TSTP Solution File: ITP012+2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ITP012+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.MYMyltJTFq true

% Computer : n024.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 05:21:06 EDT 2023

% Result   : Theorem 248.64s 36.16s
% Output   : Refutation 248.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  194 (  65 unt;  16 typ;   0 def)
%            Number of atoms       :  490 (  91 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 2025 ( 261   ~; 282   |;   1   &;1452   @)
%                                         (   7 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;  13 con; 0-2 aty)
%            Number of variables   :  163 (   0   ^; 163   !;   0   ?; 163   :)

% Comments : 
%------------------------------------------------------------------------------
thf(bool_type,type,
    bool: $i ).

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

thf(c_2Einteger_2Eint__sub_type,type,
    c_2Einteger_2Eint__sub: $i ).

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

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

thf(sk__10_type,type,
    sk__10: $i ).

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

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

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

thf(c_2Einteger_2Eint__add_type,type,
    c_2Einteger_2Eint__add: $i ).

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

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

thf(c_2Einteger_2Eint__divides_type,type,
    c_2Einteger_2Eint__divides: $i ).

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

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

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

thf(conj_thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ty_2Einteger_2Eint )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ty_2Einteger_2Eint )
         => ( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ ( ap @ c_2Einteger_2Eint__neg @ V1q ) ) )
            <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V1q ) ) )
            & ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ ( ap @ c_2Einteger_2Eint__neg @ V0p ) ) @ V1q ) )
            <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V1q ) ) ) ) ) ) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG]) ).

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

thf(zip_derived_cl21,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(mem_c_2Einteger_2Eint__sub,axiom,
    mem @ c_2Einteger_2Eint__sub @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ) ).

thf(zip_derived_cl17,plain,
    mem @ c_2Einteger_2Eint__sub @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__sub]) ).

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_cl2195,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__sub @ X0 ) @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl3]) ).

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_cl2199,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X0 ) @ X1 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2195,zip_derived_cl3]) ).

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

thf(zip_derived_cl35,plain,
    mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
    inference(cnf,[status(esa)],[mem_c_2Ebool_2E_7E]) ).

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_cl2198,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl21_003,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_cl2203,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ c_2Ebool_2EF )
      | ( p @ X0 )
      | ( X0 = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl5]) ).

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

thf(zip_derived_cl22,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl2207,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ X0 )
      | ( X0 = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl2203,zip_derived_cl22]) ).

thf(zip_derived_cl2227,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_cl2198,zip_derived_cl2207]) ).

thf(zip_derived_cl2198_004,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(conj_thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ty_2Einteger_2Eint )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ty_2Einteger_2Eint )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ ty_2Einteger_2Eint )
             => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V1q ) )
               => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ V2r ) @ V1q ) ) )
                <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V2r ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [V0p: $i] :
        ( ( mem @ V0p @ ty_2Einteger_2Eint )
       => ! [V1q: $i] :
            ( ( mem @ V1q @ ty_2Einteger_2Eint )
           => ! [V2r: $i] :
                ( ( mem @ V2r @ ty_2Einteger_2Eint )
               => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V1q ) )
                 => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ V2r ) @ V1q ) ) )
                  <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V2r ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__RSUB]) ).

thf(zip_derived_cl222,plain,
    ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(mem_c_2Einteger_2Eint__divides,axiom,
    mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ) ).

thf(zip_derived_cl20,plain,
    mem @ c_2Einteger_2Eint__divides @ ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__divides]) ).

thf(zip_derived_cl3_005,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_cl2201,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__divides @ X0 ) @ ( arr @ ty_2Einteger_2Eint @ bool ) )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl3]) ).

thf(zip_derived_cl3_006,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_cl2236,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X0 ) @ X1 ) @ bool )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2201,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_cl2279,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ bool )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) )
      | ~ ( p @ X2 )
      | ( X2
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2236,zip_derived_cl4]) ).

thf(zip_derived_cl3461,plain,
    ! [X0: $i] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
      | ( X0
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
      | ~ ( p @ X0 )
      | ~ ( mem @ X0 @ bool )
      | ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl222,zip_derived_cl2279]) ).

