TSTP Solution File: SWC297+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWC297+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6pPfpV6Brw true

% Computer : n002.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 21:30:34 EDT 2023

% Result   : Theorem 26.54s 4.42s
% Output   : Refutation 26.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   52
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  317 ( 104 unt;  24 typ;   0 def)
%            Number of atoms       :  832 ( 261 equ;   0 cnn)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives : 2153 ( 412   ~; 458   |;   9   &;1202   @)
%                                         (   6 <=>;  66  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  11 con; 0-2 aty)
%            Number of variables   :  247 (   0   ^; 244   !;   3   ?; 247   :)

% Comments : 
%------------------------------------------------------------------------------
thf(duplicatefreeP_type,type,
    duplicatefreeP: $i > $o ).

thf(ssItem_type,type,
    ssItem: $i > $o ).

thf(sk__55_type,type,
    sk__55: $i ).

thf(sk__50_type,type,
    sk__50: $i ).

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

thf(nil_type,type,
    nil: $i ).

thf(lt_type,type,
    lt: $i > $i > $o ).

thf(app_type,type,
    app: $i > $i > $i ).

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

thf(hd_type,type,
    hd: $i > $i ).

thf(ssList_type,type,
    ssList: $i > $o ).

thf(tl_type,type,
    tl: $i > $i ).

thf(rearsegP_type,type,
    rearsegP: $i > $i > $o ).

thf(sk__51_type,type,
    sk__51: $i ).

thf(sk__53_type,type,
    sk__53: $i ).

thf(sk__52_type,type,
    sk__52: $i ).

thf(sk__49_type,type,
    sk__49: $i ).

thf(sk__47_type,type,
    sk__47: $i ).

thf(sk__48_type,type,
    sk__48: $i ).

thf(neq_type,type,
    neq: $i > $i > $o ).

thf(cons_type,type,
    cons: $i > $i > $i ).

thf(sk__54_type,type,
    sk__54: $i ).

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

thf(memberP_type,type,
    memberP: $i > $i > $o ).

thf(co1,conjecture,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ! [X: $i] :
                  ( ( ssList @ X )
                 => ( ( V != X )
                    | ( U != W )
                    | ! [Y: $i] :
                        ( ( ssItem @ Y )
                       => ! [Z: $i] :
                            ( ( ssList @ Z )
                           => ! [X1: $i] :
                                ( ( ssList @ X1 )
                               => ( ( ( app @ ( app @ Z @ ( cons @ Y @ nil ) ) @ X1 )
                                   != U )
                                  | ! [X2: $i] :
                                      ( ( ssItem @ X2 )
                                     => ( ( ~ ( memberP @ Z @ X2 )
                                          | ( lt @ X2 @ Y ) )
                                        & ( ~ ( memberP @ X1 @ X2 )
                                          | ( lt @ Y @ X2 ) ) ) ) ) ) ) )
                    | ( ( nil != W )
                      & ( nil = X ) )
                    | ( ! [X3: $i] :
                          ( ( ssItem @ X3 )
                         => ( ( ( cons @ X3 @ nil )
                             != W )
                            | ~ ( memberP @ X @ X3 ) ) )
                      & ( neq @ X @ nil ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [U: $i] :
        ( ( ssList @ U )
       => ! [V: $i] :
            ( ( ssList @ V )
           => ! [W: $i] :
                ( ( ssList @ W )
               => ! [X: $i] :
                    ( ( ssList @ X )
                   => ( ( V != X )
                      | ( U != W )
                      | ! [Y: $i] :
                          ( ( ssItem @ Y )
                         => ! [Z: $i] :
                              ( ( ssList @ Z )
                             => ! [X1: $i] :
                                  ( ( ssList @ X1 )
                                 => ( ( ( app @ ( app @ Z @ ( cons @ Y @ nil ) ) @ X1 )
                                     != U )
                                    | ! [X2: $i] :
                                        ( ( ssItem @ X2 )
                                       => ( ( ~ ( memberP @ Z @ X2 )
                                            | ( lt @ X2 @ Y ) )
                                          & ( ~ ( memberP @ X1 @ X2 )
                                            | ( lt @ Y @ X2 ) ) ) ) ) ) ) )
                      | ( ( nil != W )
                        & ( nil = X ) )
                      | ( ! [X3: $i] :
                            ( ( ssItem @ X3 )
                           => ( ( ( cons @ X3 @ nil )
                               != W )
                              | ~ ( memberP @ X @ X3 ) ) )
                        & ( neq @ X @ nil ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[co1]) ).

thf(zip_derived_cl194,plain,
    ( ( memberP @ sk__53 @ sk__55 )
    | ( memberP @ sk__54 @ sk__55 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl194_001,plain,
    ( ( memberP @ sk__53 @ sk__55 )
    | ( memberP @ sk__54 @ sk__55 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(ax16,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( ssList @ ( cons @ V @ U ) ) ) ) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(ax26,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ssList @ ( app @ U @ V ) ) ) ) ).

