TSTP Solution File: SET723+4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET723+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RPCFULhngB true

% Computer : n022.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 16:15:44 EDT 2023

% Result   : Theorem 152.82s 22.67s
% Output   : Refutation 152.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  172 (  17 unt;  22 typ;   0 def)
%            Number of atoms       :  586 (  76 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 2824 ( 368   ~; 388   |;  27   &;2020   @)
%                                         (   8 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   61 (  61   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   7 con; 0-5 aty)
%            Number of variables   :  397 (   0   ^; 394   !;   3   ?; 397   :)

% Comments : 
%------------------------------------------------------------------------------
thf(member_type,type,
    member: $i > $i > $o ).

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

thf(sk__13_type,type,
    sk__13: $i ).

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

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

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

thf(sk__7_type,type,
    sk__7: $i > $i > $i > $i > $i ).

thf(compose_function_type,type,
    compose_function: $i > $i > $i > $i > $i > $i ).

thf(sk__12_type,type,
    sk__12: $i ).

thf(maps_type,type,
    maps: $i > $i > $i > $o ).

thf(sk__17_type,type,
    sk__17: $i ).

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

thf(injective_type,type,
    injective: $i > $i > $i > $o ).

thf(apply_type,type,
    apply: $i > $i > $i > $o ).

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

thf(equal_maps_type,type,
    equal_maps: $i > $i > $i > $i > $o ).

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

thf(sk__16_type,type,
    sk__16: $i ).

thf(sk__15_type,type,
    sk__15: $i ).

thf(thII14,conjecture,
    ! [F: $i,G: $i,H: $i,A: $i,B: $i,C: $i] :
      ( ( ( maps @ F @ B @ C )
        & ( maps @ G @ A @ B )
        & ( maps @ H @ A @ B )
        & ( injective @ F @ B @ C )
        & ( equal_maps @ ( compose_function @ F @ G @ A @ B @ C ) @ ( compose_function @ F @ H @ A @ B @ C ) @ A @ C ) )
     => ( equal_maps @ G @ H @ A @ B ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [F: $i,G: $i,H: $i,A: $i,B: $i,C: $i] :
        ( ( ( maps @ F @ B @ C )
          & ( maps @ G @ A @ B )
          & ( maps @ H @ A @ B )
          & ( injective @ F @ B @ C )
          & ( equal_maps @ ( compose_function @ F @ G @ A @ B @ C ) @ ( compose_function @ F @ H @ A @ B @ C ) @ A @ C ) )
       => ( equal_maps @ G @ H @ A @ B ) ),
    inference('cnf.neg',[status(esa)],[thII14]) ).

thf(zip_derived_cl40,plain,
    maps @ sk__13 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(maps,axiom,
    ! [F: $i,A: $i,B: $i] :
      ( ( maps @ F @ A @ B )
    <=> ( ! [X: $i,Y1: $i,Y2: $i] :
            ( ( ( member @ Y2 @ B )
              & ( member @ Y1 @ B )
              & ( member @ X @ A ) )
           => ( ( ( apply @ F @ X @ Y2 )
                & ( apply @ F @ X @ Y1 ) )
             => ( Y1 = Y2 ) ) )
        & ! [X: $i] :
            ( ( member @ X @ A )
           => ? [Y: $i] :
                ( ( member @ Y @ B )
                & ( apply @ F @ X @ Y ) ) ) ) ) ).

thf(zf_stmt_1,type,
    zip_tseitin_2: $i > $i > $i > $i > $o ).

thf(zf_stmt_2,axiom,
    ! [X: $i,B: $i,A: $i,F: $i] :
      ( ( zip_tseitin_2 @ X @ B @ A @ F )
    <=> ( ( member @ X @ A )
       => ? [Y: $i] :
            ( ( apply @ F @ X @ Y )
            & ( member @ Y @ B ) ) ) ) ).

thf(zf_stmt_3,type,
    zip_tseitin_1: $i > $i > $i > $i > $o ).

thf(zf_stmt_4,axiom,
    ! [Y2: $i,Y1: $i,X: $i,F: $i] :
      ( ( zip_tseitin_1 @ Y2 @ Y1 @ X @ F )
    <=> ( ( ( apply @ F @ X @ Y1 )
          & ( apply @ F @ X @ Y2 ) )
       => ( Y1 = Y2 ) ) ) ).

thf(zf_stmt_5,type,
    zip_tseitin_0: $i > $i > $i > $i > $i > $o ).

