TSTP Solution File: SWC072+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.sbai3tWb3k true

% Computer : n028.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 21:28:57 EDT 2023

% Result   : Theorem 260.58s 38.13s
% Output   : Refutation 260.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   84
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  656 ( 226 unt;  23 typ;   0 def)
%            Number of atoms       : 1827 ( 579 equ;   0 cnn)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives : 5502 ( 985   ~;1070   |;  41   &;3323   @)
%                                         (   9 <=>;  74  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;   6 con; 0-2 aty)
%            Number of variables   :  583 (   0   ^; 566   !;  17   ?; 583   :)

% Comments : 
%------------------------------------------------------------------------------
thf(frontsegP_type,type,
    frontsegP: $i > $i > $o ).

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

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

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

thf(sk__4_type,type,
    sk__4: $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__43_type,type,
    sk__43: $i > $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(sk__7_type,type,
    sk__7: $i > $i > $i ).

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

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

thf(sk__44_type,type,
    sk__44: $i > $i ).

thf(sk__5_type,type,
    sk__5: $i > $i > $i ).

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

thf(singletonP_type,type,
    singletonP: $i > $o ).

thf(segmentP_type,type,
    segmentP: $i > $i > $o ).

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(ax55,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( segmentP @ U @ U ) ) ).

thf(zip_derived_cl134,plain,
    ! [X0: $i] :
      ( ( segmentP @ X0 @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax55]) ).

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

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

thf(zip_derived_cl193,plain,
    ! [X0: $i] :
      ( ~ ( segmentP @ sk__47 @ X0 )
      | ~ ( segmentP @ sk__48 @ X0 )
      | ~ ( neq @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl238,plain,
    ( ~ ( ssList @ sk__47 )
    | ~ ( segmentP @ sk__48 @ sk__47 )
    | ~ ( neq @ sk__47 @ nil )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl134,zip_derived_cl193]) ).

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

thf(zip_derived_cl190_001,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl240,plain,
    ( ~ ( segmentP @ sk__48 @ sk__47 )
    | ~ ( neq @ sk__47 @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl238,zip_derived_cl190,zip_derived_cl190]) ).

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(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(zip_derived_cl91_002,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

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_cl81_003,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl81_004,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl195,plain,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( neq @ sk__50 @ nil )
      | ~ ( ssList @ X1 )
      | ( sk__49 = X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ X3 @ X2 )
       != X1 )
      | ~ ( neq @ nil @ sk__50 )
      | ( ( hd @ sk__50 )
       != X4 )
      | ( ( cons @ X4 @ nil )
       != X2 )
      | ~ ( ssItem @ X4 )
      | ( ( tl @ sk__50 )
       != X3 )
      | ~ ( neq @ nil @ sk__50 )
      | ~ ( ssList @ X3 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl206,plain,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssList @ X3 )
      | ( ( tl @ sk__50 )
       != X3 )
      | ~ ( ssItem @ X4 )
      | ( ( cons @ X4 @ nil )
       != X2 )
      | ( ( hd @ sk__50 )
       != X4 )
      | ~ ( neq @ nil @ sk__50 )
      | ( ( app @ X3 @ X2 )
       != X1 )
      | ~ ( ssList @ X2 )
      | ( sk__49 = X1 )
      | ~ ( ssList @ X1 )
      | ~ ( neq @ sk__50 @ nil ) ),
    inference(simplify,[status(thm)],[zip_derived_cl195]) ).

thf(zip_derived_cl197,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_005,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_006,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl194,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_007,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl207,plain,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssList @ X3 )
      | ( ( tl @ sk__48 )
       != X3 )
      | ~ ( ssItem @ X4 )
      | ( ( cons @ X4 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X4 )
      | ~ ( neq @ nil @ sk__48 )
      | ( ( app @ X3 @ X2 )
       != X1 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X1 )
      | ~ ( ssList @ X1 )
      | ~ ( neq @ sk__48 @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl206,zip_derived_cl197,zip_derived_cl197,zip_derived_cl197,zip_derived_cl194,zip_derived_cl197]) ).

thf(zip_derived_cl1609,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ nil )
      | ( nil = sk__48 )
      | ~ ( ssList @ sk__48 )
      | ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 )
      | ~ ( neq @ sk__48 @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl207]) ).

thf(ax17,axiom,
    ssList @ nil ).

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

thf(zip_derived_cl198,plain,
    ssList @ sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_008,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl201,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl1611,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( nil = sk__48 )
      | ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 )
      | ~ ( neq @ sk__48 @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl1609,zip_derived_cl83,zip_derived_cl201]) ).

thf(zip_derived_cl196,plain,
    ( ( nil != sk__50 )
    | ( nil = sk__49 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_009,plain,
    sk__48 = sk__50,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl194_010,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl202,plain,
    ( ( nil != sk__48 )
    | ( nil = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl197,zip_derived_cl194]) ).

thf(zip_derived_cl192,plain,
    ( ( nil != sk__47 )
    | ( nil != sk__48 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl203,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1612,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 )
      | ~ ( neq @ sk__48 @ nil ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1611,zip_derived_cl203]) ).

thf(zip_derived_cl1614,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( sk__48 = nil )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl1612]) ).

thf(zip_derived_cl201_011,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl83_012,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1616,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( sk__48 = nil )
      | ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1614,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl203_013,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1617,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ sk__48 )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( ( cons @ X1 @ nil )
       != X2 )
      | ( ( hd @ sk__48 )
       != X1 )
      | ( ( app @ X0 @ X2 )
       != X3 )
      | ~ ( ssList @ X2 )
      | ( sk__47 = X3 )
      | ~ ( ssList @ X3 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1616,zip_derived_cl203]) ).

thf(zip_derived_cl1618,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( tl @ sk__48 ) @ X1 )
       != X0 )
      | ( ( hd @ sk__48 )
       != X2 )
      | ( ( cons @ X2 @ nil )
       != X1 )
      | ~ ( ssItem @ X2 )
      | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1617]) ).

thf(zip_derived_cl1681,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( nil = sk__48 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( tl @ sk__48 ) @ X1 )
       != X0 )
      | ( ( hd @ sk__48 )
       != X2 )
      | ( ( cons @ X2 @ nil )
       != X1 )
      | ~ ( ssItem @ X2 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1618]) ).

thf(zip_derived_cl201_014,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl1682,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( nil = sk__48 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( tl @ sk__48 ) @ X1 )
       != X0 )
      | ( ( hd @ sk__48 )
       != X2 )
      | ( ( cons @ X2 @ nil )
       != X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1681,zip_derived_cl201]) ).

thf(zip_derived_cl203_015,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1683,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( tl @ sk__48 ) @ X1 )
       != X0 )
      | ( ( hd @ sk__48 )
       != X2 )
      | ( ( cons @ X2 @ nil )
       != X1 )
      | ~ ( ssItem @ X2 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1682,zip_derived_cl203]) ).

thf(zip_derived_cl1684,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ ( hd @ sk__48 ) )
      | ( ( cons @ ( hd @ sk__48 ) @ nil )
       != X0 )
      | ( ( app @ ( tl @ sk__48 ) @ X0 )
       != X1 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1683]) ).

thf(zip_derived_cl1685,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( nil = sk__48 )
      | ( ( cons @ ( hd @ sk__48 ) @ nil )
       != X0 )
      | ( ( app @ ( tl @ sk__48 ) @ X0 )
       != X1 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X1 )
      | ~ ( ssList @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl1684]) ).

thf(zip_derived_cl201_016,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl1686,plain,
    ! [X0: $i,X1: $i] :
      ( ( nil = sk__48 )
      | ( ( cons @ ( hd @ sk__48 ) @ nil )
       != X0 )
      | ( ( app @ ( tl @ sk__48 ) @ X0 )
       != X1 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1685,zip_derived_cl201]) ).

thf(zip_derived_cl203_017,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1687,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cons @ ( hd @ sk__48 ) @ nil )
       != X0 )
      | ( ( app @ ( tl @ sk__48 ) @ X0 )
       != X1 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X1 )
      | ~ ( ssList @ X1 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1686,zip_derived_cl203]) ).

thf(zip_derived_cl1688,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1687]) ).

thf(zip_derived_cl1689,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ ( hd @ sk__48 ) )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl1688]) ).