thf(zip_derived_cl95,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl198,plain,
    ( ( app @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) @ sk__54 )
    = sk__47 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(ax6,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( rearsegP @ U @ V )
          <=> ? [W: $i] :
                ( ( ( app @ W @ V )
                  = U )
                & ( ssList @ W ) ) ) ) ) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( app @ X2 @ X0 )
       != X1 )
      | ~ ( ssList @ X2 )
      | ( rearsegP @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax6]) ).

thf(zip_derived_cl1685,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__54 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl198,zip_derived_cl17]) ).

thf(zip_derived_cl199,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1691,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ~ ( ssList @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1685,zip_derived_cl199]) ).

thf(zip_derived_cl1819,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__53 )
      | ~ ( ssList @ ( cons @ sk__52 @ nil ) )
      | ( sk__47 != X0 )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl95,zip_derived_cl1691]) ).

thf(zip_derived_cl192,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1821,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( cons @ sk__52 @ nil ) )
      | ( sk__47 != X0 )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1819,zip_derived_cl192]) ).

thf(zip_derived_cl1908,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ sk__52 )
      | ( sk__47 != X0 )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl1821]) ).

thf(ax17,axiom,
    ssList @ nil ).

thf(zip_derived_cl83,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl200,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1909,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( rearsegP @ X0 @ sk__54 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1908,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ X1 @ X0 )
      | ( ( app @ ( sk__6 @ X0 @ X1 ) @ X0 )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax6]) ).

thf(ax36,axiom,
    ! [U: $i] :
      ( ( ssItem @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( memberP @ ( app @ V @ W ) @ U )
              <=> ( ( memberP @ V @ U )
                  | ( memberP @ W @ U ) ) ) ) ) ) ).

thf(zip_derived_cl109,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X1 @ X2 )
      | ( memberP @ ( app @ X0 @ X1 ) @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(cnf,[status(esa)],[ax36]) ).

thf(zip_derived_cl2238,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ X0 @ X2 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ ( sk__6 @ X2 @ X0 ) )
      | ~ ( memberP @ X2 @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl109]) ).

thf(zip_derived_cl2246,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssItem @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( memberP @ X2 @ X1 )
      | ~ ( ssList @ ( sk__6 @ X2 @ X0 ) )
      | ~ ( ssList @ X2 )
      | ~ ( rearsegP @ X0 @ X2 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2238]) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ X1 @ X0 )
      | ( ssList @ ( sk__6 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax6]) ).

thf(zip_derived_cl3686,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ X0 @ X2 )
      | ~ ( ssList @ X2 )
      | ~ ( memberP @ X2 @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( ssItem @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2246,zip_derived_cl16]) ).

thf(zip_derived_cl3689,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ sk__54 )
      | ~ ( memberP @ sk__54 @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( ssItem @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1909,zip_derived_cl3686]) ).

thf(zip_derived_cl199_002,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3695,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ X0 )
      | ~ ( memberP @ sk__54 @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( ssItem @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3689,zip_derived_cl199]) ).

thf(zip_derived_cl3696,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X1 )
      | ( memberP @ X0 @ X1 )
      | ~ ( memberP @ sk__54 @ X1 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3695]) ).

thf(zip_derived_cl3709,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__47 )
      | ~ ( memberP @ sk__54 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl3696]) ).

thf(zip_derived_cl190,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3710,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ sk__54 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3709,zip_derived_cl190]) ).

thf(zip_derived_cl3741,plain,
    ( ( memberP @ sk__53 @ sk__55 )
    | ( memberP @ sk__47 @ sk__55 )
    | ~ ( ssItem @ sk__55 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl194,zip_derived_cl3710]) ).

thf(zip_derived_cl193,plain,
    ssItem @ sk__55,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3743,plain,
    ( ( memberP @ sk__53 @ sk__55 )
    | ( memberP @ sk__47 @ sk__55 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3741,zip_derived_cl193]) ).

thf(zip_derived_cl82_003,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(ax81,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( ( cons @ V @ U )
            = ( app @ ( cons @ V @ nil ) @ U ) ) ) ) ).

thf(zip_derived_cl171,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( cons @ X0 @ X1 )
        = ( app @ ( cons @ X0 @ nil ) @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax81]) ).

thf(zip_derived_cl82_004,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl198_005,plain,
    ( ( app @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) @ sk__54 )
    = sk__47 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(ax82,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( app @ ( app @ U @ V ) @ W )
                = ( app @ U @ ( app @ V @ W ) ) ) ) ) ) ).