thf(zf_stmt_6,axiom,
    ! [Y2: $i,Y1: $i,X: $i,B: $i,A: $i] :
      ( ( zip_tseitin_0 @ Y2 @ Y1 @ X @ B @ A )
    <=> ( ( member @ X @ A )
        & ( member @ Y1 @ B )
        & ( member @ Y2 @ B ) ) ) ).

thf(zf_stmt_7,axiom,
    ! [F: $i,A: $i,B: $i] :
      ( ( maps @ F @ A @ B )
    <=> ( ! [X: $i] : ( zip_tseitin_2 @ X @ B @ A @ F )
        & ! [X: $i,Y1: $i,Y2: $i] :
            ( ( zip_tseitin_0 @ Y2 @ Y1 @ X @ B @ A )
           => ( zip_tseitin_1 @ Y2 @ Y1 @ X @ F ) ) ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( zip_tseitin_2 @ X0 @ X1 @ X2 @ X3 )
      | ~ ( maps @ X3 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( member @ X0 @ X1 )
      | ( apply @ X2 @ X0 @ ( sk_ @ X2 @ X3 @ X0 ) )
      | ~ ( zip_tseitin_2 @ X0 @ X3 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl61,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( apply @ X0 @ X3 @ ( sk_ @ X0 @ X2 @ X3 ) )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl9]) ).

thf(zip_derived_cl73,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( apply @ sk__13 @ X0 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl61]) ).

thf(zip_derived_cl39,plain,
    maps @ sk__12 @ sk__16 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl61_001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( apply @ X0 @ X3 @ ( sk_ @ X0 @ X2 @ X3 ) )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl9]) ).

thf(zip_derived_cl72,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(zip_derived_cl73_002,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( apply @ sk__13 @ X0 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl61]) ).

thf(zip_derived_cl40_003,plain,
    maps @ sk__13 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( zip_tseitin_0 @ X0 @ X1 @ X2 @ X3 @ X4 )
      | ~ ( member @ X0 @ X3 )
      | ~ ( member @ X1 @ X3 )
      | ~ ( member @ X2 @ X4 ) ),
    inference(cnf,[status(esa)],[zf_stmt_6]) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( zip_tseitin_0 @ X0 @ X1 @ X2 @ X3 @ X4 )
      | ( zip_tseitin_1 @ X0 @ X1 @ X2 @ X5 )
      | ~ ( maps @ X5 @ X4 @ X3 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl56,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X2 @ X0 )
      | ~ ( member @ X3 @ X1 )
      | ~ ( member @ X4 @ X1 )
      | ~ ( maps @ X5 @ X0 @ X1 )
      | ( zip_tseitin_1 @ X4 @ X3 @ X2 @ X5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl13]) ).

thf(zip_derived_cl58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X2 @ X1 @ X0 @ sk__13 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl56]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( apply @ X0 @ X1 @ X2 )
      | ~ ( apply @ X0 @ X1 @ X3 )
      | ( X2 = X3 )
      | ~ ( zip_tseitin_1 @ X3 @ X2 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl68,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X2 @ sk__16 )
      | ( X1 = X2 )
      | ~ ( apply @ sk__13 @ X0 @ X2 )
      | ~ ( apply @ sk__13 @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl58,zip_derived_cl4]) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl68]) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 )
      | ( X1
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl40_004,plain,
    maps @ sk__13 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl12_005,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( zip_tseitin_2 @ X0 @ X1 @ X2 @ X3 )
      | ~ ( maps @ X3 @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( member @ X0 @ X1 )
      | ( member @ ( sk_ @ X2 @ X3 @ X0 ) @ X3 )
      | ~ ( zip_tseitin_2 @ X0 @ X3 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl52,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( member @ ( sk_ @ X0 @ X2 @ X3 ) @ X2 )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl8]) ).

thf(zip_derived_cl54,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl52]) ).

thf(zip_derived_cl409,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( member @ X1 @ sk__16 ) ),
    inference(clc,[status(thm)],[zip_derived_cl93,zip_derived_cl54]) ).

thf(zip_derived_cl72_006,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(zip_derived_cl41,plain,
    maps @ sk__14 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl61_007,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( apply @ X0 @ X3 @ ( sk_ @ X0 @ X2 @ X3 ) )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl9]) ).

thf(zip_derived_cl74,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( apply @ sk__14 @ X0 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl61]) ).

