TSTP Solution File: ITP015+2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Gpo0SdMHWD 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 05:21:14 EDT 2023

% Result   : Theorem 234.99s 34.24s
% Output   : Refutation 234.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   45
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  257 (  69 unt;  29 typ;   0 def)
%            Number of atoms       :  708 ( 166 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 3175 ( 367   ~; 418   |;   8   &;2328   @)
%                                         (   8 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  26 usr;  14 con; 0-3 aty)
%            Number of variables   :  286 (   0   ^; 286   !;   0   ?; 286   :)

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

thf(bool_type,type,
    bool: $i ).

thf(ty_2Einteger_2Eint_type,type,
    ty_2Einteger_2Eint: $i ).

thf(c_2Ebool_2ET_type,type,
    c_2Ebool_2ET: $i ).

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

thf(c_2Ewords_2Eword__2comp_type,type,
    c_2Ewords_2Eword__2comp: $i > $i ).

thf(c_2Ewords_2En2w_type,type,
    c_2Ewords_2En2w: $i > $i ).

thf(c_2Einteger__word_2Ei2w_type,type,
    c_2Einteger__word_2Ei2w: $i > $i ).

thf(mem_type,type,
    mem: $i > $i > $o ).

thf(c_2Ebool_2E_7E_type,type,
    c_2Ebool_2E_7E: $i ).

thf(c_2Einteger_2Eint__lt_type,type,
    c_2Einteger_2Eint__lt: $i ).

thf(ne_type,type,
    ne: $i > $o ).

thf(ty_2Efcp_2Ecart_type,type,
    ty_2Efcp_2Ecart: $i > $i > $i ).

thf(c_2Ebool_2ECOND_type,type,
    c_2Ebool_2ECOND: $i > $i ).

thf(ap_type,type,
    ap: $i > $i > $i ).

thf(c_2Einteger_2ENum_type,type,
    c_2Einteger_2ENum: $i ).

thf(c_2Einteger_2Eint__of__num_type,type,
    c_2Einteger_2Eint__of__num: $i ).

thf(zip_tseitin_5_type,type,
    zip_tseitin_5: $i > $i > $o ).

thf(c_2Eprim__rec_2E_3C_type,type,
    c_2Eprim__rec_2E_3C: $i ).

thf(c_2Einteger_2Eint__neg_type,type,
    c_2Einteger_2Eint__neg: $i ).

thf(ty_2Enum_2Enum_type,type,
    ty_2Enum_2Enum: $i ).

thf(p_type,type,
    p: $i > $o ).

thf(c_2Enum_2E0_type,type,
    c_2Enum_2E0: $i ).

thf(c_2Ebool_2EF_type,type,
    c_2Ebool_2EF: $i ).

thf(arr_type,type,
    arr: $i > $i > $i ).

thf(zip_tseitin_4_type,type,
    zip_tseitin_4: $i > $i > $i > $o ).

thf(mem_c_2Einteger_2Eint__of__num,axiom,
    mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ) ).

thf(zip_derived_cl30,plain,
    mem @ c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__of__num]) ).

thf(ap_tp,axiom,
    ! [A: $i,B: $i,F: $i] :
      ( ( mem @ F @ ( arr @ A @ B ) )
     => ! [X: $i] :
          ( ( mem @ X @ A )
         => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl696,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).

thf(mem_c_2Einteger_2Eint__lt,axiom,
    mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).

thf(zip_derived_cl31,plain,
    mem @ c_2Einteger_2Eint__lt @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__lt]) ).

thf(zip_derived_cl3_001,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl762,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ ( arr @ ty_2Einteger_2Eint @ bool ) )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl3]) ).

thf(zip_derived_cl3_002,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl1139,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ X1 ) @ bool )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl762,zip_derived_cl3]) ).

thf(ne_ty_2Efcp_2Ecart,axiom,
    ! [A0: $i] :
      ( ( ne @ A0 )
     => ! [A1: $i] :
          ( ( ne @ A1 )
         => ( ne @ ( ty_2Efcp_2Ecart @ A0 @ A1 ) ) ) ) ).

thf(zip_derived_cl33,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ne @ X0 )
      | ( ne @ ( ty_2Efcp_2Ecart @ X1 @ X0 ) )
      | ~ ( ne @ X1 ) ),
    inference(cnf,[status(esa)],[ne_ty_2Efcp_2Ecart]) ).

thf(mem_c_2Ewords_2En2w,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).

thf(zip_derived_cl48,plain,
    ! [X0: $i] :
      ( ( mem @ ( c_2Ewords_2En2w @ X0 ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) )
      | ~ ( ne @ X0 ) ),
    inference(cnf,[status(esa)],[mem_c_2Ewords_2En2w]) ).

thf(zip_derived_cl3_003,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl896,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ne @ X0 )
      | ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ X1 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl3]) ).

thf(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Ewords_2EWORD__NEG__0]) ).