thf(zip_derived_cl172,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( app @ ( app @ X1 @ X0 ) @ X2 )
        = ( app @ X1 @ ( app @ X0 @ X2 ) ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax82]) ).

thf(zip_derived_cl3005,plain,
    ( ~ ( ssList @ ( cons @ sk__52 @ nil ) )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) )
    | ~ ( ssList @ sk__54 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl198,zip_derived_cl172]) ).

thf(zip_derived_cl199_006,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl192_007,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3023,plain,
    ( ~ ( ssList @ ( cons @ sk__52 @ nil ) )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3005,zip_derived_cl199,zip_derived_cl192]) ).

thf(zip_derived_cl5137,plain,
    ( ~ ( ssList @ nil )
    | ~ ( ssItem @ sk__52 )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3023]) ).

thf(zip_derived_cl83_008,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl200_009,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5138,plain,
    ( sk__47
    = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5137,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl5285,plain,
    ( ~ ( ssList @ sk__54 )
    | ~ ( ssItem @ sk__52 )
    | ( sk__47
      = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl171,zip_derived_cl5138]) ).

thf(zip_derived_cl199_010,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl200_011,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5287,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5285,zip_derived_cl199,zip_derived_cl200]) ).

thf(zip_derived_cl108,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X0 @ X1 )
      | ( memberP @ ( app @ X0 @ X2 ) @ X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference(cnf,[status(esa)],[ax36]) ).

thf(zip_derived_cl5413,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__53 )
      | ~ ( memberP @ sk__53 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssList @ ( cons @ sk__52 @ sk__54 ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl5287,zip_derived_cl108]) ).

thf(zip_derived_cl192_012,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5467,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ sk__53 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssList @ ( cons @ sk__52 @ sk__54 ) )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5413,zip_derived_cl192]) ).

thf(zip_derived_cl5603,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__54 )
      | ~ ( ssItem @ sk__52 )
      | ~ ( memberP @ sk__53 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl5467]) ).

thf(zip_derived_cl199_013,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl200_014,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5604,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ sk__53 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5603,zip_derived_cl199,zip_derived_cl200]) ).

thf(zip_derived_cl5628,plain,
    ( ( memberP @ sk__47 @ sk__55 )
    | ( memberP @ sk__47 @ sk__55 )
    | ~ ( ssItem @ sk__55 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3743,zip_derived_cl5604]) ).

thf(zip_derived_cl193_015,plain,
    ssItem @ sk__55,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5630,plain,
    ( ( memberP @ sk__47 @ sk__55 )
    | ( memberP @ sk__47 @ sk__55 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5628,zip_derived_cl193]) ).

thf(zip_derived_cl5631,plain,
    memberP @ sk__47 @ sk__55,
    inference(simplify,[status(thm)],[zip_derived_cl5630]) ).

thf(ax15,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( neq @ U @ V )
          <=> ( U != V ) ) ) ) ).

thf(zip_derived_cl81,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl203,plain,
    ( ( ( cons @ sk__51 @ nil )
      = sk__49 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1500,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ( cons @ sk__51 @ nil )
      = sk__49 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl203]) ).

thf(zip_derived_cl206,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl207,plain,
    ssList @ sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl206_016,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1552,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl207,zip_derived_cl206]) ).

thf(zip_derived_cl206_017,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_018,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl201,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1606,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1500,zip_derived_cl206,zip_derived_cl1552,zip_derived_cl206,zip_derived_cl83,zip_derived_cl201]) ).

thf(ax23,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( ( hd @ ( cons @ V @ U ) )
            = V ) ) ) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( hd @ ( cons @ X0 @ X1 ) )
        = X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax23]) ).

thf(zip_derived_cl2007,plain,
    ( ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 )
    | ( ( hd @ sk__47 )
      = sk__51 )
    | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1606,zip_derived_cl92]) ).

thf(zip_derived_cl83_019,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2008,plain,
    ( ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 )
    | ( ( hd @ sk__47 )
      = sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2007,zip_derived_cl83]) ).

thf(zip_derived_cl81_020,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl204,plain,
    ( ( ssItem @ sk__51 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1501,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ssItem @ sk__51 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl204]) ).

thf(zip_derived_cl206_021,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1552_022,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl207,zip_derived_cl206]) ).

thf(zip_derived_cl206_023,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_024,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1574,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1501,zip_derived_cl206,zip_derived_cl1552,zip_derived_cl206,zip_derived_cl83]) ).

thf(zip_derived_cl2011,plain,
    ( ( ( hd @ sk__47 )
      = sk__51 )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2008,zip_derived_cl1574]) ).

thf(ax22,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( nil != U )
       => ( ssItem @ ( hd @ U ) ) ) ) ).

thf(zip_derived_cl91,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

thf(zip_derived_cl2012,plain,
    ( ( sk__48 = nil )
    | ( nil = sk__47 )
    | ( ssItem @ sk__51 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2011,zip_derived_cl91]) ).