thf(compose_function,axiom,
    ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
      ( ( ( member @ X @ A )
        & ( member @ Z @ C ) )
     => ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
      <=> ? [Y: $i] :
            ( ( apply @ G @ Y @ Z )
            & ( apply @ F @ X @ Y )
            & ( member @ Y @ B ) ) ) ) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ~ ( member @ X0 @ X1 )
      | ~ ( member @ X2 @ X3 )
      | ( apply @ ( compose_function @ X4 @ X5 @ X1 @ X6 @ X3 ) @ X0 @ X2 )
      | ~ ( member @ X7 @ X6 )
      | ~ ( apply @ X5 @ X0 @ X7 )
      | ~ ( apply @ X4 @ X7 @ X2 ) ),
    inference(cnf,[status(esa)],[compose_function]) ).

thf(zip_derived_cl497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ X2 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ X1 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ X3 )
      | ( apply @ ( compose_function @ X2 @ sk__14 @ X5 @ X3 @ X4 ) @ X0 @ X1 )
      | ~ ( member @ X1 @ X4 )
      | ~ ( member @ X0 @ X5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl19]) ).

thf(zip_derived_cl73_008,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( apply @ sk__13 @ X0 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl61]) ).

thf(zip_derived_cl19_009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( ~ ( member @ X0 @ X1 )
      | ~ ( member @ X2 @ X3 )
      | ( apply @ ( compose_function @ X4 @ X5 @ X1 @ X6 @ X3 ) @ X0 @ X2 )
      | ~ ( member @ X7 @ X6 )
      | ~ ( apply @ X5 @ X0 @ X7 )
      | ~ ( apply @ X4 @ X7 @ X2 ) ),
    inference(cnf,[status(esa)],[compose_function]) ).

thf(zip_derived_cl495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ X2 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X1 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X3 )
      | ( apply @ ( compose_function @ X2 @ sk__13 @ X5 @ X3 @ X4 ) @ X0 @ X1 )
      | ~ ( member @ X1 @ X4 )
      | ~ ( member @ X0 @ X5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl19]) ).

thf(zip_derived_cl37,plain,
    equal_maps @ ( compose_function @ sk__12 @ sk__13 @ sk__15 @ sk__16 @ sk__17 ) @ ( compose_function @ sk__12 @ sk__14 @ sk__15 @ sk__16 @ sk__17 ) @ sk__15 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(equal_maps,axiom,
    ! [F: $i,G: $i,A: $i,B: $i] :
      ( ( equal_maps @ F @ G @ A @ B )
    <=> ! [X: $i,Y1: $i,Y2: $i] :
          ( ( ( member @ X @ A )
            & ( member @ Y1 @ B )
            & ( member @ Y2 @ B ) )
         => ( ( ( apply @ F @ X @ Y1 )
              & ( apply @ G @ X @ Y2 ) )
           => ( Y1 = Y2 ) ) ) ) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( apply @ X0 @ X1 @ X2 )
      | ( X3 = X2 )
      | ~ ( member @ X2 @ X4 )
      | ~ ( member @ X1 @ X5 )
      | ~ ( member @ X3 @ X4 )
      | ~ ( apply @ X6 @ X1 @ X3 )
      | ~ ( equal_maps @ X6 @ X0 @ X5 @ X4 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl64,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( apply @ ( compose_function @ sk__12 @ sk__13 @ sk__15 @ sk__16 @ sk__17 ) @ X1 @ X0 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X2 @ sk__17 )
      | ( X0 = X2 )
      | ~ ( apply @ ( compose_function @ sk__12 @ sk__14 @ sk__15 @ sk__16 @ sk__17 ) @ X1 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl20]) ).

thf(zip_derived_cl14324,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ sk__16 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X0 )
      | ~ ( member @ X1 @ sk__15 )
      | ~ ( apply @ ( compose_function @ sk__12 @ sk__14 @ sk__15 @ sk__16 @ sk__17 ) @ X1 @ X2 )
      | ( X0 = X2 )
      | ~ ( member @ X2 @ sk__17 )
      | ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl495,zip_derived_cl64]) ).

thf(zip_derived_cl14386,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X2 @ sk__17 )
      | ( X0 = X2 )
      | ~ ( apply @ ( compose_function @ sk__12 @ sk__14 @ sk__15 @ sk__16 @ sk__17 ) @ X1 @ X2 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X0 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ sk__16 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X1 @ sk__15 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl14324]) ).

thf(zip_derived_cl54_010,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl52]) ).