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

thf(zip_derived_cl1690,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ ( hd @ sk__48 ) )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1689,zip_derived_cl83]) ).

thf(zip_derived_cl1720,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( nil = sk__48 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl1690]) ).

thf(zip_derived_cl201_019,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl1721,plain,
    ! [X0: $i] :
      ( ( nil = sk__48 )
      | ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1720,zip_derived_cl201]) ).

thf(zip_derived_cl203_020,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1722,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( sk__47 = X0 )
      | ( ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) )
       != X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1721,zip_derived_cl203]) ).

thf(zip_derived_cl1723,plain,
    ( ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1722]) ).

thf(zip_derived_cl81_021,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X1 = X0 )
      | ( neq @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax15]) ).

thf(zip_derived_cl93_022,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl93_023,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl93_024,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl93_025,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(ax42,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( frontsegP @ U @ U ) ) ).

thf(zip_derived_cl117,plain,
    ! [X0: $i] :
      ( ( frontsegP @ X0 @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax42]) ).

thf(zip_derived_cl91_026,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

thf(zip_derived_cl82_027,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl93_028,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl93_029,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl1723_030,plain,
    ( ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1722]) ).

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_cl1823,plain,
    ( ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1723,zip_derived_cl95]) ).

thf(zip_derived_cl1825,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1823]) ).

thf(zip_derived_cl201_031,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl1826,plain,
    ( ( nil = sk__48 )
    | ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1825,zip_derived_cl201]) ).

thf(zip_derived_cl203_032,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl1827,plain,
    ( ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1826,zip_derived_cl203]) ).

thf(ax43,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( frontsegP @ U @ V )
               => ( frontsegP @ ( app @ U @ W ) @ V ) ) ) ) ) ).

thf(zip_derived_cl118,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( frontsegP @ ( app @ X1 @ X2 ) @ X0 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax43]) ).

thf(zip_derived_cl1848,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
      | ~ ( ssList @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
      | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1827,zip_derived_cl118]) ).

thf(zip_derived_cl1880,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( tl @ sk__48 ) )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1848]) ).

thf(zip_derived_cl2049,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( nil = sk__48 )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl1880]) ).

thf(zip_derived_cl201_033,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2050,plain,
    ! [X0: $i] :
      ( ( nil = sk__48 )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2049,zip_derived_cl201]) ).

thf(zip_derived_cl203_034,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl2051,plain,
    ! [X0: $i] :
      ( ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2050,zip_derived_cl203]) ).

thf(zip_derived_cl2052,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ ( hd @ sk__48 ) )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl2051]) ).

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

thf(zip_derived_cl2053,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ ( hd @ sk__48 ) )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2052,zip_derived_cl83]) ).

thf(zip_derived_cl2054,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__48 )
      | ( nil = sk__48 )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl2053]) ).

thf(zip_derived_cl201_036,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2055,plain,
    ! [X0: $i] :
      ( ( nil = sk__48 )
      | ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2054,zip_derived_cl201]) ).

thf(zip_derived_cl203_037,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl2056,plain,
    ! [X0: $i] :
      ( ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2055,zip_derived_cl203]) ).

thf(zip_derived_cl2057,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( frontsegP @ sk__47 @ ( tl @ sk__48 ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl117,zip_derived_cl2056]) ).

thf(zip_derived_cl2059,plain,
    ( ( frontsegP @ sk__47 @ ( tl @ sk__48 ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2057]) ).

thf(zip_derived_cl2509,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( frontsegP @ sk__47 @ ( tl @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2059]) ).

thf(zip_derived_cl201_038,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2510,plain,
    ( ( nil = sk__48 )
    | ( frontsegP @ sk__47 @ ( tl @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2509,zip_derived_cl201]) ).

thf(zip_derived_cl203_039,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl2511,plain,
    frontsegP @ sk__47 @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2510,zip_derived_cl203]) ).

thf(ax5,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( frontsegP @ U @ V )
          <=> ? [W: $i] :
                ( ( ( app @ V @ W )
                  = U )
                & ( ssList @ W ) ) ) ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl2512,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2511,zip_derived_cl12]) ).

thf(zip_derived_cl190_040,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2517,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2512,zip_derived_cl190]) ).

thf(zip_derived_cl91848,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
      = sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2517]) ).

thf(zip_derived_cl201_041,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl91849,plain,
    ( ( nil = sk__48 )
    | ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl91848,zip_derived_cl201]) ).

thf(zip_derived_cl203_042,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl91850,plain,
    ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).

thf(zip_derived_cl134_043,plain,
    ! [X0: $i] :
      ( ( segmentP @ X0 @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax55]) ).

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(ax56,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ! [X: $i] :
                  ( ( ssList @ X )
                 => ( ( segmentP @ U @ V )
                   => ( segmentP @ ( app @ ( app @ W @ U ) @ X ) @ V ) ) ) ) ) ) ).

thf(zip_derived_cl135,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( segmentP @ ( app @ ( app @ X2 @ X3 ) @ X1 ) @ X0 )
      | ~ ( segmentP @ X3 @ X0 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X3 ) ),
    inference(cnf,[status(esa)],[ax56]) ).

thf(zip_derived_cl1477,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
      | ~ ( segmentP @ X0 @ X1 )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl135]) ).

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

thf(zip_derived_cl1492,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
      | ~ ( segmentP @ X0 @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1477,zip_derived_cl83]) ).

thf(zip_derived_cl1493,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( segmentP @ X0 @ X1 )
      | ( segmentP @ ( app @ X0 @ X2 ) @ X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1492]) ).

thf(zip_derived_cl54766,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( segmentP @ ( app @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl134,zip_derived_cl1493]) ).

thf(zip_derived_cl54850,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( segmentP @ ( app @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl54766]) ).

thf(zip_derived_cl92019,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( segmentP @ sk__47 @ ( tl @ sk__48 ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl91850,zip_derived_cl54850]) ).

thf(zip_derived_cl93_045,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl2511_046,plain,
    frontsegP @ sk__47 @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2510,zip_derived_cl203]) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ssList @ ( sk__5 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl2513,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2511,zip_derived_cl13]) ).

thf(zip_derived_cl190_047,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2518,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2513,zip_derived_cl190]) ).

thf(zip_derived_cl2651,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2518]) ).

thf(zip_derived_cl201_048,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2652,plain,
    ( ( nil = sk__48 )
    | ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2651,zip_derived_cl201]) ).

thf(zip_derived_cl203_049,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl2653,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl92205,plain,
    ( ( segmentP @ sk__47 @ ( tl @ sk__48 ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl92019,zip_derived_cl2653]) ).

thf(zip_derived_cl92248,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( segmentP @ sk__47 @ ( tl @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl92205]) ).

thf(zip_derived_cl201_050,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl92249,plain,
    ( ( nil = sk__48 )
    | ( segmentP @ sk__47 @ ( tl @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl92248,zip_derived_cl201]) ).

thf(zip_derived_cl203_051,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl92250,plain,
    segmentP @ sk__47 @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl92249,zip_derived_cl203]) ).

thf(zip_derived_cl193_052,plain,
    ! [X0: $i] :
      ( ~ ( segmentP @ sk__47 @ X0 )
      | ~ ( segmentP @ sk__48 @ X0 )
      | ~ ( neq @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl92265,plain,
    ( ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
    | ~ ( neq @ ( tl @ sk__48 ) @ nil )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl92250,zip_derived_cl193]) ).

thf(zip_derived_cl92280,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
    | ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl92265]) ).

thf(zip_derived_cl201_053,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl92281,plain,
    ( ( nil = sk__48 )
    | ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
    | ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl92280,zip_derived_cl201]) ).

thf(zip_derived_cl203_054,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl92282,plain,
    ( ~ ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
    | ~ ( neq @ ( tl @ sk__48 ) @ nil ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl92281,zip_derived_cl203]) ).

thf(zip_derived_cl91850_055,plain,
    ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).

thf(ax86,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( nil != U )
           => ( ( tl @ ( app @ U @ V ) )
              = ( app @ ( tl @ U ) @ V ) ) ) ) ) ).

thf(zip_derived_cl178,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

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(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_cl528,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X1 )
      | ( nil
        = ( app @ X0 @ X1 ) )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
        = ( app @ X0 @ X1 ) )
      | ~ ( ssList @ ( app @ X0 @ X1 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl177,zip_derived_cl168]) ).

thf(ax83,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( nil
              = ( app @ U @ V ) )
          <=> ( ( nil = V )
              & ( nil = U ) ) ) ) ) ).

thf(zip_derived_cl174,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil
       != ( app @ X1 @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl4501,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ ( app @ X0 @ X1 ) )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
        = ( app @ X0 @ X1 ) )
      | ~ ( ssList @ X1 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl528,zip_derived_cl174]) ).

thf(zip_derived_cl95_056,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl4502,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X1 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
        = ( app @ X0 @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4501,zip_derived_cl95]) ).

thf(zip_derived_cl4546,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ( ( cons @ ( hd @ X1 ) @ ( app @ ( tl @ X1 ) @ X0 ) )
        = ( app @ X1 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl4502]) ).