thf(conj_thm_2Einteger_2EINT__NEG__0,axiom,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ).

thf(zip_derived_cl80,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

thf(conj_thm_2Einteger_2ENUM__OF__INT,axiom,
    ! [V0n: $i] :
      ( ( mem @ V0n @ ty_2Enum_2Enum )
     => ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) )
        = V0n ) ) ).

thf(zip_derived_cl89,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
        = X0 )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2ENUM__OF__INT]) ).

thf(ax_thm_2Einteger__word_2Ei2w__def,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ! [V0i: $i] :
          ( ( mem @ V0i @ ty_2Einteger_2Eint )
         => ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ V0i )
            = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ V0i ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ V0i ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ V0i ) ) ) ) ) ) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ X0 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ X0 ) ) ) )
      | ~ ( ne @ X1 ) ),
    inference(cnf,[status(esa)],[ax_thm_2Einteger__word_2Ei2w__def]) ).

thf(zip_derived_cl1031,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ X0 ) ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ~ ( ne @ X1 )
      | ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint ) ),
    inference('sup+',[status(thm)],[zip_derived_cl89,zip_derived_cl90]) ).

thf(zip_derived_cl696_004,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).

thf(zip_derived_cl6186,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ne @ X1 )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X1 ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X1 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X1 ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X1 ) @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1031,zip_derived_cl696]) ).

thf(zip_derived_cl6187,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
      | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
      | ~ ( ne @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl80,zip_derived_cl6186]) ).

thf(mem_c_2Enum_2E0,axiom,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ).

thf(zip_derived_cl47,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl6189,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
      | ~ ( ne @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6187,zip_derived_cl47]) ).

thf(zip_derived_cl89_005,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
        = X0 )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2ENUM__OF__INT]) ).

thf(mem_c_2Ebool_2EF,axiom,
    mem @ c_2Ebool_2EF @ bool ).

thf(zip_derived_cl16,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl47_006,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl696_007,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl3]) ).

thf(mem_c_2Einteger_2ENum,axiom,
    mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ) ).

thf(zip_derived_cl29,plain,
    mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2ENum]) ).

thf(zip_derived_cl3_008,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl697,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2ENum @ X0 ) @ ty_2Enum_2Enum )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl3]) ).

thf(mem_c_2Ebool_2E_7E,axiom,
    mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).

thf(zip_derived_cl36,plain,
    mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
    inference(cnf,[status(esa)],[mem_c_2Ebool_2E_7E]) ).

thf(zip_derived_cl3_009,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl698,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(zip_derived_cl16_010,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(boolext,axiom,
    ! [Q: $i] :
      ( ( mem @ Q @ bool )
     => ! [R: $i] :
          ( ( mem @ R @ bool )
         => ( ( ( p @ Q )
            <=> ( p @ R ) )
           => ( Q = R ) ) ) ) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( X1 = X0 )
      | ( p @ X1 )
      | ( p @ X0 )
      | ~ ( mem @ X1 @ bool ) ),
    inference(cnf,[status(esa)],[boolext]) ).

thf(zip_derived_cl703,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ c_2Ebool_2EF )
      | ( p @ X0 )
      | ( X0 = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl5]) ).

thf(ax_false_p,axiom,
    ~ ( p @ c_2Ebool_2EF ) ).

thf(zip_derived_cl17,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl707,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ X0 )
      | ( X0 = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl703,zip_derived_cl17]) ).

thf(zip_derived_cl722,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).

thf(zip_derived_cl698_011,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(conj_thm_2Einteger_2EINT__LT__CALCULATE,axiom,
    ! [V0n: $i] :
      ( ( mem @ V0n @ ty_2Enum_2Enum )
     => ! [V1m: $i] :
          ( ( mem @ V1m @ ty_2Enum_2Enum )
         => ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) )
            <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V0n ) @ V1m ) ) )
            & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) ) )
            <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1m ) @ V0n ) ) )
            & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) )
            <=> ( ( V0n != c_2Enum_2E0 )
                | ( V1m != c_2Enum_2E0 ) ) )
            & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ V0n ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ V1m ) ) ) )
            <=> $false ) ) ) ) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( X1 = c_2Enum_2E0 )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).

thf(zip_derived_cl80_012,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

thf(zip_derived_cl86,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).

thf(zip_derived_cl971,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl86]) ).

thf(zip_derived_cl47_013,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl973,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl971,zip_derived_cl47]) ).

thf(zip_derived_cl1009,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( X0 = c_2Enum_2E0 )
      | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl973]) ).

thf(zip_derived_cl47_014,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl1012,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( X0 = c_2Enum_2E0 )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(demod,[status(thm)],[zip_derived_cl1009,zip_derived_cl47]) ).

thf(zip_derived_cl1013,plain,
    ! [X0: $i] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ( X0 = c_2Enum_2E0 )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1012]) ).