thf(zip_derived_cl14427,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X0 )
      | ~ ( apply @ ( compose_function @ sk__12 @ sk__14 @ sk__15 @ sk__16 @ sk__17 ) @ X1 @ X2 )
      | ( X0 = X2 )
      | ~ ( member @ X2 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl14386,zip_derived_cl54]) ).

thf(zip_derived_cl15012,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X1 ) @ sk__16 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__14 @ sk__16 @ X1 ) @ X0 )
      | ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 )
      | ( X2 = X0 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X2 )
      | ~ ( member @ X2 @ sk__17 )
      | ~ ( member @ X1 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl497,zip_derived_cl14427]) ).

thf(zip_derived_cl15081,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X2 @ sk__17 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X2 )
      | ( X2 = X0 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__14 @ sk__16 @ X1 ) @ X0 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X1 ) @ sk__16 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X1 @ sk__15 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl15012]) ).

thf(zip_derived_cl41_011,plain,
    maps @ sk__14 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl52_012,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( member @ ( sk_ @ X0 @ X2 @ X3 ) @ X2 )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl8]) ).

thf(zip_derived_cl55,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl52]) ).

thf(zip_derived_cl15283,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__14 @ sk__16 @ X1 ) @ X0 )
      | ( X2 = X0 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X1 ) @ X2 )
      | ~ ( member @ X2 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl15081,zip_derived_cl55]) ).

thf(zip_derived_cl15284,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 )
      | ~ ( member @ X1 @ sk__17 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X1 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) @ sk__17 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl15283]) ).

thf(zip_derived_cl55_013,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl52]) ).

thf(zip_derived_cl15390,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) @ sk__17 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X1 )
      | ~ ( member @ X1 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl15284,zip_derived_cl55]) ).

thf(zip_derived_cl39_014,plain,
    maps @ sk__12 @ sk__16 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl52_015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( maps @ X0 @ X1 @ X2 )
      | ( member @ ( sk_ @ X0 @ X2 @ X3 ) @ X2 )
      | ~ ( member @ X3 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl8]) ).

thf(zip_derived_cl53,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl52]) ).

thf(zip_derived_cl15391,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__17 )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X1 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl15390,zip_derived_cl53]) ).

thf(zip_derived_cl55_016,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl52]) ).

thf(zip_derived_cl15513,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( apply @ sk__12 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ X1 )
      | ~ ( member @ X1 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl15391,zip_derived_cl55]) ).

thf(zip_derived_cl72_017,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(zip_derived_cl15562,plain,
    ! [X0: $i] :
      ( ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) ) @ sk__17 )
      | ( ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) )
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl15513,zip_derived_cl72]) ).

thf(zip_derived_cl53_018,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl52]) ).

thf(zip_derived_cl16132,plain,
    ! [X0: $i] :
      ( ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 )
      | ~ ( member @ X0 @ sk__15 )
      | ( ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) )
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl15562,zip_derived_cl53]) ).

thf(zip_derived_cl54_019,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl52]) ).

thf(zip_derived_cl16133,plain,
    ! [X0: $i] :
      ( ( ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__13 @ sk__16 @ X0 ) )
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference(clc,[status(thm)],[zip_derived_cl16132,zip_derived_cl54]) ).

thf(zip_derived_cl16185,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ sk__12 @ sk__17 @ X0 )
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X1 ) ) )
      | ~ ( member @ X0 @ sk__16 )
      | ~ ( apply @ sk__13 @ X1 @ X0 )
      | ~ ( member @ X1 @ sk__15 )
      | ~ ( member @ X1 @ sk__15 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl409,zip_derived_cl16133]) ).

thf(zip_derived_cl16191,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__15 )
      | ~ ( apply @ sk__13 @ X1 @ X0 )
      | ~ ( member @ X0 @ sk__16 )
      | ( ( sk_ @ sk__12 @ sk__17 @ X0 )
        = ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X1 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl16185]) ).

thf(zip_derived_cl72_020,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(zip_derived_cl38,plain,
    injective @ sk__12 @ sk__16 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl72_021,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(zip_derived_cl39_022,plain,
    maps @ sk__12 @ sk__16 @ sk__17,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl56_023,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X2 @ X0 )
      | ~ ( member @ X3 @ X1 )
      | ~ ( member @ X4 @ X1 )
      | ~ ( maps @ X5 @ X0 @ X1 )
      | ( zip_tseitin_1 @ X4 @ X3 @ X2 @ X5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl13]) ).

thf(zip_derived_cl57,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X2 @ X1 @ X0 @ sk__12 )
      | ~ ( member @ X2 @ sk__17 )
      | ~ ( member @ X1 @ sk__17 )
      | ~ ( member @ X0 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl56]) ).