thf(zip_derived_cl4582,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cons @ ( hd @ X1 ) @ ( app @ ( tl @ X1 ) @ X0 ) )
        = ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X0 )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4546]) ).

thf(zip_derived_cl175202,plain,
    ( ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
      = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
    | ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl91850,zip_derived_cl4582]) ).

thf(zip_derived_cl2653_057,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl201_058,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl175278,plain,
    ( ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
      = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl175202,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl203_059,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl175279,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl14,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( app @ X0 @ X2 )
       != X1 )
      | ~ ( ssList @ X2 )
      | ( frontsegP @ X1 @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl344,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ( frontsegP @ ( app @ X1 @ X0 ) @ X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl95_060,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl2777,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ( frontsegP @ ( app @ X1 @ X0 ) @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl344,zip_derived_cl95]) ).

thf(zip_derived_cl196252,plain,
    ( ~ ( ssList @ sk__48 )
    | ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( frontsegP @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl2777]) ).

thf(zip_derived_cl201_061,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2653_062,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl196523,plain,
    frontsegP @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl196252,zip_derived_cl201,zip_derived_cl2653]) ).

thf(ax20,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( nil = U )
        | ? [V: $i] :
            ( ? [W: $i] :
                ( ( ( cons @ W @ V )
                  = U )
                & ( ssItem @ W ) )
            & ( ssList @ V ) ) ) ) ).

thf(zip_derived_cl88,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
        = X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(ax44,axiom,
    ! [U: $i] :
      ( ( ssItem @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ! [X: $i] :
                  ( ( ssList @ X )
                 => ( ( frontsegP @ ( cons @ U @ W ) @ ( cons @ V @ X ) )
                  <=> ( ( U = V )
                      & ( frontsegP @ W @ X ) ) ) ) ) ) ) ).

thf(zip_derived_cl121,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( frontsegP @ ( cons @ X2 @ X3 ) @ ( cons @ X0 @ X1 ) )
      | ( X2 = X0 )
      | ~ ( ssList @ X3 )
      | ~ ( ssItem @ X2 ) ),
    inference(cnf,[status(esa)],[ax44]) ).

thf(zip_derived_cl969,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssItem @ ( sk__44 @ X0 ) )
      | ~ ( ssList @ ( sk__43 @ X0 ) )
      | ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
      | ( X2
        = ( sk__44 @ X0 ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl88,zip_derived_cl121]) ).

thf(zip_derived_cl87,plain,
    ! [X0: $i] :
      ( ( ssItem @ ( sk__44 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(zip_derived_cl16177,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssItem @ X2 )
      | ~ ( ssList @ X1 )
      | ( X2
        = ( sk__44 @ X0 ) )
      | ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
      | ~ ( ssList @ ( sk__43 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl969,zip_derived_cl87]) ).

thf(zip_derived_cl89,plain,
    ! [X0: $i] :
      ( ( ssList @ ( sk__43 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(zip_derived_cl16178,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( frontsegP @ ( cons @ X2 @ X1 ) @ X0 )
      | ( X2
        = ( sk__44 @ X0 ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl16177,zip_derived_cl89]) ).

thf(zip_derived_cl198778,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( ( hd @ sk__48 )
      = ( sk__44 @ sk__48 ) )
    | ~ ( ssList @ sk__47 )
    | ~ ( ssItem @ ( hd @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl196523,zip_derived_cl16178]) ).

thf(zip_derived_cl201_063,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl190_064,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl175279_065,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl177_066,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_cl196232,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
      = ( hd @ sk__48 ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl177]) ).

thf(zip_derived_cl2653_067,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl201_068,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl196497,plain,
    ( ( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
      = ( hd @ sk__48 ) )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl196232,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl203_069,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl196498,plain,
    ( ( hd @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    = ( hd @ sk__48 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl196497,zip_derived_cl203]) ).

thf(zip_derived_cl91_070,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax22]) ).

thf(zip_derived_cl197126,plain,
    ( ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( ssItem @ ( hd @ sk__48 ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl196498,zip_derived_cl91]) ).

thf(zip_derived_cl175279_071,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl95_072,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl196226,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl95]) ).

thf(zip_derived_cl2653_073,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl201_074,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl196490,plain,
    ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl196226,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl197272,plain,
    ( ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( ssItem @ ( hd @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl197126,zip_derived_cl196490]) ).

thf(zip_derived_cl175279_075,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl174_076,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil
       != ( app @ X1 @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl196230,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( nil
     != ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl175279,zip_derived_cl174]) ).

thf(zip_derived_cl2653_077,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl201_078,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl196494,plain,
    ( ( nil
     != ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl196230,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl203_079,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl196495,plain,
    ( nil
   != ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).

thf(zip_derived_cl197273,plain,
    ssItem @ ( hd @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).

thf(zip_derived_cl198791,plain,
    ( ( nil = sk__48 )
    | ( ( hd @ sk__48 )
      = ( sk__44 @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl198778,zip_derived_cl201,zip_derived_cl190,zip_derived_cl197273]) ).

thf(zip_derived_cl203_080,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl198792,plain,
    ( ( hd @ sk__48 )
    = ( sk__44 @ sk__48 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl198791,zip_derived_cl203]) ).

thf(zip_derived_cl88_081,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
        = X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

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_cl491,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssItem @ ( sk__44 @ X0 ) )
      | ( ( tl @ X0 )
        = ( sk__43 @ X0 ) )
      | ~ ( ssList @ ( sk__43 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl94]) ).

thf(zip_derived_cl87_082,plain,
    ! [X0: $i] :
      ( ( ssItem @ ( sk__44 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(zip_derived_cl4316,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( sk__43 @ X0 ) )
      | ( ( tl @ X0 )
        = ( sk__43 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl491,zip_derived_cl87]) ).

thf(zip_derived_cl89_083,plain,
    ! [X0: $i] :
      ( ( ssList @ ( sk__43 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(zip_derived_cl4317,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ( ( tl @ X0 )
        = ( sk__43 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4316,zip_derived_cl89]) ).

thf(zip_derived_cl88_084,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( sk__44 @ X0 ) @ ( sk__43 @ X0 ) )
        = X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax20]) ).

thf(zip_derived_cl4318,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ~ ( ssList @ X0 )
      | ( ( cons @ ( sk__44 @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl4317,zip_derived_cl88]) ).

thf(zip_derived_cl4321,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( sk__44 @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ~ ( ssList @ X0 )
      | ( nil = X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4318]) ).

thf(zip_derived_cl198824,plain,
    ( ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
      = sk__48 )
    | ~ ( ssList @ sk__48 )
    | ( nil = sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl198792,zip_derived_cl4321]) ).

thf(zip_derived_cl201_085,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl198886,plain,
    ( ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
      = sk__48 )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl198824,zip_derived_cl201]) ).

thf(zip_derived_cl203_086,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl198887,plain,
    ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
    = sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).

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(ax84,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( app @ U @ nil )
        = U ) ) ).

thf(zip_derived_cl176,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(ax7,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ( ( segmentP @ U @ V )
          <=> ? [W: $i] :
                ( ? [X: $i] :
                    ( ( ( app @ ( app @ W @ V ) @ X )
                      = U )
                    & ( ssList @ X ) )
                & ( ssList @ W ) ) ) ) ) ).

thf(zip_derived_cl21,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( app @ X3 @ X0 ) @ X1 )
       != X2 )
      | ~ ( ssList @ X3 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(cnf,[status(esa)],[ax7]) ).

thf(zip_derived_cl587,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ( ( app @ X1 @ X0 )
       != X2 )
      | ~ ( ssList @ X1 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl21]) ).

thf(zip_derived_cl83_087,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl595,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X0 )
      | ( ( app @ X1 @ X0 )
       != X2 )
      | ~ ( ssList @ X1 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl587,zip_derived_cl83]) ).

thf(zip_derived_cl95_088,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl5131,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ X1 @ X0 )
       != X2 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl595,zip_derived_cl95]) ).

thf(zip_derived_cl5144,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X2 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ ( cons @ X1 @ nil ) )
      | ( ( cons @ X1 @ X0 )
       != X2 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl171,zip_derived_cl5131]) ).

thf(zip_derived_cl5172,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( cons @ X1 @ X0 )
       != X2 )
      | ~ ( ssList @ ( cons @ X1 @ nil ) )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl5144]) ).

thf(zip_derived_cl82_089,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(ax4,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( singletonP @ U )
      <=> ? [V: $i] :
            ( ( ( cons @ V @ nil )
              = U )
            & ( ssItem @ V ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i] :
      ( ~ ( singletonP @ X0 )
      | ( ( cons @ ( sk__4 @ X0 ) @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax4]) ).

