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Zipperpin---2.1.9999.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWC377+1 : TPTP v9.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KwDjK5i86G true

% Computer : n018.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 Oct  2 04:59:34 PM UTC 2025

% Result   : Theorem 270.13s 39.63s
% Output   : Refutation 270.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  159 (  38 unt;   0 typ;   0 def)
%            Number of atoms       :  503 ( 154 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives : 1207 ( 213   ~; 307   |;   8   &; 650   @)
%                                         (   3 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   9 con; 0-2 aty)
%            Number of variables   :  102 (   0   ^; 102   !;   0   ?; 102   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(zip_derived_cl193,plain,
    ( ( memberP @ sk__48 @ sk__53 )
    | ( memberP @ sk__47 @ sk__53 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl193_001,plain,
    ( ( memberP @ sk__48 @ sk__53 )
    | ( memberP @ sk__47 @ sk__53 ) ),
    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(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_cl198,plain,
    ( ( ( app @ sk__52 @ ( cons @ sk__51 @ nil ) )
      = sk__50 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1485,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ( app @ sk__52 @ ( cons @ sk__51 @ nil ) )
      = sk__50 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl198]) ).

thf(zip_derived_cl201,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl202,plain,
    ssList @ sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl201_002,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1537,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl201]) ).

thf(zip_derived_cl201_003,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(ax17,axiom,
    ssList @ nil ).

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

thf(zip_derived_cl201_004,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1658,plain,
    ( ( sk__48 = nil )
    | ( ( app @ sk__52 @ ( cons @ sk__51 @ nil ) )
      = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1485,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83,zip_derived_cl201]) ).

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_cl107,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ ( app @ X0 @ X1 ) @ X2 )
      | ( memberP @ X0 @ X2 )
      | ( memberP @ X1 @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(cnf,[status(esa)],[ax36]) ).

thf(zip_derived_cl2198,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssList @ sk__52 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1658,zip_derived_cl107]) ).

thf(zip_derived_cl81_005,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl196,plain,
    ( ( ssList @ sk__52 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1483,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ssList @ sk__52 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl196]) ).

thf(zip_derived_cl201_006,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1537_007,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl201]) ).

thf(zip_derived_cl201_008,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_009,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1551,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl5341,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2198,zip_derived_cl1551]) ).

thf(zip_derived_cl5342,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl5341]) ).

thf(zip_derived_cl83_010,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl5343,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl5342,zip_derived_cl83]) ).

thf(zip_derived_cl81_011,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl199,plain,
    ( ( ssItem @ sk__51 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1486,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ssItem @ sk__51 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl199]) ).

thf(zip_derived_cl201_012,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1537_013,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl201]) ).

thf(zip_derived_cl201_014,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_015,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1562,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl15060,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl5343,zip_derived_cl1562]) ).

thf(zip_derived_cl82_016,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl81_017,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl197,plain,
    ( ( ( app @ ( cons @ sk__51 @ nil ) @ sk__52 )
      = sk__49 )
    | ~ ( neq @ sk__50 @ nil ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1484,plain,
    ( ~ ( ssList @ sk__50 )
    | ( sk__50 = nil )
    | ~ ( ssList @ nil )
    | ( ( app @ ( cons @ sk__51 @ nil ) @ sk__52 )
      = sk__49 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl81,zip_derived_cl197]) ).

thf(zip_derived_cl201_018,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1537_019,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl201]) ).

thf(zip_derived_cl201_020,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_021,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl195,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1632,plain,
    ( ( sk__48 = nil )
    | ( ( app @ ( cons @ sk__51 @ nil ) @ sk__52 )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1484,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83,zip_derived_cl195]) ).

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_cl2219,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssList @ sk__52 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1632,zip_derived_cl108]) ).

thf(zip_derived_cl1551_022,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl5400,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2219,zip_derived_cl1551]) ).

thf(zip_derived_cl5401,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( sk__48 = nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl5400]) ).

thf(zip_derived_cl83_023,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl5402,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( sk__48 = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl5401,zip_derived_cl83]) ).

thf(zip_derived_cl1562_024,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl15245,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl5402,zip_derived_cl1562]) ).

thf(zip_derived_cl15253,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil )
      | ( sk__48 = nil )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl15060,zip_derived_cl15245]) ).

thf(zip_derived_cl15263,plain,
    ! [X0: $i] :
      ( ( memberP @ sk__47 @ X0 )
      | ( sk__48 = nil )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl15253]) ).

thf(zip_derived_cl1632_025,plain,
    ( ( sk__48 = nil )
    | ( ( app @ ( cons @ sk__51 @ nil ) @ sk__52 )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1484,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83,zip_derived_cl195]) ).