thf(zip_derived_cl4_024,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( apply @ X0 @ X1 @ X2 )
      | ~ ( apply @ X0 @ X1 @ X3 )
      | ( X2 = X3 )
      | ~ ( zip_tseitin_1 @ X3 @ X2 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl65,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( member @ X1 @ sk__17 )
      | ~ ( member @ X2 @ sk__17 )
      | ( X1 = X2 )
      | ~ ( apply @ sk__12 @ X0 @ X2 )
      | ~ ( apply @ sk__12 @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl4]) ).

thf(zip_derived_cl77,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( apply @ sk__12 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 )
      | ~ ( member @ X1 @ sk__17 )
      | ~ ( member @ X0 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl65]) ).

thf(zip_derived_cl78,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__17 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( apply @ sk__12 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl53_025,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl52]) ).

thf(zip_derived_cl312,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( apply @ sk__12 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ X1 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl78,zip_derived_cl53]) ).

thf(zip_derived_cl312_026,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( apply @ sk__12 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ X1 @ sk__17 ) ),
    inference(clc,[status(thm)],[zip_derived_cl78,zip_derived_cl53]) ).

thf(zip_derived_cl72_027,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( apply @ sk__12 @ X0 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl61]) ).

thf(injective,axiom,
    ! [F: $i,A: $i,B: $i] :
      ( ( injective @ F @ A @ B )
    <=> ! [X1: $i,X2: $i,Y: $i] :
          ( ( ( member @ X1 @ A )
            & ( member @ X2 @ A )
            & ( member @ Y @ B ) )
         => ( ( ( apply @ F @ X1 @ Y )
              & ( apply @ F @ X2 @ Y ) )
           => ( X1 = X2 ) ) ) ) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( apply @ X0 @ X1 @ X2 )
      | ~ ( apply @ X0 @ X3 @ X2 )
      | ~ ( member @ X2 @ X4 )
      | ~ ( member @ X1 @ X5 )
      | ~ ( member @ X3 @ X5 )
      | ( X1 = X3 )
      | ~ ( injective @ X0 @ X5 @ X4 ) ),
    inference(cnf,[status(esa)],[injective]) ).

thf(zip_derived_cl75,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( injective @ sk__12 @ X2 @ X1 )
      | ( X0 = X3 )
      | ~ ( member @ X3 @ X2 )
      | ~ ( member @ X0 @ X2 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ X1 )
      | ~ ( apply @ sk__12 @ X3 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl27]) ).

thf(zip_derived_cl324,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( apply @ sk__12 @ X2 @ X0 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X1 ) @ X3 )
      | ~ ( member @ X1 @ X4 )
      | ~ ( member @ X2 @ X4 )
      | ( X1 = X2 )
      | ~ ( injective @ sk__12 @ X4 @ X3 )
      | ~ ( member @ X1 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl312,zip_derived_cl75]) ).

thf(zip_derived_cl345,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( injective @ sk__12 @ X4 @ X3 )
      | ( X1 = X2 )
      | ~ ( member @ X2 @ X4 )
      | ~ ( member @ X1 @ X4 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X1 ) @ X3 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ X2 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl324]) ).

thf(zip_derived_cl404,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ X2 @ X0 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( apply @ sk__12 @ X4 @ X3 )
      | ~ ( member @ X3 @ sk__17 )
      | ~ ( apply @ sk__12 @ X2 @ X3 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( member @ X2 @ X5 )
      | ~ ( member @ X4 @ X5 )
      | ( X2 = X4 )
      | ~ ( injective @ sk__12 @ X5 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl312,zip_derived_cl345]) ).

thf(zip_derived_cl407,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( injective @ sk__12 @ X5 @ X1 )
      | ( X2 = X4 )
      | ~ ( member @ X4 @ X5 )
      | ~ ( member @ X2 @ X5 )
      | ~ ( apply @ sk__12 @ X2 @ X3 )
      | ~ ( member @ X3 @ sk__17 )
      | ~ ( apply @ sk__12 @ X4 @ X3 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( apply @ sk__12 @ X2 @ X0 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X0 @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl404]) ).

thf(zip_derived_cl1276,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X3 @ X2 )
      | ~ ( member @ X2 @ sk__17 )
      | ~ ( apply @ sk__12 @ X1 @ X2 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X3 @ sk__16 )
      | ( X1 = X3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl407]) ).