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_cl359,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( singletonP @ X0 )
      | ~ ( ssItem @ ( sk__4 @ X0 ) )
      | ( ( hd @ X0 )
        = ( sk__4 @ X0 ) )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl92]) ).

thf(zip_derived_cl83_090,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl360,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( singletonP @ X0 )
      | ~ ( ssItem @ ( sk__4 @ X0 ) )
      | ( ( hd @ X0 )
        = ( sk__4 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl83]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i] :
      ( ~ ( singletonP @ X0 )
      | ( ssItem @ ( sk__4 @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax4]) ).

thf(zip_derived_cl3022,plain,
    ! [X0: $i] :
      ( ( ( hd @ X0 )
        = ( sk__4 @ X0 ) )
      | ~ ( singletonP @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl360,zip_derived_cl10]) ).

thf(zip_derived_cl11_091,plain,
    ! [X0: $i] :
      ( ~ ( singletonP @ X0 )
      | ( ( cons @ ( sk__4 @ X0 ) @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax4]) ).

thf(zip_derived_cl3024,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( singletonP @ X0 )
      | ~ ( singletonP @ X0 )
      | ( ( cons @ ( hd @ X0 ) @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3022,zip_derived_cl11]) ).

thf(zip_derived_cl3028,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( hd @ X0 ) @ nil )
        = X0 )
      | ~ ( singletonP @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3024]) ).

thf(zip_derived_cl82_092,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cons @ X1 @ nil )
       != X0 )
      | ~ ( ssItem @ X1 )
      | ( singletonP @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax4]) ).

thf(zip_derived_cl261,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( cons @ X0 @ nil ) )
      | ( singletonP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl2074,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 )
      | ( singletonP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl261]) ).

thf(zip_derived_cl83_093,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2077,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( singletonP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2074,zip_derived_cl83]) ).

thf(zip_derived_cl2078,plain,
    ! [X0: $i] :
      ( ( singletonP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2077]) ).

thf(zip_derived_cl3051,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( cons @ X0 @ nil ) )
      | ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
        = ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3028,zip_derived_cl2078]) ).

thf(zip_derived_cl3729,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 )
      | ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
        = ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3051]) ).

thf(zip_derived_cl83_094,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3733,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
        = ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3729,zip_derived_cl83]) ).

thf(zip_derived_cl3734,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( hd @ ( cons @ X0 @ nil ) ) @ nil )
        = ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3733]) ).

thf(zip_derived_cl82_095,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl3740,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ( ssList @ ( cons @ X0 @ nil ) )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3734,zip_derived_cl82]) ).

thf(zip_derived_cl83_096,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3806,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ( ssList @ ( cons @ X0 @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3740,zip_derived_cl83]) ).

thf(zip_derived_cl82_097,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl3022_098,plain,
    ! [X0: $i] :
      ( ( ( hd @ X0 )
        = ( sk__4 @ X0 ) )
      | ~ ( singletonP @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl360,zip_derived_cl10]) ).

thf(zip_derived_cl10_099,plain,
    ! [X0: $i] :
      ( ~ ( singletonP @ X0 )
      | ( ssItem @ ( sk__4 @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax4]) ).

thf(zip_derived_cl3023,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( singletonP @ X0 )
      | ~ ( singletonP @ X0 )
      | ( ssItem @ ( hd @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3022,zip_derived_cl10]) ).

thf(zip_derived_cl3027,plain,
    ! [X0: $i] :
      ( ( ssItem @ ( hd @ X0 ) )
      | ~ ( singletonP @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3023]) ).

thf(zip_derived_cl2078_100,plain,
    ! [X0: $i] :
      ( ( singletonP @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2077]) ).

thf(zip_derived_cl3047,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( cons @ X0 @ nil ) )
      | ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3027,zip_derived_cl2078]) ).

thf(zip_derived_cl3054,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 )
      | ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3047]) ).

thf(zip_derived_cl83_101,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3058,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3054,zip_derived_cl83]) ).

thf(zip_derived_cl3059,plain,
    ! [X0: $i] :
      ( ( ssItem @ ( hd @ ( cons @ X0 @ nil ) ) )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3058]) ).

thf(zip_derived_cl3961,plain,
    ! [X0: $i] :
      ( ( ssList @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3806,zip_derived_cl3059]) ).

thf(zip_derived_cl209900,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X2 )
      | ( segmentP @ X2 @ X0 )
      | ( ( cons @ X1 @ X0 )
       != X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl5172,zip_derived_cl3961]) ).

thf(zip_derived_cl209930,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( tl @ sk__48 ) )
      | ~ ( ssItem @ ( hd @ sk__48 ) )
      | ~ ( ssList @ X0 )
      | ( segmentP @ X0 @ ( tl @ sk__48 ) )
      | ( sk__48 != X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl198887,zip_derived_cl209900]) ).

thf(zip_derived_cl198887_102,plain,
    ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
    = sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).

thf(zip_derived_cl177_103,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_cl176_104,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(zip_derived_cl178_105,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl785,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ( ( tl @ X0 )
        = ( app @ ( tl @ X0 ) @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl178]) ).

thf(zip_derived_cl83_106,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl792,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ X0 )
        = ( app @ ( tl @ X0 ) @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl785,zip_derived_cl83]) ).

thf(zip_derived_cl793,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ( tl @ X0 )
        = ( app @ ( tl @ X0 ) @ nil ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl792]) ).

thf(zip_derived_cl178_107,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl168_108,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax78]) ).

thf(zip_derived_cl783,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ( nil
        = ( app @ X1 @ X0 ) )
      | ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
        = ( app @ X1 @ X0 ) )
      | ~ ( ssList @ ( app @ X1 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl168]) ).

thf(zip_derived_cl174_109,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil
       != ( app @ X1 @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl8584,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
        = ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X0 )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl783,zip_derived_cl174]) ).

thf(zip_derived_cl95_110,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl8585,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ( ( cons @ ( hd @ ( app @ X1 @ X0 ) ) @ ( app @ ( tl @ X1 ) @ X0 ) )
        = ( app @ X1 @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl8584,zip_derived_cl95]) ).

thf(zip_derived_cl8641,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ nil )
      | ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl793,zip_derived_cl8585]) ).

thf(zip_derived_cl83_111,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl8687,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8641,zip_derived_cl83]) ).

thf(zip_derived_cl8688,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( hd @ ( app @ X0 @ nil ) ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8687]) ).

thf(zip_derived_cl9796,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ nil )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl177,zip_derived_cl8688]) ).

thf(zip_derived_cl83_112,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl9813,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl9796,zip_derived_cl83]) ).

thf(zip_derived_cl9814,plain,
    ! [X0: $i] :
      ( ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = ( app @ X0 @ nil ) )
      | ( nil = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl9813]) ).

thf(zip_derived_cl199185,plain,
    ( ( sk__48
      = ( app @ sk__48 @ nil ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl198887,zip_derived_cl9814]) ).

thf(zip_derived_cl201_113,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl199442,plain,
    ( ( sk__48
      = ( app @ sk__48 @ nil ) )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl199185,zip_derived_cl201]) ).

thf(zip_derived_cl203_114,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl199443,plain,
    ( sk__48
    = ( app @ sk__48 @ nil ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl199442,zip_derived_cl203]) ).

thf(zip_derived_cl178_115,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl199540,plain,
    ( ~ ( ssList @ nil )
    | ( ( tl @ sk__48 )
      = ( app @ ( tl @ sk__48 ) @ nil ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl199443,zip_derived_cl178]) ).

thf(zip_derived_cl83_116,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl201_117,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl200024,plain,
    ( ( ( tl @ sk__48 )
      = ( app @ ( tl @ sk__48 ) @ nil ) )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl199540,zip_derived_cl83,zip_derived_cl201]) ).

thf(zip_derived_cl203_118,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl200025,plain,
    ( ( tl @ sk__48 )
    = ( app @ ( tl @ sk__48 ) @ nil ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl200024,zip_derived_cl203]) ).

thf(zip_derived_cl178_119,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl93_120,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(zip_derived_cl782,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ( nil
        = ( app @ X1 @ X0 ) )
      | ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) )
      | ~ ( ssList @ ( app @ X1 @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl93]) ).

thf(zip_derived_cl174_121,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil
       != ( app @ X1 @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl8514,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) )
      | ~ ( ssList @ X0 )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl782,zip_derived_cl174]) ).

thf(zip_derived_cl95_122,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl8515,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( nil = X1 )
      | ~ ( ssList @ X0 )
      | ( ssList @ ( app @ ( tl @ X1 ) @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl8514,zip_derived_cl95]) ).

thf(zip_derived_cl202808,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ~ ( ssList @ nil )
    | ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl200025,zip_derived_cl8515]) ).

thf(zip_derived_cl201_123,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl83_124,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl203153,plain,
    ( ( nil = sk__48 )
    | ( ssList @ ( tl @ sk__48 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl202808,zip_derived_cl201,zip_derived_cl83]) ).