thf(mem_c_2Eprim__rec_2E_3C,axiom,
    mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).

thf(zip_derived_cl35,plain,
    mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ),
    inference(cnf,[status(esa)],[mem_c_2Eprim__rec_2E_3C]) ).

thf(zip_derived_cl3_015,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl768,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ ( arr @ ty_2Enum_2Enum @ bool ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl3_016,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( mem @ ( ap @ X2 @ X0 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X1 @ X3 ) ) ),
    inference(cnf,[status(esa)],[ap_tp]) ).

thf(zip_derived_cl1150,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( mem @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) @ bool )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl768,zip_derived_cl3]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( X1 = X0 )
      | ~ ( p @ X1 )
      | ~ ( p @ X0 )
      | ~ ( mem @ X1 @ bool ) ),
    inference(cnf,[status(esa)],[boolext]) ).

thf(zip_derived_cl1422,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum )
      | ~ ( mem @ X2 @ bool )
      | ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X1 ) @ X0 ) )
      | ~ ( p @ X2 )
      | ( X2
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X1 ) @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1150,zip_derived_cl4]) ).

thf(zip_derived_cl5798,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( X0 = c_2Enum_2E0 )
      | ( X1
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ~ ( p @ X1 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1013,zip_derived_cl1422]) ).

thf(zip_derived_cl47_017,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl5802,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( X0 = c_2Enum_2E0 )
      | ( X1
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ~ ( p @ X1 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(demod,[status(thm)],[zip_derived_cl5798,zip_derived_cl47]) ).

thf(zip_derived_cl5803,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X1 @ bool )
      | ~ ( p @ X1 )
      | ( X1
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) )
      | ( X0 = c_2Enum_2E0 )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5802]) ).

thf(zip_derived_cl5815,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum )
      | ( X1 = c_2Enum_2E0 )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
      | ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl5803]) ).

thf(zip_derived_cl5834,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
      | ( X1 = c_2Enum_2E0 )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl722,zip_derived_cl5815]) ).

thf(zip_derived_cl5856,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X1 @ ty_2Enum_2Enum )
      | ( X1 = c_2Enum_2E0 )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X1 ) )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5834]) ).

thf(zip_derived_cl5880,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( ( ap @ c_2Ebool_2E_7E @ X1 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X1 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X1 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ X0 ) ) )
      | ( ( ap @ c_2Einteger_2ENum @ X0 )
        = c_2Enum_2E0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl697,zip_derived_cl5856]) ).

thf(zip_derived_cl7340,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) )
        = c_2Enum_2E0 )
      | ( ( ap @ c_2Ebool_2E_7E @ X1 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
      | ~ ( mem @ X1 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X1 )
        = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl696,zip_derived_cl5880]) ).

thf(zip_derived_cl8227,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
      | ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = c_2Enum_2E0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl7340]) ).

thf(zip_derived_cl8249,plain,
    ( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
      = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
      = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl8227]) ).

thf(mem_c_2Ebool_2ET,axiom,
    mem @ c_2Ebool_2ET @ bool ).

thf(zip_derived_cl14,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl698_018,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(zip_derived_cl14_019,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl4_020,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( X1 = X0 )
      | ~ ( p @ X1 )
      | ~ ( p @ X0 )
      | ~ ( mem @ X1 @ bool ) ),
    inference(cnf,[status(esa)],[boolext]) ).

thf(zip_derived_cl681,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( p @ c_2Ebool_2ET )
      | ~ ( p @ X0 )
      | ( X0 = c_2Ebool_2ET ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl4]) ).

thf(ax_true_p,axiom,
    p @ c_2Ebool_2ET ).

thf(zip_derived_cl15,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl685,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 )
      | ( X0 = c_2Ebool_2ET ) ),
    inference(demod,[status(thm)],[zip_derived_cl681,zip_derived_cl15]) ).

thf(zip_derived_cl721,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2ET )
      | ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl685]) ).

thf(zip_derived_cl722_021,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).

thf(zip_derived_cl776,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup+',[status(thm)],[zip_derived_cl721,zip_derived_cl722]) ).

thf(zip_derived_cl779,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2ET ) ),
    inference(simplify,[status(thm)],[zip_derived_cl776]) ).

thf(zip_derived_cl698_022,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(zip_derived_cl16_023,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl722_024,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl707]) ).

thf(zip_derived_cl698_025,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(ax_neg_p,axiom,
    ! [Q: $i] :
      ( ( mem @ Q @ bool )
     => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
      <=> ~ ( p @ Q ) ) ) ).

thf(zip_derived_cl37,plain,
    ! [X0: $i] :
      ( ( p @ X0 )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( mem @ X0 @ bool ) ),
    inference(cnf,[status(esa)],[ax_neg_p]) ).

thf(zip_derived_cl698_026,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(zip_derived_cl4_027,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( X1 = X0 )
      | ~ ( p @ X1 )
      | ~ ( p @ X0 )
      | ~ ( mem @ X1 @ bool ) ),
    inference(cnf,[status(esa)],[boolext]) ).