thf(zip_derived_cl190_025,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2013,plain,
    ( ( sk__48 = nil )
    | ( nil = sk__47 )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2012,zip_derived_cl190]) ).

thf(zip_derived_cl205,plain,
    ( ( nil = sk__49 )
    | ( nil != sk__50 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl201_026,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1549,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__50 ) ),
    inference(demod,[status(thm)],[zip_derived_cl205,zip_derived_cl201]) ).

thf(zip_derived_cl206_027,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1550,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1549,zip_derived_cl206]) ).

thf(zip_derived_cl2018,plain,
    ( ( ssItem @ sk__51 )
    | ( nil = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2013,zip_derived_cl1550]) ).

thf(zip_derived_cl2011_028,plain,
    ( ( ( hd @ sk__47 )
      = sk__51 )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2008,zip_derived_cl1574]) ).

thf(zip_derived_cl1606_029,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1500,zip_derived_cl206,zip_derived_cl1552,zip_derived_cl206,zip_derived_cl83,zip_derived_cl201]) ).

thf(ax25,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( ( tl @ ( cons @ V @ U ) )
            = U ) ) ) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( tl @ ( cons @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax25]) ).

thf(zip_derived_cl2016,plain,
    ( ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1606,zip_derived_cl94]) ).

thf(zip_derived_cl83_030,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2017,plain,
    ( ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl2016,zip_derived_cl83]) ).

thf(zip_derived_cl1574_031,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1501,zip_derived_cl206,zip_derived_cl1552,zip_derived_cl206,zip_derived_cl83]) ).

thf(zip_derived_cl2019,plain,
    ( ( ( tl @ sk__47 )
      = nil )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2017,zip_derived_cl1574]) ).

thf(ax78,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( nil != U )
       => ( ( cons @ ( hd @ U ) @ ( tl @ U ) )
          = U ) ) ) ).

thf(zip_derived_cl168,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax78]) ).

thf(zip_derived_cl2875,plain,
    ( ( sk__48 = nil )
    | ( nil = sk__47 )
    | ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2019,zip_derived_cl168]) ).

thf(zip_derived_cl190_032,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2878,plain,
    ( ( sk__48 = nil )
    | ( nil = sk__47 )
    | ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2875,zip_derived_cl190]) ).

thf(zip_derived_cl1550_033,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1549,zip_derived_cl206]) ).

thf(zip_derived_cl3121,plain,
    ( ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2878,zip_derived_cl1550]) ).

thf(zip_derived_cl3162,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2011,zip_derived_cl3121]) ).

thf(zip_derived_cl1550_034,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1549,zip_derived_cl206]) ).

thf(zip_derived_cl3261,plain,
    ( ( nil = sk__47 )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3162,zip_derived_cl1550]) ).

thf(ax37,axiom,
    ! [U: $i] :
      ( ( ssItem @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( memberP @ ( cons @ V @ W ) @ U )
              <=> ( ( U = V )
                  | ( memberP @ W @ U ) ) ) ) ) ) ).

thf(zip_derived_cl110,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ ( cons @ X0 @ X1 ) @ X2 )
      | ( X2 = X0 )
      | ( memberP @ X1 @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(cnf,[status(esa)],[ax37]) ).

thf(zip_derived_cl3268,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3261,zip_derived_cl110]) ).

thf(zip_derived_cl83_035,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3305,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3268,zip_derived_cl83]) ).

thf(zip_derived_cl5287_036,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5285,zip_derived_cl199,zip_derived_cl200]) ).

thf(ax3,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( ( memberP @ U @ V )
          <=> ? [W: $i] :
                ( ? [X: $i] :
                    ( ( ( app @ W @ ( cons @ V @ X ) )
                      = U )
                    & ( ssList @ X ) )
                & ( ssList @ W ) ) ) ) ) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ X3 @ ( cons @ X0 @ X1 ) )
       != X2 )
      | ~ ( ssList @ X3 )
      | ( memberP @ X2 @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(cnf,[status(esa)],[ax3]) ).

thf(zip_derived_cl5436,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__52 )
      | ~ ( ssList @ sk__54 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ sk__53 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5287,zip_derived_cl8]) ).

thf(zip_derived_cl200_037,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl199_038,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl192_039,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5490,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5436,zip_derived_cl200,zip_derived_cl199,zip_derived_cl192]) ).

thf(ax38,axiom,
    ! [U: $i] :
      ( ( ssItem @ U )
     => ~ ( memberP @ nil @ U ) ) ).

thf(zip_derived_cl113,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax38]) ).

thf(zip_derived_cl5949,plain,
    ( ~ ( ssList @ nil )
    | ( sk__47 != nil )
    | ~ ( ssItem @ sk__52 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5490,zip_derived_cl113]) ).