thf(zip_derived_cl1277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X1 = X3 )
      | ~ ( member @ X3 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ X2 )
      | ~ ( member @ X2 @ sk__17 )
      | ~ ( apply @ sk__12 @ X3 @ X2 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X0 @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1276]) ).

thf(zip_derived_cl1292,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X0 @ sk__17 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X2 @ X0 )
      | ~ ( member @ X0 @ sk__17 )
      | ~ ( member @ X2 @ sk__16 )
      | ( X1 = X2 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl1277]) ).

thf(zip_derived_cl1294,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( apply @ sk__12 @ X2 @ X0 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ X0 )
      | ~ ( member @ X0 @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1292]) ).

thf(zip_derived_cl1308,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 )
      | ~ ( apply @ sk__12 @ X1 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X0 @ sk__16 )
      | ( X1 = X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl1294]) ).

thf(zip_derived_cl1312,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = X0 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 )
      | ~ ( member @ X0 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1308]) ).

thf(zip_derived_cl53_028,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ( member @ ( sk_ @ sk__12 @ sk__17 @ X0 ) @ sk__17 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl52]) ).

thf(zip_derived_cl1314,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__16 )
      | ~ ( apply @ sk__12 @ X1 @ ( sk_ @ sk__12 @ sk__17 @ X0 ) )
      | ~ ( member @ X1 @ sk__16 )
      | ( X1 = X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1312,zip_derived_cl53]) ).

thf(zip_derived_cl16388,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( apply @ sk__12 @ X2 @ ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__15 )
      | ( X2 = X1 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( member @ X1 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16191,zip_derived_cl1314]) ).

thf(zip_derived_cl16524,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X2 @ sk__16 )
      | ( X2 = X1 )
      | ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__12 @ X2 @ ( sk_ @ sk__12 @ sk__17 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl16388]) ).

thf(zip_derived_cl16893,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__15 )
      | ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = X1 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl16524]) ).

thf(zip_derived_cl16914,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = X1 )
      | ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl16893]) ).

thf(zip_derived_cl55_029,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl52]) ).

thf(zip_derived_cl17135,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__16 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__15 )
      | ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl16914,zip_derived_cl55]) ).

thf(zip_derived_cl17348,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl17135]) ).

thf(zip_derived_cl17351,plain,
    ! [X0: $i] :
      ( ~ ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 )
      | ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl17348]) ).

thf(zip_derived_cl54_030,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__13 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl52]) ).

thf(zip_derived_cl17839,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( ( sk_ @ sk__14 @ sk__16 @ X0 )
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl17351,zip_derived_cl54]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( member @ ( sk__6 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( member @ ( sk__7 @ X3 @ X2 @ X1 @ X0 ) @ X3 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl21,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( apply @ X0 @ ( sk__6 @ X3 @ X2 @ X1 @ X0 ) @ ( sk__7 @ X3 @ X2 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl409_031,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__13 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__13 @ sk__16 @ X0 ) )
      | ~ ( member @ X1 @ sk__16 ) ),
    inference(clc,[status(thm)],[zip_derived_cl93,zip_derived_cl54]) ).

thf(zip_derived_cl686,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( equal_maps @ sk__13 @ X0 @ X1 @ X2 )
      | ~ ( member @ ( sk__7 @ X2 @ X1 @ X0 @ sk__13 ) @ sk__16 )
      | ( ( sk__7 @ X2 @ X1 @ X0 @ sk__13 )
        = ( sk_ @ sk__13 @ sk__16 @ ( sk__6 @ X2 @ X1 @ X0 @ sk__13 ) ) )
      | ~ ( member @ ( sk__6 @ X2 @ X1 @ X0 @ sk__13 ) @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl409]) ).

thf(zip_derived_cl10931,plain,
    ! [X0: $i,X1: $i] :
      ( ( equal_maps @ sk__13 @ X0 @ X1 @ sk__16 )
      | ~ ( member @ ( sk__6 @ sk__16 @ X1 @ X0 @ sk__13 ) @ sk__15 )
      | ( ( sk__7 @ sk__16 @ X1 @ X0 @ sk__13 )
        = ( sk_ @ sk__13 @ sk__16 @ ( sk__6 @ sk__16 @ X1 @ X0 @ sk__13 ) ) )
      | ( equal_maps @ sk__13 @ X0 @ X1 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl686]) ).