thf(zip_derived_cl719,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X1 @ bool )
      | ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( p @ X1 )
      | ( X1
        = ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl4]) ).

thf(zip_derived_cl1054,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ X0 )
      | ( X1
        = ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( p @ X1 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl719]) ).

thf(zip_derived_cl1059,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X1 @ bool )
      | ~ ( p @ X1 )
      | ( X1
        = ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ( p @ X0 )
      | ~ ( mem @ X0 @ bool ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1054]) ).

thf(zip_derived_cl1087,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X1 @ bool )
      | ( p @ X1 )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ X1 ) )
      | ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl1059]) ).

thf(zip_derived_cl1474,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ X1 ) )
      | ( p @ X1 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl722,zip_derived_cl1087]) ).

thf(zip_derived_cl1479,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X1 @ bool )
      | ( p @ X1 )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ X1 ) )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1474]) ).

thf(zip_derived_cl1583,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
      | ( p @ c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl1479]) ).

thf(zip_derived_cl17_028,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl1590,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1583,zip_derived_cl17]) ).

thf(zip_derived_cl1597,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
        = ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
      | ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
        = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl698,zip_derived_cl1590]) ).

thf(zip_derived_cl1764,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
       != c_2Ebool_2EF )
      | ( ( ap @ c_2Ebool_2E_7E @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl1597]) ).

thf(zip_derived_cl37_029,plain,
    ! [X0: $i] :
      ( ( p @ X0 )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( mem @ X0 @ bool ) ),
    inference(cnf,[status(esa)],[ax_neg_p]) ).

thf(zip_derived_cl1771,plain,
    ! [X0: $i] :
      ( ( p @ c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
       != c_2Ebool_2EF )
      | ~ ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1764,zip_derived_cl37]) ).

thf(zip_derived_cl17_030,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl1799,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
       != c_2Ebool_2EF )
      | ~ ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1771,zip_derived_cl17]) ).

thf(zip_derived_cl698_031,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl3]) ).

thf(zip_derived_cl1812,plain,
    ! [X0: $i] :
      ( ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
       != c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool ) ),
    inference(clc,[status(thm)],[zip_derived_cl1799,zip_derived_cl698]) ).

thf(zip_derived_cl1815,plain,
    ! [X0: $i] :
      ( ( c_2Ebool_2EF != c_2Ebool_2EF )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
        = c_2Ebool_2ET )
      | ~ ( mem @ c_2Ebool_2EF @ bool )
      | ~ ( mem @ X0 @ bool )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl779,zip_derived_cl1812]) ).

thf(zip_derived_cl16_032,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl1819,plain,
    ! [X0: $i] :
      ( ( c_2Ebool_2EF != c_2Ebool_2EF )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
        = c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1815,zip_derived_cl16]) ).

thf(zip_derived_cl1820,plain,
    ! [X0: $i] :
      ( ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
        = c_2Ebool_2ET ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1819]) ).

thf(zip_derived_cl1830,plain,
    ( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
      = c_2Ebool_2ET )
    | ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1820]) ).

thf(zip_derived_cl38,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( p @ X0 )
      | ~ ( mem @ X0 @ bool ) ),
    inference(cnf,[status(esa)],[ax_neg_p]) ).

thf(zip_derived_cl14_033,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl1590_034,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1583,zip_derived_cl17]) ).

thf(zip_derived_cl1599,plain,
    ( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
      = ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF ) )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
      = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1590]) ).

thf(zip_derived_cl37_035,plain,
    ! [X0: $i] :
      ( ( p @ X0 )
      | ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( mem @ X0 @ bool ) ),
    inference(cnf,[status(esa)],[ax_neg_p]) ).

thf(zip_derived_cl1607,plain,
    ( ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
      = c_2Ebool_2EF )
    | ~ ( mem @ c_2Ebool_2EF @ bool )
    | ( p @ c_2Ebool_2EF ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1599,zip_derived_cl37]) ).

thf(zip_derived_cl16_036,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl17_037,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl1617,plain,
    ( ( p @ ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET ) )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
      = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl1607,zip_derived_cl16,zip_derived_cl17]) ).

thf(zip_derived_cl1675,plain,
    ( ~ ( mem @ c_2Ebool_2ET @ bool )
    | ~ ( p @ c_2Ebool_2ET )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
      = c_2Ebool_2EF ) ),
    inference('sup+',[status(thm)],[zip_derived_cl38,zip_derived_cl1617]) ).

thf(zip_derived_cl14_038,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl15_039,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl1681,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
    = c_2Ebool_2EF ),
    inference(demod,[status(thm)],[zip_derived_cl1675,zip_derived_cl14,zip_derived_cl15]) ).