thf(zip_derived_cl83_040,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl200_041,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5954,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl7980,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl3305,zip_derived_cl5954]) ).

thf(zip_derived_cl113_042,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax38]) ).

thf(zip_derived_cl7981,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ sk__51 ) ),
    inference(clc,[status(thm)],[zip_derived_cl7980,zip_derived_cl113]) ).

thf(zip_derived_cl7983,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2018,zip_derived_cl7981]) ).

thf(zip_derived_cl5954_043,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl7984,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl7983,zip_derived_cl5954]) ).

thf(zip_derived_cl10971,plain,
    ( ~ ( ssItem @ sk__55 )
    | ( sk__55 = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5631,zip_derived_cl7984]) ).

thf(zip_derived_cl193_044,plain,
    ssItem @ sk__55,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10976,plain,
    sk__55 = sk__51,
    inference(demod,[status(thm)],[zip_derived_cl10971,zip_derived_cl193]) ).

thf(zip_derived_cl10976_045,plain,
    sk__55 = sk__51,
    inference(demod,[status(thm)],[zip_derived_cl10971,zip_derived_cl193]) ).

thf(zip_derived_cl11088,plain,
    ( ( memberP @ sk__53 @ sk__51 )
    | ( memberP @ sk__54 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl194,zip_derived_cl10976,zip_derived_cl10976]) ).

thf(zip_derived_cl3121_046,plain,
    ( ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2878,zip_derived_cl1550]) ).

thf(zip_derived_cl91_047,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

thf(zip_derived_cl91_048,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

thf(zip_derived_cl3121_049,plain,
    ( ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2878,zip_derived_cl1550]) ).

thf(zip_derived_cl111,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X1 != X0 )
      | ( memberP @ ( cons @ X0 @ X2 ) @ X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference(cnf,[status(esa)],[ax37]) ).

thf(zip_derived_cl2120,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl111]) ).

thf(zip_derived_cl2121,plain,
    ! [X0: $i,X1: $i] :
      ( ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2120]) ).

thf(zip_derived_cl3132,plain,
    ( ( nil = sk__47 )
    | ( memberP @ sk__47 @ ( hd @ sk__47 ) )
    | ~ ( ssList @ nil )
    | ~ ( ssItem @ ( hd @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3121,zip_derived_cl2121]) ).

thf(zip_derived_cl83_050,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3173,plain,
    ( ( nil = sk__47 )
    | ( memberP @ sk__47 @ ( hd @ sk__47 ) )
    | ~ ( ssItem @ ( hd @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3132,zip_derived_cl83]) ).

thf(zip_derived_cl5954_051,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl7548,plain,
    ( ( memberP @ sk__47 @ ( hd @ sk__47 ) )
    | ~ ( ssItem @ ( hd @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl3173,zip_derived_cl5954]) ).

thf(zip_derived_cl7549,plain,
    ( ~ ( ssList @ sk__47 )
    | ( nil = sk__47 )
    | ( memberP @ sk__47 @ ( hd @ sk__47 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl7548]) ).

thf(zip_derived_cl190_052,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7552,plain,
    ( ( nil = sk__47 )
    | ( memberP @ sk__47 @ ( hd @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl7549,zip_derived_cl190]) ).

thf(zip_derived_cl5954_053,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl7553,plain,
    memberP @ sk__47 @ ( hd @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl7552,zip_derived_cl5954]) ).

thf(zip_derived_cl7984_054,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl7983,zip_derived_cl5954]) ).

thf(zip_derived_cl10969,plain,
    ( ~ ( ssItem @ ( hd @ sk__47 ) )
    | ( ( hd @ sk__47 )
      = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl7553,zip_derived_cl7984]) ).

thf(zip_derived_cl11368,plain,
    ( ~ ( ssList @ sk__47 )
    | ( nil = sk__47 )
    | ( ( hd @ sk__47 )
      = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl10969]) ).

thf(zip_derived_cl190_055,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl11371,plain,
    ( ( nil = sk__47 )
    | ( ( hd @ sk__47 )
      = sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl11368,zip_derived_cl190]) ).

thf(zip_derived_cl5954_056,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl11372,plain,
    ( ( hd @ sk__47 )
    = sk__51 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl11371,zip_derived_cl5954]) ).

thf(zip_derived_cl11386,plain,
    ( ( ( cons @ sk__51 @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3121,zip_derived_cl11372]) ).

thf(zip_derived_cl5954_057,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl5949,zip_derived_cl83,zip_derived_cl200]) ).

thf(zip_derived_cl11387,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl11386,zip_derived_cl5954]) ).

thf(ax24,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( nil != U )
       => ( ssList @ ( tl @ U ) ) ) ) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl95_058,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl5138_059,plain,
    ( sk__47
    = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5137,zip_derived_cl83,zip_derived_cl200]) ).