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_cl2833,plain,
    ( ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 )
    | ( ( cons @ sk__51 @ sk__52 )
      = sk__47 )
    | ~ ( ssList @ sk__52 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1632,zip_derived_cl171]) ).

thf(zip_derived_cl1562_026,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl2871,plain,
    ( ~ ( ssList @ sk__52 )
    | ( ( cons @ sk__51 @ sk__52 )
      = sk__47 )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2833,zip_derived_cl1562]) ).

thf(zip_derived_cl1551_027,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl2872,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ sk__52 )
      = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2871,zip_derived_cl1551]) ).

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_cl112,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ X1 @ X2 )
      | ( memberP @ ( cons @ X0 @ X1 ) @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(cnf,[status(esa)],[ax37]) ).

thf(zip_derived_cl2880,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssList @ sk__52 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2872,zip_derived_cl112]) ).

thf(zip_derived_cl1562_028,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl6347,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ sk__52 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2880,zip_derived_cl1562]) ).

thf(zip_derived_cl1551_029,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl6348,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl6347,zip_derived_cl1551]) ).

thf(zip_derived_cl98184,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil )
      | ( memberP @ sk__47 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl15263,zip_derived_cl6348]) ).

thf(zip_derived_cl98197,plain,
    ( ( memberP @ sk__47 @ sk__53 )
    | ~ ( ssItem @ sk__53 )
    | ( sk__48 = nil )
    | ( memberP @ sk__47 @ sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl193,zip_derived_cl98184]) ).

thf(zip_derived_cl194,plain,
    ssItem @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl98213,plain,
    ( ( memberP @ sk__47 @ sk__53 )
    | ( sk__48 = nil )
    | ( memberP @ sk__47 @ sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl98197,zip_derived_cl194]) ).

thf(zip_derived_cl98214,plain,
    ( ( sk__48 = nil )
    | ( memberP @ sk__47 @ sk__53 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl98213]) ).

thf(zip_derived_cl2872_030,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ sk__52 )
      = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2871,zip_derived_cl1551]) ).

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_cl2879,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( ssList @ sk__52 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2872,zip_derived_cl110]) ).

thf(zip_derived_cl1562_031,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl6335,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ sk__52 )
      | ( memberP @ sk__52 @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2879,zip_derived_cl1562]) ).

thf(zip_derived_cl1551_032,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl6336,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ sk__52 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl6335,zip_derived_cl1551]) ).

thf(zip_derived_cl82_033,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl1658_034,plain,
    ( ( sk__48 = nil )
    | ( ( app @ sk__52 @ ( cons @ sk__51 @ nil ) )
      = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1485,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83,zip_derived_cl201]) ).

thf(zip_derived_cl108_035,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_cl2223,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssList @ sk__52 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1658,zip_derived_cl108]) ).

thf(zip_derived_cl1551_036,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl5405,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2223,zip_derived_cl1551]) ).

thf(zip_derived_cl5406,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( sk__48 = nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl5405]) ).

thf(zip_derived_cl83_037,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl5407,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( sk__48 = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl5406,zip_derived_cl83]) ).

thf(zip_derived_cl1562_038,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl7023,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ sk__52 @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl5407,zip_derived_cl1562]) ).

thf(zip_derived_cl7026,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( sk__48 = nil )
      | ( sk__48 = nil )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6336,zip_derived_cl7023]) ).

thf(zip_derived_cl7029,plain,
    ! [X0: $i] :
      ( ( memberP @ sk__48 @ X0 )
      | ( sk__48 = nil )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7026]) ).

thf(zip_derived_cl192,plain,
    ( ~ ( memberP @ sk__48 @ sk__53 )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl31185,plain,
    ( ~ ( ssItem @ sk__53 )
    | ( sk__53 = sk__51 )
    | ~ ( memberP @ sk__47 @ sk__53 )
    | ( sk__48 = nil )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl7029,zip_derived_cl192]) ).