thf(zip_derived_cl17_040,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl1837,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl1830,zip_derived_cl1681,zip_derived_cl17]) ).

thf(zip_derived_cl1837_041,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl1830,zip_derived_cl1681,zip_derived_cl17]) ).

thf(zip_derived_cl8262,plain,
    ( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 )
    | ( c_2Ebool_2ET
      = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
    | ( c_2Ebool_2ET = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl8249,zip_derived_cl1837,zip_derived_cl1837]) ).

thf(zip_derived_cl14_042,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl779_043,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2ET ) ),
    inference(simplify,[status(thm)],[zip_derived_cl776]) ).

thf(zip_derived_cl836,plain,
    ! [X0: $i] :
      ( ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl779]) ).

thf(zip_derived_cl38_044,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ~ ( p @ X0 )
      | ~ ( mem @ X0 @ bool ) ),
    inference(cnf,[status(esa)],[ax_neg_p]) ).

thf(zip_derived_cl852,plain,
    ! [X0: $i] :
      ( ~ ( p @ c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl836,zip_derived_cl38]) ).

thf(zip_derived_cl15_045,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl861,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl852,zip_derived_cl15]) ).

thf(zip_derived_cl862,plain,
    ! [X0: $i] :
      ( ~ ( p @ X0 )
      | ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool ) ),
    inference(simplify,[status(thm)],[zip_derived_cl861]) ).

thf(zip_derived_cl903,plain,
    ( ( c_2Ebool_2EF != c_2Ebool_2ET )
    | ~ ( p @ c_2Ebool_2ET ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl862]) ).

thf(zip_derived_cl15_046,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl905,plain,
    c_2Ebool_2EF != c_2Ebool_2ET,
    inference(demod,[status(thm)],[zip_derived_cl903,zip_derived_cl15]) ).

thf(zip_derived_cl8263,plain,
    ( ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 )
    | ( c_2Ebool_2ET
      = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8262,zip_derived_cl905]) ).

thf(zip_derived_cl8395,plain,
    ( ( c_2Ebool_2ET
      = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
    | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
    | ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl89,zip_derived_cl8263]) ).

thf(zip_derived_cl47_047,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl8396,plain,
    ( ( c_2Ebool_2ET
      = ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
    | ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8395,zip_derived_cl47]) ).

thf(zip_derived_cl85,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ X1 ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X1 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) )
      | ~ ( mem @ X1 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__LT__CALCULATE]) ).

thf(zip_derived_cl8429,plain,
    ( ~ ( p @ c_2Ebool_2ET )
    | ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 )
    | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
    | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
    | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl8396,zip_derived_cl85]) ).

thf(zip_derived_cl15_048,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl47_049,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl80_050,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

thf(zip_derived_cl80_051,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

thf(conj_thm_2Eprim__rec_2ENOT__LESS__0,axiom,
    ! [V0n: $i] :
      ( ( mem @ V0n @ ty_2Enum_2Enum )
     => ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V0n ) @ c_2Enum_2E0 ) ) ) ).

thf(zip_derived_cl91,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum ) ),
    inference(cnf,[status(esa)],[conj_thm_2Eprim__rec_2ENOT__LESS__0]) ).

thf(zip_derived_cl80_052,plain,
    ( ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__NEG__0]) ).

thf(zip_derived_cl973_053,plain,
    ! [X0: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ X0 ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ~ ( mem @ X0 @ ty_2Enum_2Enum )
      | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl971,zip_derived_cl47]) ).

thf(zip_derived_cl1011,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) )
    | ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ) ),
    inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl973]) ).

thf(zip_derived_cl47_054,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl1016,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1011,zip_derived_cl47]) ).

thf(zip_derived_cl1021,plain,
    ( ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl91,zip_derived_cl1016]) ).

thf(zip_derived_cl47_055,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl1023,plain,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1021,zip_derived_cl47]) ).

thf(zip_derived_cl47_056,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl8446,plain,
    ( ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = c_2Enum_2E0 ),
    inference(demod,[status(thm)],[zip_derived_cl8429,zip_derived_cl15,zip_derived_cl47,zip_derived_cl80,zip_derived_cl80,zip_derived_cl1023,zip_derived_cl47]) ).

thf(zip_derived_cl214762,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ X0 ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
      | ~ ( ne @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6189,zip_derived_cl8446]) ).

thf(zip_derived_cl214769,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) )
      | ~ ( ne @ X0 )
      | ~ ( ne @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl214762]) ).

thf(zip_derived_cl214776,plain,
    ! [X0: $i] :
      ( ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ X0 ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl214769]) ).

