) ).

thf(zip_derived_cl7_082,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ordinal @ X0 )
      | ~ ( zip_tseitin_2 @ X1 @ X0 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl36428,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( ordinal @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36427,zip_derived_cl7]) ).

thf(zip_derived_cl36564,plain,
    ! [X0: $i] :
      ( ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) )
      | ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl36428]) ).

thf(zip_derived_cl36597,plain,
    ! [X0: $i] : ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl36564]) ).

thf(zip_derived_cl51096,plain,
    ( ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( ( sk_ @ ( sk__4 @ sk__8 ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
      = ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl51081,zip_derived_cl36597]) ).

thf(zip_derived_cl22635_083,plain,
    ! [X0: $i,X1: $i] :
      ( ( in @ ( sk_ @ ( sk__4 @ X1 ) @ X0 ) @ ( sk__4 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( ordinal @ X0 )
      | ( sk__2 != sk__3 ) ),
    inference(clc,[status(thm)],[zip_derived_cl19698,zip_derived_cl163]) ).

thf(zip_derived_cl51309,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( sk__2 != sk__3 )
    | ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl51096,zip_derived_cl22635]) ).

thf(zip_derived_cl36597_084,plain,
    ! [X0: $i] : ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl36564]) ).

thf(zip_derived_cl51351,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( sk__2 != sk__3 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 ) ),
    inference(demod,[status(thm)],[zip_derived_cl51309,zip_derived_cl36597]) ).

thf(zip_derived_cl51352,plain,
    ( ( sk__2 != sk__3 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl51351]) ).

thf(zip_derived_cl24391_085,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__1 = sk__3 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl24240]) ).

thf(zip_derived_cl28673_086,plain,
    sk__1 = sk__2,
    inference(clc,[status(thm)],[zip_derived_cl28672,zip_derived_cl494]) ).

thf(zip_derived_cl28981,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ( sk__2 = sk__3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl24391,zip_derived_cl28673]) ).

thf(zip_derived_cl51520,plain,
    ( ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 ) ),
    inference(clc,[status(thm)],[zip_derived_cl51352,zip_derived_cl28981]) ).

thf(zip_derived_cl23_087,plain,
    ! [X0: $i] :
      ( ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl51521,plain,
    in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ),
    inference(clc,[status(thm)],[zip_derived_cl51520,zip_derived_cl23]) ).

thf(zip_derived_cl36429_088,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( ( sk_ @ X0 @ X1 )
        = X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36427,zip_derived_cl8]) ).

thf(zip_derived_cl51538,plain,
    ( ( sk_ @ sk__8 @ ( sk__9 @ ( sk__4 @ sk__8 ) ) )
    = ( sk__9 @ ( sk__4 @ sk__8 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51521,zip_derived_cl36429]) ).

thf(zip_derived_cl36427_089,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__4 @ X0 ) )
      | ( zip_tseitin_2 @ ( sk_ @ X0 @ X1 ) @ X1 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl28703,zip_derived_cl53]) ).

thf(zip_derived_cl51901,plain,
    ( ( zip_tseitin_2 @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8 )
    | ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl51538,zip_derived_cl36427]) ).

thf(zip_derived_cl51521_090,plain,
    in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ),
    inference(clc,[status(thm)],[zip_derived_cl51520,zip_derived_cl23]) ).

thf(zip_derived_cl51938,plain,
    zip_tseitin_2 @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8,
    inference(demod,[status(thm)],[zip_derived_cl51901,zip_derived_cl51521]) ).

thf(zip_derived_cl9_091,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( in @ X0 @ X1 )
      | ~ ( zip_tseitin_2 @ X0 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl52865,plain,
    in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ sk__8,
    inference('sup-',[status(thm)],[zip_derived_cl51938,zip_derived_cl9]) ).

thf(zip_derived_cl25_092,plain,
    ! [X0: $i] :
      ( ~ ( ordinal @ ( sk__9 @ X0 ) )
      | ~ ( in @ ( sk__9 @ X0 ) @ sk__8 )
      | ~ ( in @ ( sk__9 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_9]) ).

thf(zip_derived_cl52879,plain,
    ( ~ ( in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ) )
    | ~ ( ordinal @ ( sk__9 @ ( sk__4 @ sk__8 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl52865,zip_derived_cl25]) ).

thf(zip_derived_cl51521_093,plain,
    in @ ( sk__9 @ ( sk__4 @ sk__8 ) ) @ ( sk__4 @ sk__8 ),
    inference(clc,[status(thm)],[zip_derived_cl51520,zip_derived_cl23]) ).

thf(zip_derived_cl36597_094,plain,
    ! [X0: $i] : ( ordinal @ ( sk__9 @ ( sk__4 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl36564]) ).

thf(zip_derived_cl52891,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl52879,zip_derived_cl51521,zip_derived_cl36597]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU280+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fl50i9cRPG true
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 12:45:06 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in FO mode
% 0.21/0.71  % Total configuration time : 435
% 0.21/0.71  % Estimated wc time : 1092
% 0.21/0.71  % Estimated cpu time (7 cpus) : 156.0
% 0.99/0.80  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.99/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.99/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.99/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.99/0.81  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.99/0.82  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.99/0.82  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 150.62/22.43  % Solved by fo/fo4.sh.
% 150.62/22.43  % done 6116 iterations in 21.555s
% 150.62/22.43  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 150.62/22.43  % SZS output start Refutation
% See solution above
% 150.62/22.43  
% 150.62/22.43  
% 150.62/22.43  % Terminating...
% 150.62/22.56  % Runner terminated.
% 150.62/22.57  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------