thf(zip_derived_cl194_039,plain,
    ssItem @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl31192,plain,
    ( ( sk__53 = sk__51 )
    | ~ ( memberP @ sk__47 @ sk__53 )
    | ( sk__48 = nil )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl31185,zip_derived_cl194]) ).

thf(zip_derived_cl31193,plain,
    ( ( sk__48 = nil )
    | ~ ( memberP @ sk__47 @ sk__53 )
    | ( sk__53 = sk__51 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl31192]) ).

thf(zip_derived_cl98249,plain,
    ( ( sk__48 = nil )
    | ( sk__48 = nil )
    | ( sk__53 = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl98214,zip_derived_cl31193]) ).

thf(zip_derived_cl98252,plain,
    ( ( sk__53 = sk__51 )
    | ( sk__48 = nil ) ),
    inference(simplify,[status(thm)],[zip_derived_cl98249]) ).

thf(zip_derived_cl192_040,plain,
    ( ~ ( memberP @ sk__48 @ sk__53 )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl98257,plain,
    ( ( sk__48 = nil )
    | ~ ( memberP @ sk__48 @ sk__51 )
    | ~ ( memberP @ sk__47 @ sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl98252,zip_derived_cl192]) ).

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_cl2124,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_cl2125,plain,
    ! [X0: $i,X1: $i] :
      ( ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2124]) ).

thf(zip_derived_cl82_041,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl1658_042,plain,
    ( ( sk__48 = nil )
    | ( ( app @ sk__52 @ ( cons @ sk__51 @ nil ) )
      = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1485,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83,zip_derived_cl201]) ).

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_cl2250,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssList @ sk__52 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1658,zip_derived_cl109]) ).

thf(zip_derived_cl1551_043,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl5439,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ sk__51 @ nil ) )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2250,zip_derived_cl1551]) ).

thf(zip_derived_cl5440,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( sk__48 = nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl5439]) ).

thf(zip_derived_cl83_044,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl5441,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( ssItem @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( sk__48 = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl5440,zip_derived_cl83]) ).

thf(zip_derived_cl1562_045,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl15268,plain,
    ! [X0: $i] :
      ( ( sk__48 = nil )
      | ~ ( memberP @ ( cons @ sk__51 @ nil ) @ X0 )
      | ( memberP @ sk__48 @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl5441,zip_derived_cl1562]) ).

thf(zip_derived_cl15274,plain,
    ( ~ ( ssItem @ sk__51 )
    | ~ ( ssList @ nil )
    | ( sk__48 = nil )
    | ( memberP @ sk__48 @ sk__51 )
    | ~ ( ssItem @ sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2125,zip_derived_cl15268]) ).

thf(zip_derived_cl83_046,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl15283,plain,
    ( ~ ( ssItem @ sk__51 )
    | ( sk__48 = nil )
    | ( memberP @ sk__48 @ sk__51 )
    | ~ ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl15274,zip_derived_cl83]) ).

thf(zip_derived_cl15284,plain,
    ( ( memberP @ sk__48 @ sk__51 )
    | ( sk__48 = nil )
    | ~ ( ssItem @ sk__51 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl15283]) ).

thf(zip_derived_cl1562_047,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl15290,plain,
    ( ( sk__48 = nil )
    | ( memberP @ sk__48 @ sk__51 ) ),
    inference(clc,[status(thm)],[zip_derived_cl15284,zip_derived_cl1562]) ).

thf(zip_derived_cl98278,plain,
    ( ~ ( memberP @ sk__47 @ sk__51 )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl98257,zip_derived_cl15290]) ).

thf(zip_derived_cl2872_048,plain,
    ( ( sk__48 = nil )
    | ( ( cons @ sk__51 @ sk__52 )
      = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2871,zip_derived_cl1551]) ).

thf(zip_derived_cl2125_049,plain,
    ! [X0: $i,X1: $i] :
      ( ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2124]) ).

thf(zip_derived_cl2883,plain,
    ( ( sk__48 = nil )
    | ( memberP @ sk__47 @ sk__51 )
    | ~ ( ssList @ sk__52 )
    | ~ ( ssItem @ sk__51 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2872,zip_derived_cl2125]) ).