thf(conj_thm_2Ebool_2ECOND__CONG,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ! [V0P: $i] :
          ( ( mem @ V0P @ bool )
         => ! [V1Q: $i] :
              ( ( mem @ V1Q @ bool )
             => ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ! [V3x_27: $i] :
                      ( ( mem @ V3x_27 @ A_27a )
                     => ! [V4y: $i] :
                          ( ( mem @ V4y @ A_27a )
                         => ! [V5y_27: $i] :
                              ( ( mem @ V5y_27 @ A_27a )
                             => ( ( ( ~ ( p @ V1Q )
                                   => ( V4y = V5y_27 ) )
                                  & ( ( p @ V1Q )
                                   => ( V2x = V3x_27 ) )
                                  & ( ( p @ V0P )
                                  <=> ( p @ V1Q ) ) )
                               => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
                                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [V1Q: $i,V0P: $i] :
      ( ( ( p @ V0P )
      <=> ( p @ V1Q ) )
     => ( zip_tseitin_5 @ V1Q @ V0P ) ) ).

thf(zip_derived_cl76,plain,
    ! [X0: $i,X1: $i] :
      ( ( zip_tseitin_5 @ X0 @ X1 )
      | ( p @ X0 )
      | ( p @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zf_stmt_1,axiom,
    ! [V3x_27: $i,V2x: $i,V1Q: $i] :
      ( ( ( p @ V1Q )
       => ( V2x = V3x_27 ) )
     => ( zip_tseitin_4 @ V3x_27 @ V2x @ V1Q ) ) ).

thf(zip_derived_cl74,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_4 @ X0 @ X1 @ X2 )
      | ( p @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zf_stmt_2,axiom,
    ! [V5y_27: $i,V4y: $i,V1Q: $i] :
      ( ( ~ ( p @ V1Q )
       => ( V4y = V5y_27 ) )
     => ( zip_tseitin_3 @ V5y_27 @ V4y @ V1Q ) ) ).

thf(zip_derived_cl71,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( zip_tseitin_3 @ X0 @ X1 @ X2 )
      | ( X1 != X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zf_stmt_3,type,
    zip_tseitin_5: $i > $i > $o ).

thf(zf_stmt_4,type,
    zip_tseitin_4: $i > $i > $i > $o ).

thf(zf_stmt_5,type,
    zip_tseitin_3: $i > $i > $i > $o ).

thf(zf_stmt_6,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ! [V0P: $i] :
          ( ( mem @ V0P @ bool )
         => ! [V1Q: $i] :
              ( ( mem @ V1Q @ bool )
             => ! [V2x: $i] :
                  ( ( mem @ V2x @ A_27a )
                 => ! [V3x_27: $i] :
                      ( ( mem @ V3x_27 @ A_27a )
                     => ! [V4y: $i] :
                          ( ( mem @ V4y @ A_27a )
                         => ! [V5y_27: $i] :
                              ( ( mem @ V5y_27 @ A_27a )
                             => ( ( ( zip_tseitin_5 @ V1Q @ V0P )
                                  & ( zip_tseitin_4 @ V3x_27 @ V2x @ V1Q )
                                  & ( zip_tseitin_3 @ V5y_27 @ V4y @ V1Q ) )
                               => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
                                  = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ) ).

thf(zip_derived_cl77,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X1 @ X2 )
      | ~ ( mem @ X3 @ X2 )
      | ~ ( zip_tseitin_5 @ X4 @ X0 )
      | ~ ( zip_tseitin_4 @ X5 @ X1 @ X4 )
      | ~ ( zip_tseitin_3 @ X6 @ X3 @ X4 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X1 ) @ X3 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X4 ) @ X5 ) @ X6 ) )
      | ~ ( mem @ X6 @ X2 )
      | ~ ( mem @ X5 @ X2 )
      | ~ ( mem @ X4 @ bool )
      | ~ ( ne @ X2 ) ),
    inference(cnf,[status(esa)],[zf_stmt_6]) ).

thf(zip_derived_cl661,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X1 != X2 )
      | ~ ( ne @ X4 )
      | ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X6 @ X4 )
      | ~ ( mem @ X2 @ X4 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X4 ) @ X3 ) @ X5 ) @ X1 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X4 ) @ X0 ) @ X6 ) @ X2 ) )
      | ~ ( zip_tseitin_4 @ X6 @ X5 @ X0 )
      | ~ ( zip_tseitin_5 @ X0 @ X3 )
      | ~ ( mem @ X1 @ X4 )
      | ~ ( mem @ X5 @ X4 )
      | ~ ( mem @ X3 @ bool ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl71,zip_derived_cl77]) ).

thf(zip_derived_cl673,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( p @ X0 )
      | ~ ( mem @ X6 @ bool )
      | ~ ( mem @ X1 @ X5 )
      | ~ ( mem @ X3 @ X5 )
      | ~ ( zip_tseitin_5 @ X0 @ X6 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X5 ) @ X6 ) @ X1 ) @ X3 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X5 ) @ X0 ) @ X2 ) @ X4 ) )
      | ~ ( mem @ X4 @ X5 )
      | ~ ( mem @ X2 @ X5 )
      | ~ ( mem @ X0 @ bool )
      | ~ ( ne @ X5 )
      | ( X3 != X4 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl74,zip_derived_cl661]) ).