thf(zip_derived_cl10935,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk__7 @ sk__16 @ X1 @ X0 @ sk__13 )
        = ( sk_ @ sk__13 @ sk__16 @ ( sk__6 @ sk__16 @ X1 @ X0 @ sk__13 ) ) )
      | ~ ( member @ ( sk__6 @ sk__16 @ X1 @ X0 @ sk__13 ) @ sk__15 )
      | ( equal_maps @ sk__13 @ X0 @ X1 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl10931]) ).

thf(zip_derived_cl10938,plain,
    ! [X0: $i] :
      ( ( equal_maps @ sk__13 @ X0 @ sk__15 @ sk__16 )
      | ( equal_maps @ sk__13 @ X0 @ sk__15 @ sk__16 )
      | ( ( sk__7 @ sk__16 @ sk__15 @ X0 @ sk__13 )
        = ( sk_ @ sk__13 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ X0 @ sk__13 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl10935]) ).

thf(zip_derived_cl10942,plain,
    ! [X0: $i] :
      ( ( ( sk__7 @ sk__16 @ sk__15 @ X0 @ sk__13 )
        = ( sk_ @ sk__13 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ X0 @ sk__13 ) ) )
      | ( equal_maps @ sk__13 @ X0 @ sk__15 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl10938]) ).

thf(zip_derived_cl17975,plain,
    ! [X0: $i] :
      ( ( ( sk__7 @ sk__16 @ sk__15 @ X0 @ sk__13 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ X0 @ sk__13 ) ) )
      | ~ ( member @ ( sk__6 @ sk__16 @ sk__15 @ X0 @ sk__13 ) @ sk__15 )
      | ( equal_maps @ sk__13 @ X0 @ sk__15 @ sk__16 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl17839,zip_derived_cl10942]) ).

thf(zip_derived_cl23_032,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( member @ ( sk__6 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl41674,plain,
    ! [X0: $i] :
      ( ( equal_maps @ sk__13 @ X0 @ sk__15 @ sk__16 )
      | ( ( sk__7 @ sk__16 @ sk__15 @ X0 @ sk__13 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ X0 @ sk__13 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl17975,zip_derived_cl23]) ).

thf(zip_derived_cl23_033,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( member @ ( sk__6 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl24,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( member @ ( sk__8 @ X3 @ X2 @ X1 @ X0 ) @ X3 ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( apply @ X1 @ ( sk__6 @ X3 @ X2 @ X1 @ X0 ) @ ( sk__8 @ X3 @ X2 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl74_034,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( apply @ sk__14 @ X0 @ ( sk_ @ sk__14 @ sk__16 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl61]) ).

thf(zip_derived_cl41_035,plain,
    maps @ sk__14 @ sk__15 @ sk__16,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl56_036,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( member @ X2 @ X0 )
      | ~ ( member @ X3 @ X1 )
      | ~ ( member @ X4 @ X1 )
      | ~ ( maps @ X5 @ X0 @ X1 )
      | ( zip_tseitin_1 @ X4 @ X3 @ X2 @ X5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl13]) ).

thf(zip_derived_cl59,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_1 @ X2 @ X1 @ X0 @ sk__14 )
      | ~ ( member @ X2 @ sk__16 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl56]) ).

thf(zip_derived_cl4_037,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( apply @ X0 @ X1 @ X2 )
      | ~ ( apply @ X0 @ X1 @ X3 )
      | ( X2 = X3 )
      | ~ ( zip_tseitin_1 @ X3 @ X2 @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl69,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X2 @ sk__16 )
      | ( X1 = X2 )
      | ~ ( apply @ sk__14 @ X0 @ X2 )
      | ~ ( apply @ sk__14 @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl59,zip_derived_cl4]) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__14 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__14 @ sk__16 @ X0 ) )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 )
      | ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl69]) ).

thf(zip_derived_cl97,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ sk__16 )
      | ~ ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 )
      | ( X1
        = ( sk_ @ sk__14 @ sk__16 @ X0 ) )
      | ~ ( apply @ sk__14 @ X0 @ X1 )
      | ~ ( member @ X0 @ sk__15 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl55_038,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ( member @ ( sk_ @ sk__14 @ sk__16 @ X0 ) @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl52]) ).

thf(zip_derived_cl449,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__15 )
      | ~ ( apply @ sk__14 @ X0 @ X1 )
      | ( X1
        = ( sk_ @ sk__14 @ sk__16 @ X0 ) )
      | ~ ( member @ X1 @ sk__16 ) ),
    inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl55]) ).