thf(zip_derived_cl220,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3470,plain,
    ! [X0: $i] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
      | ( X0
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
      | ~ ( p @ X0 )
      | ~ ( mem @ X0 @ bool )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint ) ),
    inference(demod,[status(thm)],[zip_derived_cl3461,zip_derived_cl220]) ).

thf(zip_derived_cl94_007,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__NEG]) ).

thf(zip_derived_cl223,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(ax_thm_2Einteger_2Eint__sub,axiom,
    ! [V0x: $i] :
      ( ( mem @ V0x @ ty_2Einteger_2Eint )
     => ! [V1y: $i] :
          ( ( mem @ V1y @ ty_2Einteger_2Eint )
         => ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ V0x ) @ V1y )
            = ( ap @ ( ap @ c_2Einteger_2Eint__add @ V0x ) @ ( ap @ c_2Einteger_2Eint__neg @ V1y ) ) ) ) ) ).

thf(zip_derived_cl89,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__add @ X1 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[ax_thm_2Einteger_2Eint__sub]) ).

thf(conj_thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
    ! [V0p: $i] :
      ( ( mem @ V0p @ ty_2Einteger_2Eint )
     => ! [V1q: $i] :
          ( ( mem @ V1q @ ty_2Einteger_2Eint )
         => ! [V2r: $i] :
              ( ( mem @ V2r @ ty_2Einteger_2Eint )
             => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V1q ) )
               => ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ V2r ) @ V1q ) ) )
                <=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ V0p ) @ V2r ) ) ) ) ) ) ) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X2 ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ X2 ) @ X0 ) ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__RADD]) ).

thf(zip_derived_cl2822,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint ) ),
    inference('sup+',[status(thm)],[zip_derived_cl89,zip_derived_cl90]) ).

thf(zip_derived_cl2824,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2822]) ).

thf(mem_c_2Einteger_2Eint__neg,axiom,
    mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ) ).

thf(zip_derived_cl19,plain,
    mem @ c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ),
    inference(cnf,[status(esa)],[mem_c_2Einteger_2Eint__neg]) ).

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_cl2196,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl3]) ).

thf(zip_derived_cl247862,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl2824,zip_derived_cl2196]) ).

thf(zip_derived_cl247874,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ c_2Einteger_2Eint__neg @ sk__9 ) ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__9 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__10 @ ty_2Einteger_2Eint ) ),
    inference('sup+',[status(thm)],[zip_derived_cl223,zip_derived_cl247862]) ).

thf(zip_derived_cl220_009,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl225,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl221,plain,
    mem @ sk__10 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl247880,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ c_2Einteger_2Eint__neg @ sk__9 ) ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl247874,zip_derived_cl220,zip_derived_cl225,zip_derived_cl221]) ).

thf(zip_derived_cl247881,plain,
    ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ c_2Einteger_2Eint__neg @ sk__9 ) ) )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl247880]) ).

thf(zip_derived_cl248198,plain,
    ( ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 ) )
    | ~ ( mem @ sk__9 @ ty_2Einteger_2Eint )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl247881]) ).

thf(zip_derived_cl220_010,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl224,plain,
    p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2236_011,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X0 ) @ X1 ) @ bool )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2201,zip_derived_cl3]) ).

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

thf(zip_derived_cl10,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl4_012,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_cl2182,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( p @ c_2Ebool_2ET )
      | ~ ( p @ X0 )
      | ( X0 = c_2Ebool_2ET ) ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl4]) ).

thf(ax_true_p,axiom,
    p @ c_2Ebool_2ET ).

thf(zip_derived_cl11,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl2186,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 )
      | ( X0 = c_2Ebool_2ET ) ),
    inference(demod,[status(thm)],[zip_derived_cl2182,zip_derived_cl11]) ).

thf(zip_derived_cl2281,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 )
        = c_2Ebool_2ET )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2236,zip_derived_cl2186]) ).

thf(zip_derived_cl2614,plain,
    ( ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 )
      = c_2Ebool_2ET )
    | ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__9 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl224,zip_derived_cl2281]) ).

thf(zip_derived_cl220_013,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl225_014,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2616,plain,
    ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl2614,zip_derived_cl220,zip_derived_cl225]) ).