thf(zip_derived_cl680,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( p @ X0 )
      | ( p @ X1 )
      | ( X4 != X5 )
      | ~ ( ne @ X2 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ X6 @ X2 )
      | ~ ( mem @ X5 @ X2 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X3 ) @ X4 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X6 ) @ X5 ) )
      | ~ ( mem @ X4 @ X2 )
      | ~ ( mem @ X3 @ X2 )
      | ~ ( mem @ X0 @ bool )
      | ( p @ X1 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl76,zip_derived_cl673]) ).

thf(zip_derived_cl1051,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X3 @ X2 )
      | ~ ( mem @ X4 @ X2 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X3 ) @ X4 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X6 ) @ X5 ) )
      | ~ ( mem @ X5 @ X2 )
      | ~ ( mem @ X6 @ X2 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( ne @ X2 )
      | ( X4 != X5 )
      | ( p @ X1 )
      | ( p @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl680]) ).

thf(zip_derived_cl1052,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( p @ X0 )
      | ( p @ X1 )
      | ~ ( ne @ X2 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( mem @ X3 @ X2 )
      | ~ ( mem @ X4 @ X2 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X5 ) @ X4 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X3 ) @ X4 ) )
      | ~ ( mem @ X4 @ X2 )
      | ~ ( mem @ X5 @ X2 )
      | ~ ( mem @ X0 @ bool ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1051]) ).

thf(zip_derived_cl1053,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ X5 @ X2 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X0 ) @ X5 ) @ X4 )
        = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X2 ) @ X1 ) @ X3 ) @ X4 ) )
      | ~ ( mem @ X4 @ X2 )
      | ~ ( mem @ X3 @ X2 )
      | ~ ( mem @ X1 @ bool )
      | ~ ( ne @ X2 )
      | ( p @ X1 )
      | ( p @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1052]) ).

thf(conj_thm_2Ebool_2Ebool__case__thm,axiom,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ( ! [V0t1: $i] :
            ( ( mem @ V0t1 @ A_27a )
           => ! [V1t2: $i] :
                ( ( mem @ V1t2 @ A_27a )
               => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
                  = V0t1 ) ) )
        & ! [V2t1: $i] :
            ( ( mem @ V2t1 @ A_27a )
           => ! [V3t2: $i] :
                ( ( mem @ V3t2 @ A_27a )
               => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
                  = V3t2 ) ) ) ) ) ).

thf(zip_derived_cl79,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ X0 @ X1 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X1 ) @ c_2Ebool_2EF ) @ X0 ) @ X2 )
        = X2 )
      | ~ ( mem @ X2 @ X1 )
      | ~ ( ne @ X1 ) ),
    inference(cnf,[status(esa)],[conj_thm_2Ebool_2Ebool__case__thm]) ).

thf(zip_derived_cl6742,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
        = X0 )
      | ( p @ X2 )
      | ( p @ c_2Ebool_2EF )
      | ~ ( ne @ X3 )
      | ~ ( mem @ c_2Ebool_2EF @ bool )
      | ~ ( mem @ X4 @ X3 )
      | ~ ( mem @ X0 @ X3 )
      | ~ ( mem @ X1 @ X3 )
      | ~ ( mem @ X2 @ bool )
      | ~ ( ne @ X3 )
      | ~ ( mem @ X0 @ X3 )
      | ~ ( mem @ X4 @ X3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1053,zip_derived_cl79]) ).

thf(zip_derived_cl17_057,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl16_058,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl6794,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
        = X0 )
      | ( p @ X2 )
      | ~ ( ne @ X3 )
      | ~ ( mem @ X4 @ X3 )
      | ~ ( mem @ X0 @ X3 )
      | ~ ( mem @ X1 @ X3 )
      | ~ ( mem @ X2 @ bool )
      | ~ ( ne @ X3 )
      | ~ ( mem @ X0 @ X3 )
      | ~ ( mem @ X4 @ X3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6742,zip_derived_cl17,zip_derived_cl16]) ).

thf(zip_derived_cl6795,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( mem @ X2 @ bool )
      | ~ ( mem @ X1 @ X3 )
      | ~ ( mem @ X0 @ X3 )
      | ~ ( mem @ X4 @ X3 )
      | ~ ( ne @ X3 )
      | ( p @ X2 )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X2 ) @ X1 ) @ X0 )
        = X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl6794]) ).

thf(zip_derived_cl16376,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ X3 ) @ X0 ) @ X2 ) @ X1 )
        = X1 )
      | ~ ( mem @ X1 @ X3 )
      | ~ ( mem @ X2 @ X3 )
      | ~ ( ne @ X3 )
      | ( p @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl6795]) ).

thf(zip_derived_cl222899,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference('sup+',[status(thm)],[zip_derived_cl214776,zip_derived_cl16376]) ).