thf(zip_derived_cl868,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( equal_maps @ X0 @ sk__14 @ X1 @ X2 )
      | ~ ( member @ ( sk__8 @ X2 @ X1 @ sk__14 @ X0 ) @ sk__16 )
      | ( ( sk__8 @ X2 @ X1 @ sk__14 @ X0 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ X2 @ X1 @ sk__14 @ X0 ) ) )
      | ~ ( member @ ( sk__6 @ X2 @ X1 @ sk__14 @ X0 ) @ sk__15 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl449]) ).

thf(zip_derived_cl12872,plain,
    ! [X0: $i,X1: $i] :
      ( ( equal_maps @ X0 @ sk__14 @ X1 @ sk__16 )
      | ~ ( member @ ( sk__6 @ sk__16 @ X1 @ sk__14 @ X0 ) @ sk__15 )
      | ( ( sk__8 @ sk__16 @ X1 @ sk__14 @ X0 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ X1 @ sk__14 @ X0 ) ) )
      | ( equal_maps @ X0 @ sk__14 @ X1 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl868]) ).

thf(zip_derived_cl12876,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( sk__8 @ sk__16 @ X1 @ sk__14 @ X0 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ X1 @ sk__14 @ X0 ) ) )
      | ~ ( member @ ( sk__6 @ sk__16 @ X1 @ sk__14 @ X0 ) @ sk__15 )
      | ( equal_maps @ X0 @ sk__14 @ X1 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl12872]) ).

thf(zip_derived_cl12879,plain,
    ! [X0: $i] :
      ( ( equal_maps @ X0 @ sk__14 @ sk__15 @ sk__16 )
      | ( equal_maps @ X0 @ sk__14 @ sk__15 @ sk__16 )
      | ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ X0 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ sk__14 @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl12876]) ).

thf(zip_derived_cl12883,plain,
    ! [X0: $i] :
      ( ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ X0 )
        = ( sk_ @ sk__14 @ sk__16 @ ( sk__6 @ sk__16 @ sk__15 @ sk__14 @ X0 ) ) )
      | ( equal_maps @ X0 @ sk__14 @ sk__15 @ sk__16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl12879]) ).

thf(zip_derived_cl41779,plain,
    ( ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 )
      = ( sk__7 @ sk__16 @ sk__15 @ sk__14 @ sk__13 ) )
    | ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 )
    | ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl41674,zip_derived_cl12883]) ).

thf(zip_derived_cl42,plain,
    ~ ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl42_039,plain,
    ~ ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl41804,plain,
    ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 )
    = ( sk__7 @ sk__16 @ sk__15 @ sk__14 @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl41779,zip_derived_cl42,zip_derived_cl42]) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( equal_maps @ X0 @ X1 @ X2 @ X3 )
      | ( ( sk__7 @ X3 @ X2 @ X1 @ X0 )
       != ( sk__8 @ X3 @ X2 @ X1 @ X0 ) ) ),
    inference(cnf,[status(esa)],[equal_maps]) ).

thf(zip_derived_cl41807,plain,
    ( ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 )
     != ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 ) )
    | ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41804,zip_derived_cl25]) ).

thf(zip_derived_cl42_040,plain,
    ~ ( equal_maps @ sk__13 @ sk__14 @ sk__15 @ sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl41816,plain,
    ( ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 )
   != ( sk__8 @ sk__16 @ sk__15 @ sk__14 @ sk__13 ) ),
    inference(demod,[status(thm)],[zip_derived_cl41807,zip_derived_cl42]) ).

thf(zip_derived_cl41817,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl41816]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET723+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RPCFULhngB true
% 0.18/0.35  % Computer : n022.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Sat Aug 26 13:38:25 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 0.18/0.35  % Running portfolio for 300 s
% 0.18/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.35  % Number of cores: 8
% 0.18/0.35  % Python version: Python 3.6.8
% 0.18/0.35  % Running in FO mode
% 0.21/0.63  % Total configuration time : 435
% 0.21/0.63  % Estimated wc time : 1092
% 0.21/0.63  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 1.18/0.73  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.18/0.74  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.18/0.74  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 1.18/0.74  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.18/0.74  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.18/0.77  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 152.82/22.67  % Solved by fo/fo4.sh.
% 152.82/22.67  % done 2860 iterations in 21.848s
% 152.82/22.67  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 152.82/22.67  % SZS output start Refutation
% See solution above
% 152.82/22.68  
% 152.82/22.68  
% 152.82/22.68  % Terminating...
% 153.36/22.79  % Runner terminated.
% 153.36/22.80  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------