thf(zip_derived_cl1551_050,plain,
    ( ( sk__48 = nil )
    | ( ssList @ sk__52 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1483,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl3331,plain,
    ( ~ ( ssItem @ sk__51 )
    | ( memberP @ sk__47 @ sk__51 )
    | ( sk__48 = nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl2883,zip_derived_cl1551]) ).

thf(zip_derived_cl1562_051,plain,
    ( ( sk__48 = nil )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1486,zip_derived_cl201,zip_derived_cl1537,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl3332,plain,
    ( ( sk__48 = nil )
    | ( memberP @ sk__47 @ sk__51 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3331,zip_derived_cl1562]) ).

thf(zip_derived_cl98279,plain,
    sk__48 = nil,
    inference(clc,[status(thm)],[zip_derived_cl98278,zip_derived_cl3332]) ).

thf(zip_derived_cl98281,plain,
    ( ( memberP @ nil @ sk__53 )
    | ( memberP @ sk__47 @ sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl193,zip_derived_cl98279]) ).

thf(zip_derived_cl192_052,plain,
    ( ~ ( memberP @ sk__48 @ sk__53 )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl98279_053,plain,
    sk__48 = nil,
    inference(clc,[status(thm)],[zip_derived_cl98278,zip_derived_cl3332]) ).

thf(zip_derived_cl98280,plain,
    ( ~ ( memberP @ nil @ sk__53 )
    | ~ ( memberP @ sk__47 @ sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl192,zip_derived_cl98279]) ).

thf(zip_derived_cl200,plain,
    ( ( nil = sk__49 )
    | ( nil != sk__50 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl195_054,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1534,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__50 ) ),
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl195]) ).

thf(zip_derived_cl201_055,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1535,plain,
    ( ( nil = sk__47 )
    | ( nil != sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1534,zip_derived_cl201]) ).

thf(zip_derived_cl98279_056,plain,
    sk__48 = nil,
    inference(clc,[status(thm)],[zip_derived_cl98278,zip_derived_cl3332]) ).

thf(zip_derived_cl98283,plain,
    ( ( nil = sk__47 )
    | ( nil != nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl1535,zip_derived_cl98279]) ).

thf(zip_derived_cl98284,plain,
    nil = sk__47,
    inference(simplify,[status(thm)],[zip_derived_cl98283]) ).

thf(zip_derived_cl98375,plain,
    ( ~ ( memberP @ nil @ sk__53 )
    | ~ ( memberP @ nil @ sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl98280,zip_derived_cl98284]) ).

thf(zip_derived_cl98376,plain,
    ~ ( memberP @ nil @ sk__53 ),
    inference(simplify,[status(thm)],[zip_derived_cl98375]) ).

thf(zip_derived_cl98284_057,plain,
    nil = sk__47,
    inference(simplify,[status(thm)],[zip_derived_cl98283]) ).

thf(zip_derived_cl98376_058,plain,
    ~ ( memberP @ nil @ sk__53 ),
    inference(simplify,[status(thm)],[zip_derived_cl98375]) ).

thf(zip_derived_cl98431,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl98281,zip_derived_cl98376,zip_derived_cl98284,zip_derived_cl98376]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SWC377+1 : TPTP v9.2.0. Released v2.4.0.
% 0.14/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KwDjK5i86G true
% 0.14/0.37  % Computer : n018.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Wed Oct  1 17:08:53 EDT 2025
% 0.14/0.37  % CPUTime  : 
% 0.14/0.37  % Running portfolio for 300 s
% 0.14/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37  % Number of cores: 8
% 0.14/0.37  % Python version: Python 3.6.8
% 0.14/0.37  % Running in FO mode
% 0.49/0.61  % Total configuration time : 435
% 0.49/0.61  % Estimated wc time : 1092
% 0.49/0.61  % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.66  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.71  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.72  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.73  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 270.13/39.63  % Solved by fo/fo6_bce.sh.
% 270.13/39.63  % BCE start: 204
% 270.13/39.63  % BCE eliminated: 4
% 270.13/39.63  % PE start: 200
% 270.13/39.63  logic: eq
% 270.13/39.63  % PE eliminated: 4
% 270.13/39.63  % done 12636 iterations in 38.942s
% 270.13/39.63  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 270.13/39.63  % SZS output start Refutation
% See solution above
% 270.13/39.64  
% 270.13/39.64  
% 270.13/39.64  % Terminating...
% 270.80/39.74  % Runner terminated.
% 270.85/39.76  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------