thf(zip_derived_cl203_125,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl203154,plain,
    ssList @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).

thf(zip_derived_cl197273_126,plain,
    ssItem @ ( hd @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).

thf(zip_derived_cl209952,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( segmentP @ X0 @ ( tl @ sk__48 ) )
      | ( sk__48 != X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl209930,zip_derived_cl203154,zip_derived_cl197273]) ).

thf(zip_derived_cl259913,plain,
    ( ( segmentP @ sk__48 @ ( tl @ sk__48 ) )
    | ~ ( ssList @ sk__48 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl209952]) ).

thf(zip_derived_cl201_127,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl259914,plain,
    segmentP @ sk__48 @ ( tl @ sk__48 ),
    inference(demod,[status(thm)],[zip_derived_cl259913,zip_derived_cl201]) ).

thf(zip_derived_cl259940,plain,
    ~ ( neq @ ( tl @ sk__48 ) @ nil ),
    inference(demod,[status(thm)],[zip_derived_cl92282,zip_derived_cl259914]) ).

thf(zip_derived_cl259969,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( ( tl @ sk__48 )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl259940]) ).

thf(zip_derived_cl203154_128,plain,
    ssList @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).

thf(zip_derived_cl83_129,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl259971,plain,
    ( ( tl @ sk__48 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).

thf(zip_derived_cl259971_130,plain,
    ( ( tl @ sk__48 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).

thf(zip_derived_cl259976,plain,
    ( ( sk__47
      = ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1723,zip_derived_cl259971,zip_derived_cl259971]) ).

thf(zip_derived_cl198887_131,plain,
    ( ( cons @ ( hd @ sk__48 ) @ ( tl @ sk__48 ) )
    = sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl198886,zip_derived_cl203]) ).

thf(zip_derived_cl259971_132,plain,
    ( ( tl @ sk__48 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl259969,zip_derived_cl203154,zip_derived_cl83]) ).

thf(zip_derived_cl260001,plain,
    ( ( cons @ ( hd @ sk__48 ) @ nil )
    = sk__48 ),
    inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).

thf(zip_derived_cl199443_133,plain,
    ( sk__48
    = ( app @ sk__48 @ nil ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl199442,zip_derived_cl203]) ).

thf(zip_derived_cl97_134,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax28]) ).

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_cl1219,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl172]) ).

thf(zip_derived_cl83_135,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1230,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1219,zip_derived_cl83]) ).

thf(zip_derived_cl1231,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1230]) ).

thf(zip_derived_cl199699,plain,
    ( ~ ( ssList @ nil )
    | ( sk__48
      = ( app @ nil @ sk__48 ) )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl199443,zip_derived_cl1231]) ).

thf(zip_derived_cl83_136,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl201_137,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl200246,plain,
    ( sk__48
    = ( app @ nil @ sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl199699,zip_derived_cl83,zip_derived_cl201]) ).

thf(zip_derived_cl260001_138,plain,
    ( ( cons @ ( hd @ sk__48 ) @ nil )
    = sk__48 ),
    inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).

thf(zip_derived_cl200246_139,plain,
    ( sk__48
    = ( app @ nil @ sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl199699,zip_derived_cl83,zip_derived_cl201]) ).

thf(zip_derived_cl201_140,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl275627,plain,
    sk__47 = sk__48,
    inference(demod,[status(thm)],[zip_derived_cl259976,zip_derived_cl260001,zip_derived_cl200246,zip_derived_cl260001,zip_derived_cl200246,zip_derived_cl201]) ).

thf(zip_derived_cl176_141,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(zip_derived_cl93_142,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ssList @ ( tl @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax24]) ).

thf(ax45,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( frontsegP @ U @ nil ) ) ).

thf(zip_derived_cl122,plain,
    ! [X0: $i] :
      ( ( frontsegP @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax45]) ).

thf(zip_derived_cl2056_143,plain,
    ! [X0: $i] :
      ( ( frontsegP @ sk__47 @ X0 )
      | ~ ( frontsegP @ ( tl @ sk__48 ) @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2055,zip_derived_cl203]) ).

thf(zip_derived_cl2058,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( frontsegP @ sk__47 @ nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl2056]) ).

thf(zip_derived_cl83_144,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2060,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( frontsegP @ sk__47 @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl2058,zip_derived_cl83]) ).

thf(zip_derived_cl2061,plain,
    ( ~ ( ssList @ sk__48 )
    | ( nil = sk__48 )
    | ( frontsegP @ sk__47 @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl2060]) ).

thf(zip_derived_cl201_145,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl2062,plain,
    ( ( nil = sk__48 )
    | ( frontsegP @ sk__47 @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl2061,zip_derived_cl201]) ).

thf(zip_derived_cl203_146,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl2063,plain,
    frontsegP @ sk__47 @ nil,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2062,zip_derived_cl203]) ).

thf(zip_derived_cl12_147,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl2064,plain,
    ( ~ ( ssList @ nil )
    | ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2063,zip_derived_cl12]) ).

thf(zip_derived_cl83_148,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_149,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2069,plain,
    ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2064,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl2069_150,plain,
    ( ( app @ nil @ ( sk__5 @ nil @ sk__47 ) )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2064,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl97_151,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax28]) ).

thf(zip_derived_cl2104,plain,
    ( ( sk__47
      = ( sk__5 @ nil @ sk__47 ) )
    | ~ ( ssList @ ( sk__5 @ nil @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2069,zip_derived_cl97]) ).

thf(zip_derived_cl2063_152,plain,
    frontsegP @ sk__47 @ nil,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2062,zip_derived_cl203]) ).

thf(zip_derived_cl13_153,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ssList @ ( sk__5 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl2065,plain,
    ( ~ ( ssList @ nil )
    | ( ssList @ ( sk__5 @ nil @ sk__47 ) )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2063,zip_derived_cl13]) ).

thf(zip_derived_cl83_154,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_155,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2070,plain,
    ssList @ ( sk__5 @ nil @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2065,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl2132,plain,
    ( sk__47
    = ( sk__5 @ nil @ sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2104,zip_derived_cl2070]) ).

thf(zip_derived_cl2136,plain,
    ( ( app @ nil @ sk__47 )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2069,zip_derived_cl2132]) ).

thf(zip_derived_cl21_156,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( app @ X3 @ X0 ) @ X1 )
       != X2 )
      | ~ ( ssList @ X3 )
      | ( segmentP @ X2 @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(cnf,[status(esa)],[ax7]) ).

thf(zip_derived_cl2155,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ sk__47 )
      | ~ ( ssList @ X1 )
      | ( ( app @ sk__47 @ X1 )
       != X0 )
      | ~ ( ssList @ nil )
      | ( segmentP @ X0 @ sk__47 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2136,zip_derived_cl21]) ).

thf(zip_derived_cl190_157,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_158,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2181,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( ( app @ sk__47 @ X1 )
       != X0 )
      | ( segmentP @ X0 @ sk__47 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2155,zip_derived_cl190,zip_derived_cl83]) ).

thf(zip_derived_cl2597,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ sk__47 )
      | ~ ( ssList @ nil )
      | ( sk__47 != X0 )
      | ( segmentP @ X0 @ sk__47 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl2181]) ).

thf(zip_derived_cl190_159,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_160,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2600,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( segmentP @ X0 @ sk__47 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2597,zip_derived_cl190,zip_derived_cl83]) ).

thf(zip_derived_cl2602,plain,
    ( ~ ( ssList @ sk__47 )
    | ( segmentP @ sk__47 @ sk__47 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl2600]) ).

thf(zip_derived_cl190_161,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2603,plain,
    segmentP @ sk__47 @ sk__47,
    inference(demod,[status(thm)],[zip_derived_cl2602,zip_derived_cl190]) ).

thf(zip_derived_cl275633,plain,
    ~ ( neq @ sk__47 @ nil ),
    inference(demod,[status(thm)],[zip_derived_cl240,zip_derived_cl275627,zip_derived_cl2603]) ).

thf(zip_derived_cl276655,plain,
    ( ~ ( ssList @ sk__47 )
    | ( sk__47 = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl275633]) ).

thf(zip_derived_cl190_162,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_163,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl276657,plain,
    sk__47 = nil,
    inference(demod,[status(thm)],[zip_derived_cl276655,zip_derived_cl190,zip_derived_cl83]) ).

thf(zip_derived_cl176_164,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(zip_derived_cl171_165,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_cl172_166,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_cl1217,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X0 )
      | ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
        = ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ ( cons @ X1 @ nil ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl171,zip_derived_cl172]) ).

thf(zip_derived_cl1228,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ ( cons @ X1 @ nil ) )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
        = ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1217]) ).