thf(ax85,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( nil != U )
           => ( ( hd @ ( app @ U @ V ) )
              = ( hd @ U ) ) ) ) ) ).

thf(zip_derived_cl177,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( hd @ ( app @ X1 @ X0 ) )
        = ( hd @ X1 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax85]) ).

thf(zip_derived_cl5273,plain,
    ( ~ ( ssList @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) )
    | ( ( hd @ sk__47 )
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl5138,zip_derived_cl177]) ).

thf(zip_derived_cl192_060,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5302,plain,
    ( ~ ( ssList @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) )
    | ( ( hd @ sk__47 )
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5273,zip_derived_cl192]) ).

thf(zip_derived_cl5490_061,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5436,zip_derived_cl200,zip_derived_cl199,zip_derived_cl192]) ).

thf(zip_derived_cl7984_062,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl7983,zip_derived_cl5954]) ).

thf(zip_derived_cl10968,plain,
    ( ~ ( ssList @ sk__47 )
    | ( sk__47 != sk__47 )
    | ~ ( ssItem @ sk__52 )
    | ( sk__52 = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5490,zip_derived_cl7984]) ).

thf(zip_derived_cl190_063,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl200_064,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10974,plain,
    ( ( sk__47 != sk__47 )
    | ( sk__52 = sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl10968,zip_derived_cl190,zip_derived_cl200]) ).

thf(zip_derived_cl10975,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl10974]) ).

thf(zip_derived_cl11387_065,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl11386,zip_derived_cl5954]) ).

thf(zip_derived_cl11372_066,plain,
    ( ( hd @ sk__47 )
    = sk__51 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl11371,zip_derived_cl5954]) ).

thf(zip_derived_cl16209,plain,
    ( ~ ( ssList @ ( app @ sk__47 @ sk__54 ) )
    | ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5302,zip_derived_cl10975,zip_derived_cl11387,zip_derived_cl11372]) ).

thf(zip_derived_cl16210,plain,
    ( ~ ( ssList @ sk__47 )
    | ~ ( ssList @ sk__54 )
    | ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl95,zip_derived_cl16209]) ).

thf(zip_derived_cl190_067,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl199_068,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl16213,plain,
    ( ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl16210,zip_derived_cl190,zip_derived_cl199]) ).

thf(zip_derived_cl168_069,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax78]) ).

thf(zip_derived_cl16373,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl16213,zip_derived_cl168]) ).

thf(zip_derived_cl192_070,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl16382,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl16373,zip_derived_cl192]) ).

thf(zip_derived_cl16383,plain,
    ( ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 )
    | ( nil = sk__53 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl16382]) ).

thf(zip_derived_cl2121_071,plain,
    ! [X0: $i,X1: $i] :
      ( ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2120]) ).

thf(zip_derived_cl16531,plain,
    ( ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 )
    | ~ ( ssList @ ( tl @ sk__53 ) )
    | ~ ( ssItem @ sk__51 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl16383,zip_derived_cl2121]) ).

thf(zip_derived_cl200_072,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10975_073,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl10974]) ).

thf(zip_derived_cl10981,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl16708,plain,
    ( ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 )
    | ~ ( ssList @ ( tl @ sk__53 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl16531,zip_derived_cl10981]) ).

thf(zip_derived_cl17233,plain,
    ( ~ ( ssList @ sk__53 )
    | ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl16708]) ).

thf(zip_derived_cl192_074,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl17234,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl17233,zip_derived_cl192]) ).

thf(zip_derived_cl17235,plain,
    ( ( memberP @ sk__53 @ sk__51 )
    | ( nil = sk__53 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl17234]) ).

thf(zip_derived_cl5287_075,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5285,zip_derived_cl199,zip_derived_cl200]) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ X1 @ X0 )
      | ( ( app @ ( sk__2 @ X0 @ X1 ) @ ( cons @ X0 @ ( sk__3 @ X0 @ X1 ) ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax3]) ).

thf(zip_derived_cl82_076,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(ax71,axiom,
    ! [U: $i] :
      ( ( ssItem @ U )
     => ( duplicatefreeP @ ( cons @ U @ nil ) ) ) ).

thf(zip_derived_cl159,plain,
    ! [X0: $i] :
      ( ( duplicatefreeP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax71]) ).

thf(ax13,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( duplicatefreeP @ U )
      <=> ! [V: $i] :
            ( ( ssItem @ V )
           => ! [W: $i] :
                ( ( ssItem @ W )
               => ! [X: $i] :
                    ( ( ssList @ X )
                   => ! [Y: $i] :
                        ( ( ssList @ Y )
                       => ! [Z: $i] :
                            ( ( ssList @ Z )
                           => ( ( ( app @ ( app @ X @ ( cons @ V @ Y ) ) @ ( cons @ W @ Z ) )
                                = U )
                             => ( V != W ) ) ) ) ) ) ) ) ) ).