thf(zip_derived_cl1023_059,plain,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1021,zip_derived_cl47]) ).

thf(zip_derived_cl222922,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference(demod,[status(thm)],[zip_derived_cl222899,zip_derived_cl1023]) ).

thf(zip_derived_cl222923,plain,
    ! [X0: $i] :
      ( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
      | ~ ( mem @ ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl222922]) ).

thf(zip_derived_cl222925,plain,
    ! [X0: $i] :
      ( ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum )
      | ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl896,zip_derived_cl222923]) ).

thf(zip_derived_cl47_060,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl222926,plain,
    ! [X0: $i] :
      ( ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference(demod,[status(thm)],[zip_derived_cl222925,zip_derived_cl47]) ).

thf(zip_derived_cl222927,plain,
    ! [X0: $i] :
      ( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
      | ~ ( ne @ ( ty_2Efcp_2Ecart @ bool @ X0 ) )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl222926]) ).

thf(zip_derived_cl223014,plain,
    ! [X0: $i] :
      ( ~ ( ne @ bool )
      | ~ ( ne @ X0 )
      | ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl33,zip_derived_cl222927]) ).

thf(bool_ne,axiom,
    ne @ bool ).

thf(zip_derived_cl0,plain,
    ne @ bool,
    inference(cnf,[status(esa)],[bool_ne]) ).

thf(zip_derived_cl223015,plain,
    ! [X0: $i] :
      ( ~ ( ne @ X0 )
      | ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool ) ),
    inference(demod,[status(thm)],[zip_derived_cl223014,zip_derived_cl0]) ).

thf(zip_derived_cl223016,plain,
    ! [X0: $i] :
      ( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ bool )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl223015]) ).

thf(zip_derived_cl223031,plain,
    ! [X0: $i] :
      ( ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
      | ~ ( ne @ X0 )
      | ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1139,zip_derived_cl223016]) ).

thf(zip_derived_cl223038,plain,
    ! [X0: $i] :
      ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ X0 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ X0 ) @ c_2Enum_2E0 ) )
      | ~ ( ne @ X0 )
      | ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ) ),
    inference(simplify,[status(thm)],[zip_derived_cl223031]) ).

thf(conj_thm_2Einteger__word_2Ei2w__0,conjecture,
    ! [A_27a: $i] :
      ( ( ne @ A_27a )
     => ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ) ).

thf(zf_stmt_7,negated_conjecture,
    ~ ! [A_27a: $i] :
        ( ( ne @ A_27a )
       => ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          = ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ c_2Enum_2E0 ) ) ),
    inference('cnf.neg',[status(esa)],[conj_thm_2Einteger__word_2Ei2w__0]) ).

thf(zip_derived_cl96,plain,
    ( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
   != ( ap @ ( c_2Ewords_2En2w @ sk__2 ) @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl223056,plain,
    ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     != ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    | ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint )
    | ~ ( ne @ sk__2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl223038,zip_derived_cl96]) ).

thf(zip_derived_cl95,plain,
    ne @ sk__2,
    inference(cnf,[status(esa)],[zf_stmt_7]) ).

thf(zip_derived_cl223070,plain,
    ( ( ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     != ( ap @ ( c_2Einteger__word_2Ei2w @ sk__2 ) @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    | ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ) ),
    inference(demod,[status(thm)],[zip_derived_cl223056,zip_derived_cl95]) ).

thf(zip_derived_cl223071,plain,
    ~ ( mem @ ( ap @ c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ty_2Einteger_2Eint ),
    inference(simplify,[status(thm)],[zip_derived_cl223070]) ).

thf(zip_derived_cl223073,plain,
    ~ ( mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ),
    inference('sup-',[status(thm)],[zip_derived_cl696,zip_derived_cl223071]) ).

thf(zip_derived_cl47_061,plain,
    mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
    inference(cnf,[status(esa)],[mem_c_2Enum_2E0]) ).

thf(zip_derived_cl223074,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl223073,zip_derived_cl47]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP015+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Gpo0SdMHWD true
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 14:50:39 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.36  % Running in FO mode
% 0.21/0.64  % Total configuration time : 435
% 0.21/0.64  % Estimated wc time : 1092
% 0.21/0.64  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.39/0.82  % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 234.99/34.24  % Solved by fo/fo3_bce.sh.
% 234.99/34.24  % BCE start: 97
% 234.99/34.24  % BCE eliminated: 3
% 234.99/34.24  % PE start: 94
% 234.99/34.24  logic: eq
% 234.99/34.24  % PE eliminated: 10
% 234.99/34.24  % done 13389 iterations in 33.449s
% 234.99/34.24  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 234.99/34.24  % SZS output start Refutation
% See solution above
% 234.99/34.24  
% 234.99/34.24  
% 234.99/34.24  % Terminating...
% 235.65/34.34  % Runner terminated.
% 235.69/34.36  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------