thf(zip_derived_cl3961_167,plain,
    ! [X0: $i] :
      ( ( ssList @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3806,zip_derived_cl3059]) ).

thf(zip_derived_cl33260,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( ( app @ ( cons @ X1 @ X0 ) @ X2 )
        = ( app @ ( cons @ X1 @ nil ) @ ( app @ X0 @ X2 ) ) )
      | ~ ( ssList @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1228,zip_derived_cl3961]) ).

thf(zip_derived_cl33382,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( ( app @ ( cons @ X1 @ X0 ) @ nil )
        = ( app @ ( cons @ X1 @ nil ) @ X0 ) )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl33260]) ).

thf(zip_derived_cl83_168,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl33446,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( ( app @ ( cons @ X1 @ X0 ) @ nil )
        = ( app @ ( cons @ X1 @ nil ) @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl33382,zip_derived_cl83]) ).

thf(zip_derived_cl33447,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( app @ ( cons @ X1 @ X0 ) @ nil )
        = ( app @ ( cons @ X1 @ nil ) @ X0 ) )
      | ~ ( ssItem @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl33446]) ).

thf(zip_derived_cl175279_169,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl1231_170,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1230]) ).

thf(zip_derived_cl196391,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
      = ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl1231]) ).

thf(zip_derived_cl2653_171,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl201_172,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl196698,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ nil @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl196391,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl1231_173,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1230]) ).

thf(zip_derived_cl172_174,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_cl176_175,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(ax79,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( ( app @ W @ V )
                  = ( app @ U @ V ) )
               => ( W = U ) ) ) ) ) ).

thf(zip_derived_cl169,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( app @ X2 @ X0 )
       != ( app @ X1 @ X0 ) )
      | ( X2 = X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax79]) ).

thf(zip_derived_cl657,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ( X0
       != ( app @ X1 @ nil ) )
      | ( X0 = X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl169]) ).

thf(zip_derived_cl83_176,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl671,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( X0
       != ( app @ X1 @ nil ) )
      | ( X0 = X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl657,zip_derived_cl83]) ).

thf(zip_derived_cl672,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( X0 = X1 )
      | ( X0
       != ( app @ X1 @ nil ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl671]) ).

thf(zip_derived_cl1202,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X1 )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ( X2
        = ( app @ X1 @ X0 ) )
      | ( X2
       != ( app @ X1 @ ( app @ X0 @ nil ) ) )
      | ~ ( ssList @ X2 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl172,zip_derived_cl672]) ).

thf(zip_derived_cl83_177,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1254,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ ( app @ X1 @ X0 ) )
      | ( X2
        = ( app @ X1 @ X0 ) )
      | ( X2
       != ( app @ X1 @ ( app @ X0 @ nil ) ) )
      | ~ ( ssList @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1202,zip_derived_cl83]) ).

thf(zip_derived_cl95_178,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl40036,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ( X2
       != ( app @ X1 @ ( app @ X0 @ nil ) ) )
      | ( X2
        = ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1254,zip_derived_cl95]) ).

thf(zip_derived_cl40043,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ X1 )
      | ( X1
       != ( app @ X0 @ nil ) )
      | ( X1
        = ( app @ nil @ X0 ) )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1231,zip_derived_cl40036]) ).

thf(zip_derived_cl83_179,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_180,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl40086,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( X1
       != ( app @ X0 @ nil ) )
      | ( X1
        = ( app @ nil @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl40043,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl40087,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( app @ nil @ X0 ) )
      | ( X1
       != ( app @ X0 @ nil ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl40086]) ).

thf(zip_derived_cl40546,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ ( app @ X0 @ nil ) )
      | ( ( app @ X0 @ nil )
        = ( app @ nil @ X0 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl40087]) ).

thf(ax46,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( frontsegP @ nil @ U )
      <=> ( nil = U ) ) ) ).

thf(zip_derived_cl123,plain,
    ! [X0: $i] :
      ( ( nil != X0 )
      | ( frontsegP @ nil @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax46]) ).

thf(zip_derived_cl262,plain,
    ( ~ ( ssList @ nil )
    | ( frontsegP @ nil @ nil ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl123]) ).

thf(zip_derived_cl83_181,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl263,plain,
    frontsegP @ nil @ nil,
    inference(demod,[status(thm)],[zip_derived_cl262,zip_derived_cl83]) ).

thf(zip_derived_cl12_182,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ( app @ X0 @ ( sk__5 @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl294,plain,
    ( ~ ( ssList @ nil )
    | ( ( app @ nil @ ( sk__5 @ nil @ nil ) )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl263,zip_derived_cl12]) ).

thf(zip_derived_cl83_183,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_184,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl299,plain,
    ( ( app @ nil @ ( sk__5 @ nil @ nil ) )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl299_185,plain,
    ( ( app @ nil @ ( sk__5 @ nil @ nil ) )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl294,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl97_186,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax28]) ).

thf(zip_derived_cl303,plain,
    ( ( nil
      = ( sk__5 @ nil @ nil ) )
    | ~ ( ssList @ ( sk__5 @ nil @ nil ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl299,zip_derived_cl97]) ).

thf(zip_derived_cl263_187,plain,
    frontsegP @ nil @ nil,
    inference(demod,[status(thm)],[zip_derived_cl262,zip_derived_cl83]) ).

thf(zip_derived_cl13_188,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( frontsegP @ X1 @ X0 )
      | ( ssList @ ( sk__5 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl320,plain,
    ( ~ ( ssList @ nil )
    | ( ssList @ ( sk__5 @ nil @ nil ) )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl263,zip_derived_cl13]) ).

thf(zip_derived_cl83_189,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_190,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl324,plain,
    ssList @ ( sk__5 @ nil @ nil ),
    inference(demod,[status(thm)],[zip_derived_cl320,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl325,plain,
    ( nil
    = ( sk__5 @ nil @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl324]) ).

thf(zip_derived_cl326,plain,
    ( ( app @ nil @ nil )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl299,zip_derived_cl325]) ).

thf(zip_derived_cl172_191,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_cl95_192,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl1188,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
      | ~ ( ssList @ ( app @ X2 @ X1 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl172,zip_derived_cl95]) ).

thf(zip_derived_cl1243,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ ( app @ X2 @ X1 ) )
      | ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1188]) ).

thf(zip_derived_cl95_193,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl37007,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( ssList @ ( app @ X2 @ ( app @ X1 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1243,zip_derived_cl95]) ).

thf(zip_derived_cl37072,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ nil )
      | ( ssList @ ( app @ X0 @ nil ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl326,zip_derived_cl37007]) ).

thf(zip_derived_cl83_194,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_195,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl37152,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X0 @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl37072,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl40648,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = ( app @ nil @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl40546,zip_derived_cl37152]) ).

thf(zip_derived_cl1231_196,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X1 )
      | ( ( app @ X0 @ X1 )
        = ( app @ nil @ ( app @ X0 @ X1 ) ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1230]) ).

thf(zip_derived_cl40736,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ( ( app @ X0 @ nil )
        = ( app @ nil @ ( app @ X0 @ nil ) ) )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl40648,zip_derived_cl1231]) ).

thf(zip_derived_cl83_197,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl41425,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ( ( app @ X0 @ nil )
        = ( app @ nil @ ( app @ X0 @ nil ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl40736,zip_derived_cl83]) ).

thf(zip_derived_cl41426,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = ( app @ nil @ ( app @ X0 @ nil ) ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl41425]) ).

thf(zip_derived_cl172_198,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_cl178_199,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl1194,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
        = ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
      | ( nil
        = ( app @ X2 @ X1 ) )
      | ~ ( ssList @ ( app @ X2 @ X1 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl172,zip_derived_cl178]) ).

thf(zip_derived_cl1249,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ ( app @ X2 @ X1 ) )
      | ( nil
        = ( app @ X2 @ X1 ) )
      | ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
        = ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1194]) ).

thf(zip_derived_cl95_200,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax26]) ).

thf(zip_derived_cl38127,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( tl @ ( app @ X2 @ ( app @ X1 @ X0 ) ) )
        = ( app @ ( tl @ ( app @ X2 @ X1 ) ) @ X0 ) )
      | ( nil
        = ( app @ X2 @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1249,zip_derived_cl95]) ).

thf(zip_derived_cl43040,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ nil )
      | ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X0 @ nil ) )
        = ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
      | ( nil
        = ( app @ nil @ X0 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl41426,zip_derived_cl38127]) ).

thf(zip_derived_cl83_201,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_202,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl43300,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X0 @ nil ) )
        = ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
      | ( nil
        = ( app @ nil @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl43040,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl43301,plain,
    ! [X0: $i] :
      ( ( nil
        = ( app @ nil @ X0 ) )
      | ( ( tl @ ( app @ X0 @ nil ) )
        = ( app @ ( tl @ ( app @ nil @ X0 ) ) @ nil ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl43300]) ).