thf(zip_derived_cl72,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( duplicatefreeP @ X0 )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X2 )
      | ( X3 != X1 )
      | ( ( app @ ( app @ X4 @ ( cons @ X3 @ X2 ) ) @ ( cons @ X1 @ X5 ) )
       != X0 )
      | ~ ( ssList @ X5 )
      | ~ ( ssList @ X4 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax13]) ).

thf(zip_derived_cl1517,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ X5 )
      | ~ ( ssList @ X4 )
      | ( ( app @ ( app @ X5 @ ( cons @ X3 @ X2 ) ) @ ( cons @ X1 @ X4 ) )
       != ( cons @ X0 @ nil ) )
      | ( X3 != X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl159,zip_derived_cl72]) ).

thf(zip_derived_cl3757,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( app @ X3 @ ( cons @ X0 @ X1 ) ) @ ( cons @ X0 @ X2 ) )
       != ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X3 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ X4 @ nil ) )
      | ~ ( ssItem @ X4 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1517]) ).

thf(zip_derived_cl3758,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X4 )
      | ~ ( ssList @ ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X3 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X3 @ ( cons @ X0 @ X1 ) ) @ ( cons @ X0 @ X2 ) )
       != ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3757]) ).

thf(zip_derived_cl3759,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X4 )
      | ~ ( ssItem @ X3 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3758]) ).

thf(zip_derived_cl83_077,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3763,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X4 )
      | ~ ( ssItem @ X3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3759,zip_derived_cl83]) ).

thf(zip_derived_cl3764,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X3 )
      | ~ ( ssList @ X4 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3763]) ).

thf(zip_derived_cl3782,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ ( sk__2 @ X3 @ X0 ) )
      | ~ ( ssItem @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3764]) ).

thf(zip_derived_cl3797,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X1 )
      | ~ ( ssList @ ( sk__2 @ X3 @ X0 ) )
      | ~ ( ssList @ X2 )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ~ ( ssItem @ X3 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3782]) ).

thf(zip_derived_cl7,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ X1 @ X0 )
      | ( ssList @ ( sk__2 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax3]) ).

thf(zip_derived_cl6511,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3797,zip_derived_cl7]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ X1 @ X0 )
      | ( ssList @ ( sk__3 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax3]) ).

thf(zip_derived_cl6512,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssItem @ X3 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl6511,zip_derived_cl5]) ).

thf(zip_derived_cl6521,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ sk__54 )
      | ( sk__47
       != ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ sk__52 )
      | ~ ( memberP @ sk__53 @ sk__52 )
      | ~ ( ssList @ sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5287,zip_derived_cl6512]) ).

thf(zip_derived_cl199_078,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl200_079,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl192_080,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6533,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( sk__47
       != ( cons @ X0 @ nil ) )
      | ~ ( memberP @ sk__53 @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6521,zip_derived_cl199,zip_derived_cl200,zip_derived_cl192]) ).

thf(zip_derived_cl10975_081,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl10974]) ).

thf(zip_derived_cl11032,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( sk__47
       != ( cons @ X0 @ nil ) )
      | ~ ( memberP @ sk__53 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6533,zip_derived_cl10975]) ).

thf(zip_derived_cl17249,plain,
    ! [X0: $i] :
      ( ( nil = sk__53 )
      | ~ ( ssItem @ X0 )
      | ( sk__47
       != ( cons @ X0 @ nil ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl17235,zip_derived_cl11032]) ).

thf(zip_derived_cl17265,plain,
    ( ( nil = sk__53 )
    | ~ ( ssItem @ sk__51 )
    | ( sk__47 != sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl11387,zip_derived_cl17249]) ).

thf(zip_derived_cl10981_082,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl17268,plain,
    ( ( nil = sk__53 )
    | ( sk__47 != sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl17265,zip_derived_cl10981]) ).

thf(zip_derived_cl17269,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl17268]) ).

thf(zip_derived_cl17278,plain,
    ( ( memberP @ nil @ sk__51 )
    | ( memberP @ sk__54 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl11088,zip_derived_cl17269]) ).

thf(ax28,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( app @ nil @ U )
        = U ) ) ).

thf(zip_derived_cl97,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax28]) ).

thf(zip_derived_cl82_083,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl5287_084,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5285,zip_derived_cl199,zip_derived_cl200]) ).

thf(ax80,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( ( app @ V @ W )
                  = ( app @ V @ U ) )
               => ( W = U ) ) ) ) ) ).

thf(zip_derived_cl170,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( app @ X0 @ X2 )
       != ( app @ X0 @ X1 ) )
      | ( X2 = X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax80]) ).