thf(zip_derived_cl11_015,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl225_016,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl248202,plain,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl248198,zip_derived_cl220,zip_derived_cl2616,zip_derived_cl11,zip_derived_cl225]) ).

thf(zip_derived_cl248209,plain,
    ! [X0: $i] :
      ( ( X0
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
      | ~ ( p @ X0 )
      | ~ ( mem @ X0 @ bool )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint ) ),
    inference(demod,[status(thm)],[zip_derived_cl3470,zip_derived_cl248202]) ).

thf(zip_derived_cl248333,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ c_2Ebool_2E_7E @ X0 ) )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2198,zip_derived_cl248209]) ).

thf(zip_derived_cl250072,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
      | ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2227,zip_derived_cl248333]) ).

thf(zip_derived_cl250109,plain,
    ! [X0: $i] :
      ( ~ ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) @ ty_2Einteger_2Eint )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF ) ),
    inference(simplify,[status(thm)],[zip_derived_cl250072]) ).

thf(zip_derived_cl250522,plain,
    ! [X0: $i] :
      ( ~ ( mem @ sk__9 @ ty_2Einteger_2Eint )
      | ~ ( mem @ sk__10 @ ty_2Einteger_2Eint )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2199,zip_derived_cl250109]) ).

thf(zip_derived_cl225_017,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl221_018,plain,
    mem @ sk__10 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl250523,plain,
    ! [X0: $i] :
      ( ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = c_2Ebool_2EF )
      | ~ ( mem @ X0 @ bool )
      | ( ( ap @ c_2Ebool_2E_7E @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl250522,zip_derived_cl225,zip_derived_cl221]) ).

thf(zip_derived_cl250535,plain,
    ( ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
      = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
    | ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
      = c_2Ebool_2EF ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl250523]) ).

thf(zip_derived_cl10_019,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl2198_020,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl2186_021,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 )
      | ( X0 = c_2Ebool_2ET ) ),
    inference(demod,[status(thm)],[zip_derived_cl2182,zip_derived_cl11]) ).

thf(zip_derived_cl2226,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_cl2198,zip_derived_cl2186]) ).

thf(zip_derived_cl2227_022,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_cl2198,zip_derived_cl2207]) ).

thf(zip_derived_cl2291,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_cl2226,zip_derived_cl2227]) ).

thf(zip_derived_cl2294,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_cl2291]) ).

thf(zip_derived_cl2198_023,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl21_024,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl2227_025,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_cl2198,zip_derived_cl2207]) ).

thf(zip_derived_cl2198_026,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,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_cl36,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_cl2198_027,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl4_028,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_cl2224,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_cl2198,zip_derived_cl4]) ).

thf(zip_derived_cl2900,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_cl36,zip_derived_cl2224]) ).

thf(zip_derived_cl2905,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_cl2900]) ).

thf(zip_derived_cl2914,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_cl2198,zip_derived_cl2905]) ).

thf(zip_derived_cl3595,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_cl2227,zip_derived_cl2914]) ).

thf(zip_derived_cl3600,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_cl3595]) ).

thf(zip_derived_cl4081,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_cl21,zip_derived_cl3600]) ).

thf(zip_derived_cl22_029,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl4086,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_cl4081,zip_derived_cl22]) ).

thf(zip_derived_cl4094,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_cl2198,zip_derived_cl4086]) ).

thf(zip_derived_cl5249,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_cl4094]) ).

thf(zip_derived_cl36_030,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_cl5283,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_cl5249,zip_derived_cl36]) ).

thf(zip_derived_cl22_031,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl5312,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_cl5283,zip_derived_cl22]) ).

thf(zip_derived_cl2198_032,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Ebool_2E_7E @ X0 ) @ bool )
      | ~ ( mem @ X0 @ bool ) ),
    inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl3]) ).

thf(zip_derived_cl5325,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_cl5312,zip_derived_cl2198]) ).

thf(zip_derived_cl5328,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_cl2294,zip_derived_cl5325]) ).

thf(zip_derived_cl21_033,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl5332,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_cl5328,zip_derived_cl21]) ).