thf(zip_derived_cl237867,plain,
    ( ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
      = ( app @ ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) @ nil ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl196698,zip_derived_cl43301]) ).

thf(zip_derived_cl175279_203,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ sk__48 @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl175278,zip_derived_cl203]) ).

thf(zip_derived_cl178_204,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( tl @ ( app @ X1 @ X0 ) )
        = ( app @ ( tl @ X1 ) @ X0 ) )
      | ( nil = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax86]) ).

thf(zip_derived_cl196233,plain,
    ( ~ ( ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    | ( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
      = ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) ) )
    | ( nil = sk__48 )
    | ~ ( ssList @ sk__48 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl175279,zip_derived_cl178]) ).

thf(zip_derived_cl2653_205,plain,
    ssList @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2652,zip_derived_cl203]) ).

thf(zip_derived_cl91850_206,plain,
    ( ( app @ ( tl @ sk__48 ) @ ( sk__5 @ ( tl @ sk__48 ) @ sk__47 ) )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl91849,zip_derived_cl203]) ).

thf(zip_derived_cl201_207,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl196499,plain,
    ( ( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
      = sk__47 )
    | ( nil = sk__48 ) ),
    inference(demod,[status(thm)],[zip_derived_cl196233,zip_derived_cl2653,zip_derived_cl91850,zip_derived_cl201]) ).

thf(zip_derived_cl203_208,plain,
    nil != sk__48,
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl192]) ).

thf(zip_derived_cl196500,plain,
    ( ( tl @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl196499,zip_derived_cl203]) ).

thf(zip_derived_cl176_209,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

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_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(zip_derived_cl364,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( sk__6 @ nil @ X0 ) )
      | ~ ( ssList @ nil )
      | ~ ( rearsegP @ X0 @ nil )
      | ( ( sk__6 @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl15]) ).

thf(zip_derived_cl83_210,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl369,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ ( sk__6 @ nil @ X0 ) )
      | ~ ( rearsegP @ X0 @ nil )
      | ( ( sk__6 @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl364,zip_derived_cl83]) ).

thf(ax51,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( rearsegP @ U @ nil ) ) ).

thf(zip_derived_cl129,plain,
    ! [X0: $i] :
      ( ( rearsegP @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax51]) ).

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_cl393,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ nil )
      | ( ssList @ ( sk__6 @ nil @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl16]) ).

thf(zip_derived_cl83_211,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl396,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( ssList @ ( sk__6 @ nil @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl393,zip_derived_cl83]) ).

thf(zip_derived_cl397,plain,
    ! [X0: $i] :
      ( ( ssList @ ( sk__6 @ nil @ X0 ) )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl396]) ).

thf(zip_derived_cl3064,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( ( sk__6 @ nil @ X0 )
        = X0 )
      | ~ ( rearsegP @ X0 @ nil ) ),
    inference(clc,[status(thm)],[zip_derived_cl369,zip_derived_cl397]) ).

thf(zip_derived_cl129_212,plain,
    ! [X0: $i] :
      ( ( rearsegP @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax51]) ).

thf(zip_derived_cl3065,plain,
    ! [X0: $i] :
      ( ( ( sk__6 @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl129]) ).

thf(zip_derived_cl129_213,plain,
    ! [X0: $i] :
      ( ( rearsegP @ X0 @ nil )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax51]) ).

thf(zip_derived_cl176_214,plain,
    ! [X0: $i] :
      ( ( ( app @ X0 @ nil )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax84]) ).

thf(zip_derived_cl2136_215,plain,
    ( ( app @ nil @ sk__47 )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2069,zip_derived_cl2132]) ).

thf(zip_derived_cl97_216,plain,
    ! [X0: $i] :
      ( ( ( app @ nil @ X0 )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax28]) ).

thf(ax58,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ( ( segmentP @ nil @ U )
      <=> ( nil = U ) ) ) ).

thf(zip_derived_cl137,plain,
    ! [X0: $i] :
      ( ( nil != X0 )
      | ( segmentP @ nil @ X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax58]) ).

thf(zip_derived_cl222,plain,
    ( ~ ( ssList @ nil )
    | ( segmentP @ nil @ nil ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl137]) ).

thf(zip_derived_cl83_217,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl223,plain,
    segmentP @ nil @ nil,
    inference(demod,[status(thm)],[zip_derived_cl222,zip_derived_cl83]) ).

thf(zip_derived_cl135_218,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssList @ X1 )
      | ( segmentP @ ( app @ ( app @ X2 @ X3 ) @ X1 ) @ X0 )
      | ~ ( segmentP @ X3 @ X0 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X3 ) ),
    inference(cnf,[status(esa)],[ax56]) ).

thf(zip_derived_cl1484,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssList @ X0 )
      | ( segmentP @ ( app @ ( app @ X1 @ nil ) @ X0 ) @ nil )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl135]) ).

thf(zip_derived_cl83_219,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_220,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl1501,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( segmentP @ ( app @ ( app @ X1 @ nil ) @ X0 ) @ nil )
      | ~ ( ssList @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1484,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl2733,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssList @ X0 )
      | ( segmentP @ ( app @ nil @ X0 ) @ nil )
      | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl97,zip_derived_cl1501]) ).

thf(zip_derived_cl83_221,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl83_222,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2744,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ( segmentP @ ( app @ nil @ X0 ) @ nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl2733,zip_derived_cl83,zip_derived_cl83]) ).

thf(zip_derived_cl2765,plain,
    ( ~ ( ssList @ sk__47 )
    | ( segmentP @ sk__47 @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2136,zip_derived_cl2744]) ).

thf(zip_derived_cl190_223,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2770,plain,
    segmentP @ sk__47 @ nil,
    inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( segmentP @ X1 @ X0 )
      | ( ( app @ ( app @ ( sk__7 @ X0 @ X1 ) @ X0 ) @ ( sk__8 @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax7]) ).

thf(zip_derived_cl2828,plain,
    ( ~ ( ssList @ nil )
    | ( ( app @ ( app @ ( sk__7 @ nil @ sk__47 ) @ nil ) @ ( sk__8 @ nil @ sk__47 ) )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl19]) ).

thf(zip_derived_cl83_224,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_225,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2835,plain,
    ( ( app @ ( app @ ( sk__7 @ nil @ sk__47 ) @ nil ) @ ( sk__8 @ nil @ sk__47 ) )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2828,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl2880,plain,
    ( ~ ( ssList @ ( sk__7 @ nil @ sk__47 ) )
    | ( ( app @ ( sk__7 @ nil @ sk__47 ) @ ( sk__8 @ nil @ sk__47 ) )
      = sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl176,zip_derived_cl2835]) ).

thf(zip_derived_cl2770_226,plain,
    segmentP @ sk__47 @ nil,
    inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( segmentP @ X1 @ X0 )
      | ( ssList @ ( sk__7 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax7]) ).

thf(zip_derived_cl2829,plain,
    ( ~ ( ssList @ nil )
    | ( ssList @ ( sk__7 @ nil @ sk__47 ) )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl20]) ).

thf(zip_derived_cl83_227,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_228,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2836,plain,
    ssList @ ( sk__7 @ nil @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2829,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl2881,plain,
    ( ( app @ ( sk__7 @ nil @ sk__47 ) @ ( sk__8 @ nil @ sk__47 ) )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2880,zip_derived_cl2836]) ).

thf(ax50,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssList @ W )
             => ( ( rearsegP @ U @ V )
               => ( rearsegP @ ( app @ W @ U ) @ V ) ) ) ) ) ).

thf(zip_derived_cl128,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ X1 @ X0 )
      | ( rearsegP @ ( app @ X2 @ X1 ) @ X0 )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax50]) ).

thf(zip_derived_cl2994,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ ( sk__8 @ nil @ sk__47 ) @ X0 )
      | ( rearsegP @ sk__47 @ X0 )
      | ~ ( ssList @ ( sk__7 @ nil @ sk__47 ) )
      | ~ ( ssList @ ( sk__8 @ nil @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2881,zip_derived_cl128]) ).

thf(zip_derived_cl2836_229,plain,
    ssList @ ( sk__7 @ nil @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2829,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl2770_230,plain,
    segmentP @ sk__47 @ nil,
    inference(demod,[status(thm)],[zip_derived_cl2765,zip_derived_cl190]) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( segmentP @ X1 @ X0 )
      | ( ssList @ ( sk__8 @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax7]) ).

thf(zip_derived_cl2827,plain,
    ( ~ ( ssList @ nil )
    | ( ssList @ ( sk__8 @ nil @ sk__47 ) )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2770,zip_derived_cl18]) ).