thf(zip_derived_cl5431,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__53 )
      | ( ( app @ sk__53 @ X0 )
       != sk__47 )
      | ( X0
        = ( cons @ sk__52 @ sk__54 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl5287,zip_derived_cl170]) ).

thf(zip_derived_cl192_085,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5485,plain,
    ! [X0: $i] :
      ( ( ( app @ sk__53 @ X0 )
       != sk__47 )
      | ( X0
        = ( cons @ sk__52 @ sk__54 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5431,zip_derived_cl192]) ).

thf(zip_derived_cl17269_086,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl17268]) ).

thf(zip_derived_cl10975_087,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl10974]) ).

thf(zip_derived_cl10975_088,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl10974]) ).

thf(zip_derived_cl17569,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
       != sk__47 )
      | ( X0
        = ( cons @ sk__51 @ sk__54 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5485,zip_derived_cl17269,zip_derived_cl10975,zip_derived_cl10975]) ).

thf(zip_derived_cl17570,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__54 )
      | ~ ( ssItem @ sk__51 )
      | ( ( app @ nil @ X0 )
       != sk__47 )
      | ( X0
        = ( cons @ sk__51 @ sk__54 ) )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl17569]) ).

thf(zip_derived_cl199_089,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10981_090,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl17571,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
       != sk__47 )
      | ( X0
        = ( cons @ sk__51 @ sk__54 ) )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl17570,zip_derived_cl199,zip_derived_cl10981]) ).

thf(zip_derived_cl17584,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( X0 != sk__47 )
      | ( X0
        = ( cons @ sk__51 @ sk__54 ) )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl97,zip_derived_cl17571]) ).

thf(zip_derived_cl17591,plain,
    ! [X0: $i] :
      ( ( X0
        = ( cons @ sk__51 @ sk__54 ) )
      | ( X0 != sk__47 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl17584]) ).

thf(zip_derived_cl17603,plain,
    ( ~ ( ssList @ sk__47 )
    | ( sk__47
      = ( cons @ sk__51 @ sk__54 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl17591]) ).

thf(zip_derived_cl190_091,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl17604,plain,
    ( sk__47
    = ( cons @ sk__51 @ sk__54 ) ),
    inference(demod,[status(thm)],[zip_derived_cl17603,zip_derived_cl190]) ).

thf(zip_derived_cl94_092,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( tl @ ( cons @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax25]) ).

thf(zip_derived_cl17623,plain,
    ( ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = sk__54 )
    | ~ ( ssList @ sk__54 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl17604,zip_derived_cl94]) ).

thf(zip_derived_cl10981_093,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl11387_094,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl11386,zip_derived_cl5954]) ).

thf(zip_derived_cl94_095,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( tl @ ( cons @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax25]) ).

thf(zip_derived_cl11460,plain,
    ( ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl11387,zip_derived_cl94]) ).

thf(zip_derived_cl10981_096,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl83_097,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl11635,plain,
    ( ( tl @ sk__47 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl11460,zip_derived_cl10981,zip_derived_cl83]) ).

thf(zip_derived_cl199_098,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl17804,plain,
    nil = sk__54,
    inference(demod,[status(thm)],[zip_derived_cl17623,zip_derived_cl10981,zip_derived_cl11635,zip_derived_cl199]) ).

thf(zip_derived_cl18028,plain,
    ( ( memberP @ nil @ sk__51 )
    | ( memberP @ nil @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl17278,zip_derived_cl17804]) ).

thf(zip_derived_cl18029,plain,
    memberP @ nil @ sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl18028]) ).

thf(zip_derived_cl113_099,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax38]) ).

thf(zip_derived_cl18166,plain,
    ~ ( ssItem @ sk__51 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl18029,zip_derived_cl113]) ).

thf(zip_derived_cl10981_100,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl10975]) ).

thf(zip_derived_cl18176,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl18166,zip_derived_cl10981]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC297+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6pPfpV6Brw true
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 17:21:19 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in FO mode
% 0.21/0.65  % Total configuration time : 435
% 0.21/0.65  % Estimated wc time : 1092
% 0.21/0.65  % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.69  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.76  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.78  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.78  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.90/0.80  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 26.54/4.42  % Solved by fo/fo6_bce.sh.
% 26.54/4.42  % BCE start: 209
% 26.54/4.42  % BCE eliminated: 4
% 26.54/4.42  % PE start: 205
% 26.54/4.42  logic: eq
% 26.54/4.42  % PE eliminated: 5
% 26.54/4.42  % done 2511 iterations in 3.695s
% 26.54/4.42  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 26.54/4.42  % SZS output start Refutation
% See solution above
% 26.54/4.42  
% 26.54/4.42  
% 26.54/4.42  % Terminating...
% 26.91/4.49  % Runner terminated.
% 26.91/4.51  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------