thf(zip_derived_cl5333,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_cl5332]) ).

thf(zip_derived_cl5352,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_cl10,zip_derived_cl5333]) ).

thf(zip_derived_cl37,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_cl10_034,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl4086_035,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_cl4081,zip_derived_cl22]) ).

thf(zip_derived_cl4096,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_cl10,zip_derived_cl4086]) ).

thf(zip_derived_cl36_036,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_cl4116,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_cl4096,zip_derived_cl36]) ).

thf(zip_derived_cl21_037,plain,
    mem @ c_2Ebool_2EF @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2EF]) ).

thf(zip_derived_cl22_038,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl4126,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_cl4116,zip_derived_cl21,zip_derived_cl22]) ).

thf(zip_derived_cl4264,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_cl37,zip_derived_cl4126]) ).

thf(zip_derived_cl10_039,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl11_040,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl4270,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2ET )
    = c_2Ebool_2EF ),
    inference(demod,[status(thm)],[zip_derived_cl4264,zip_derived_cl10,zip_derived_cl11]) ).

thf(zip_derived_cl22_041,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl5360,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl5352,zip_derived_cl4270,zip_derived_cl22]) ).

thf(zip_derived_cl5360_042,plain,
    ( ( ap @ c_2Ebool_2E_7E @ c_2Ebool_2EF )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl5352,zip_derived_cl4270,zip_derived_cl22]) ).

thf(zip_derived_cl250558,plain,
    ( ( c_2Ebool_2ET
      = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) )
    | ( c_2Ebool_2ET = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl250535,zip_derived_cl5360,zip_derived_cl5360]) ).

thf(zip_derived_cl10_043,plain,
    mem @ c_2Ebool_2ET @ bool,
    inference(cnf,[status(esa)],[mem_c_2Ebool_2ET]) ).

thf(zip_derived_cl2294_044,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_cl2291]) ).

thf(zip_derived_cl2349,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_cl2294]) ).

thf(zip_derived_cl37_045,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_cl2400,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_cl2349,zip_derived_cl37]) ).

thf(zip_derived_cl11_046,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl2411,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool )
      | ~ ( p @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2400,zip_derived_cl11]) ).

thf(zip_derived_cl2412,plain,
    ! [X0: $i] :
      ( ~ ( p @ X0 )
      | ( c_2Ebool_2EF != c_2Ebool_2ET )
      | ~ ( mem @ X0 @ bool ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2411]) ).

thf(zip_derived_cl2428,plain,
    ( ( c_2Ebool_2EF != c_2Ebool_2ET )
    | ~ ( p @ c_2Ebool_2ET ) ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl2412]) ).

thf(zip_derived_cl11_047,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl2430,plain,
    c_2Ebool_2EF != c_2Ebool_2ET,
    inference(demod,[status(thm)],[zip_derived_cl2428,zip_derived_cl11]) ).

thf(zip_derived_cl250559,plain,
    ( c_2Ebool_2ET
    = ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ sk__10 ) @ sk__9 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl250558,zip_derived_cl2430]) ).

thf(zip_derived_cl89_048,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 )
        = ( ap @ ( ap @ c_2Einteger_2Eint__add @ X1 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[ax_thm_2Einteger_2Eint__sub]) ).

thf(zip_derived_cl91,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ X2 ) @ X0 ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X2 ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference(cnf,[status(esa)],[conj_thm_2Einteger_2EINT__DIVIDES__RADD]) ).

thf(zip_derived_cl2927,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ~ ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl91]) ).

thf(zip_derived_cl2929,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2927]) ).

thf(zip_derived_cl2196_049,plain,
    ! [X0: $i] :
      ( ( mem @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl3]) ).

thf(zip_derived_cl332614,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ X1 ) @ X0 ) ) )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X2 @ ty_2Einteger_2Eint )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ X1 ) )
      | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X2 ) @ ( ap @ c_2Einteger_2Eint__neg @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl2929,zip_derived_cl2196]) ).

thf(zip_derived_cl332625,plain,
    ( ~ ( p @ c_2Ebool_2ET )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ c_2Einteger_2Eint__neg @ sk__9 ) ) )
    | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) )
    | ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__9 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__10 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl250559,zip_derived_cl332614]) ).