thf(zip_derived_cl83_231,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_232,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2834,plain,
    ssList @ ( sk__8 @ nil @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2827,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl3020,plain,
    ! [X0: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( rearsegP @ ( sk__8 @ nil @ sk__47 ) @ X0 )
      | ( rearsegP @ sk__47 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2994,zip_derived_cl2836,zip_derived_cl2834]) ).

thf(zip_derived_cl3085,plain,
    ( ~ ( ssList @ ( sk__8 @ nil @ sk__47 ) )
    | ~ ( ssList @ nil )
    | ( rearsegP @ sk__47 @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl3020]) ).

thf(zip_derived_cl2834_233,plain,
    ssList @ ( sk__8 @ nil @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl2827,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl83_234,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl3087,plain,
    rearsegP @ sk__47 @ nil,
    inference(demod,[status(thm)],[zip_derived_cl3085,zip_derived_cl2834,zip_derived_cl83]) ).

thf(zip_derived_cl15_235,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(zip_derived_cl3088,plain,
    ( ~ ( ssList @ nil )
    | ( ( app @ ( sk__6 @ nil @ sk__47 ) @ nil )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3087,zip_derived_cl15]) ).

thf(zip_derived_cl83_236,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl190_237,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3093,plain,
    ( ( app @ ( sk__6 @ nil @ sk__47 ) @ nil )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl3088,zip_derived_cl83,zip_derived_cl190]) ).

thf(zip_derived_cl3132,plain,
    ( ~ ( ssList @ sk__47 )
    | ( ( app @ sk__47 @ nil )
      = sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl3065,zip_derived_cl3093]) ).

thf(zip_derived_cl190_238,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3133,plain,
    ( ( app @ sk__47 @ nil )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl3132,zip_derived_cl190]) ).

thf(zip_derived_cl196490_239,plain,
    ssList @ ( cons @ ( hd @ sk__48 ) @ sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl196226,zip_derived_cl2653,zip_derived_cl201]) ).

thf(zip_derived_cl238481,plain,
    ( ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl237867,zip_derived_cl196500,zip_derived_cl3133,zip_derived_cl196490]) ).

thf(zip_derived_cl196495_240,plain,
    ( nil
   != ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).

thf(zip_derived_cl238482,plain,
    ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ sk__47 ) @ nil ) )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl238481,zip_derived_cl196495]) ).

thf(zip_derived_cl239165,plain,
    ( ~ ( ssList @ sk__47 )
    | ~ ( ssItem @ ( hd @ sk__48 ) )
    | ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) )
      = sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl33447,zip_derived_cl238482]) ).

thf(zip_derived_cl190_241,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197273_242,plain,
    ssItem @ ( hd @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).

thf(zip_derived_cl239172,plain,
    ( ( tl @ ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) )
    = sk__47 ),
    inference(demod,[status(thm)],[zip_derived_cl239165,zip_derived_cl190,zip_derived_cl197273]) ).

thf(zip_derived_cl92_243,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( hd @ ( cons @ X0 @ X1 ) )
        = X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax23]) ).

thf(zip_derived_cl4502_244,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil = X0 )
      | ~ ( ssList @ X1 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ ( app @ X0 @ X1 ) ) )
        = ( app @ X0 @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4501,zip_derived_cl95]) ).

thf(zip_derived_cl4580,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ X0 @ X2 ) )
      | ( nil
        = ( cons @ X0 @ X2 ) )
      | ~ ( ssList @ X1 )
      | ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
        = ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl92,zip_derived_cl4502]) ).

thf(zip_derived_cl82_245,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl174275,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
        = ( app @ ( cons @ X0 @ X2 ) @ X1 ) )
      | ~ ( ssList @ X1 )
      | ( nil
        = ( cons @ X0 @ X2 ) )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl4580,zip_derived_cl82]) ).

thf(ax21,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssItem @ V )
         => ( nil
           != ( cons @ V @ U ) ) ) ) ).

thf(zip_derived_cl90,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( nil
       != ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax21]) ).

thf(zip_derived_cl174276,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ssList @ X2 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( cons @ X0 @ ( tl @ ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) )
        = ( app @ ( cons @ X0 @ X2 ) @ X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl174275,zip_derived_cl90]) ).

thf(zip_derived_cl239602,plain,
    ( ~ ( ssList @ nil )
    | ~ ( ssItem @ ( hd @ sk__48 ) )
    | ~ ( ssList @ sk__47 )
    | ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
      = ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl239172,zip_derived_cl174276]) ).

thf(zip_derived_cl83_246,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl197273_247,plain,
    ssItem @ ( hd @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl197272,zip_derived_cl196495]) ).

thf(zip_derived_cl190_248,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl239756,plain,
    ( ( cons @ ( hd @ sk__48 ) @ sk__47 )
    = ( app @ ( cons @ ( hd @ sk__48 ) @ nil ) @ sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl239602,zip_derived_cl83,zip_derived_cl197273,zip_derived_cl190]) ).

thf(zip_derived_cl175,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil != X0 )
      | ( nil != X1 )
      | ( nil
        = ( app @ X1 @ X0 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl243000,plain,
    ( ~ ( ssList @ sk__47 )
    | ( nil != sk__47 )
    | ( nil
     != ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl239756,zip_derived_cl175]) ).

thf(zip_derived_cl190_249,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl243437,plain,
    ( ( nil != sk__47 )
    | ( nil
     != ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil
      = ( cons @ ( hd @ sk__48 ) @ sk__47 ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl243000,zip_derived_cl190]) ).

thf(zip_derived_cl196495_250,plain,
    ( nil
   != ( cons @ ( hd @ sk__48 ) @ sk__47 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl196494,zip_derived_cl203]) ).

thf(zip_derived_cl243438,plain,
    ( ( nil != sk__47 )
    | ( nil
     != ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl243437,zip_derived_cl196495]) ).

thf(zip_derived_cl1827_251,plain,
    ( ( sk__47
      = ( app @ ( tl @ sk__48 ) @ ( cons @ ( hd @ sk__48 ) @ nil ) ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1826,zip_derived_cl203]) ).

thf(zip_derived_cl173,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ( nil
       != ( app @ X1 @ X0 ) )
      | ( nil = X0 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax83]) ).

thf(zip_derived_cl1838,plain,
    ( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil != sk__47 )
    | ( nil
      = ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ~ ( ssList @ ( tl @ sk__48 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1827,zip_derived_cl173]) ).

thf(zip_derived_cl1870,plain,
    ( ~ ( ssList @ ( tl @ sk__48 ) )
    | ( nil
      = ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil != sk__47 )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1838]) ).

thf(zip_derived_cl203154_252,plain,
    ssList @ ( tl @ sk__48 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl203153,zip_derived_cl203]) ).

thf(zip_derived_cl203255,plain,
    ( ( nil
      = ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil != sk__47 )
    | ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1870,zip_derived_cl203154]) ).

thf(zip_derived_cl243808,plain,
    ( ~ ( ssList @ ( cons @ ( hd @ sk__48 ) @ nil ) )
    | ( nil != sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl243438,zip_derived_cl203255]) ).

thf(zip_derived_cl260001_253,plain,
    ( ( cons @ ( hd @ sk__48 ) @ nil )
    = sk__48 ),
    inference(demod,[status(thm)],[zip_derived_cl198887,zip_derived_cl259971]) ).

thf(zip_derived_cl201_254,plain,
    ssList @ sk__48,
    inference(demod,[status(thm)],[zip_derived_cl198,zip_derived_cl197]) ).

thf(zip_derived_cl261676,plain,
    nil != sk__47,
    inference(demod,[status(thm)],[zip_derived_cl243808,zip_derived_cl260001,zip_derived_cl201]) ).

thf(zip_derived_cl276658,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl276657,zip_derived_cl261676]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.sbai3tWb3k true
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Aug 28 19:20:40 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Running portfolio for 300 s
% 0.12/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  % Number of cores: 8
% 0.12/0.34  % Python version: Python 3.6.8
% 0.12/0.34  % Running in FO mode
% 0.19/0.65  % Total configuration time : 435
% 0.19/0.65  % Estimated wc time : 1092
% 0.19/0.65  % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.68  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.70  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.72/0.71  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.14/0.73  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.14/0.74  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.14/0.74  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.14/0.74  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 260.58/38.13  % Solved by fo/fo13.sh.
% 260.58/38.13  % done 23449 iterations in 37.345s
% 260.58/38.13  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 260.58/38.13  % SZS output start Refutation
% See solution above
% 260.58/38.14  
% 260.58/38.14  
% 260.58/38.14  % Terminating...
% 260.58/38.21  % Runner terminated.
% 260.58/38.23  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------