thf(zip_derived_cl11_050,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl2236_051,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ( mem @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X0 ) @ X1 ) @ bool )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2201,zip_derived_cl3]) ).

thf(zip_derived_cl2207_052,plain,
    ! [X0: $i] :
      ( ~ ( mem @ X0 @ bool )
      | ( p @ X0 )
      | ( X0 = c_2Ebool_2EF ) ),
    inference(demod,[status(thm)],[zip_derived_cl2203,zip_derived_cl22]) ).

thf(zip_derived_cl2282,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( mem @ X0 @ ty_2Einteger_2Eint )
      | ~ ( mem @ X1 @ ty_2Einteger_2Eint )
      | ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 )
        = c_2Ebool_2EF )
      | ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ X1 ) @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2236,zip_derived_cl2207]) ).

thf(zip_derived_cl248202_053,plain,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl248198,zip_derived_cl220,zip_derived_cl2616,zip_derived_cl11,zip_derived_cl225]) ).

thf(zip_derived_cl248212,plain,
    ( ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 )
      = c_2Ebool_2EF )
    | ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( mem @ sk__10 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2282,zip_derived_cl248202]) ).

thf(zip_derived_cl220_054,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl221_055,plain,
    mem @ sk__10 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl248216,plain,
    ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__10 )
    = c_2Ebool_2EF ),
    inference(demod,[status(thm)],[zip_derived_cl248212,zip_derived_cl220,zip_derived_cl221]) ).

thf(zip_derived_cl22_056,plain,
    ~ ( p @ c_2Ebool_2EF ),
    inference(cnf,[status(esa)],[ax_false_p]) ).

thf(zip_derived_cl220_057,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl225_058,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl221_059,plain,
    mem @ sk__10 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl332631,plain,
    ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ ( ap @ c_2Einteger_2Eint__neg @ sk__9 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl332625,zip_derived_cl11,zip_derived_cl248216,zip_derived_cl22,zip_derived_cl220,zip_derived_cl225,zip_derived_cl221]) ).

thf(zip_derived_cl332989,plain,
    ( ~ ( mem @ sk__8 @ ty_2Einteger_2Eint )
    | ~ ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 ) )
    | ~ ( mem @ sk__9 @ ty_2Einteger_2Eint ) ),
    inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl332631]) ).

thf(zip_derived_cl220_060,plain,
    mem @ sk__8 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2616_061,plain,
    ( ( ap @ ( ap @ c_2Einteger_2Eint__divides @ sk__8 ) @ sk__9 )
    = c_2Ebool_2ET ),
    inference(demod,[status(thm)],[zip_derived_cl2614,zip_derived_cl220,zip_derived_cl225]) ).

thf(zip_derived_cl11_062,plain,
    p @ c_2Ebool_2ET,
    inference(cnf,[status(esa)],[ax_true_p]) ).

thf(zip_derived_cl225_063,plain,
    mem @ sk__9 @ ty_2Einteger_2Eint,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl332993,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl332989,zip_derived_cl220,zip_derived_cl2616,zip_derived_cl11,zip_derived_cl225]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP012+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.MYMyltJTFq true
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 12:50:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.34  % Python version: Python 3.6.8
% 0.13/0.34  % Running in FO mode
% 0.47/0.64  % Total configuration time : 435
% 0.47/0.64  % Estimated wc time : 1092
% 0.47/0.64  % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.68  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.72  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.47/0.72  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.74  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.75  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 248.64/36.16  % Solved by fo/fo3_bce.sh.
% 248.64/36.16  % BCE start: 226
% 248.64/36.16  % BCE eliminated: 1
% 248.64/36.16  % PE start: 225
% 248.64/36.16  logic: eq
% 248.64/36.16  % PE eliminated: 122
% 248.64/36.16  % done 3461 iterations in 35.409s
% 248.64/36.16  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 248.64/36.16  % SZS output start Refutation
% See solution above
% 248.64/36.16  
% 248.64/36.16  
% 248.64/36.16  % Terminating...
% 249.45/36.24  % Runner terminated.
% 249.45/36.26  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------