TSTP Solution File: SWC183+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWC183+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.6dYi5wuuC6 true

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 21:29:43 EDT 2023

% Result   : Theorem 12.03s 2.32s
% Output   : Refutation 12.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  231 (  83 unt;  18 typ;   0 def)
%            Number of atoms       :  610 ( 235 equ;   0 cnn)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives : 1587 ( 301   ~; 326   |;  14   &; 889   @)
%                                         (   4 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :  185 (   0   ^; 181   !;   4   ?; 185   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(leq_type,type,
    leq: $i > $i > $o ).

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

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

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

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

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

thf(zip_derived_cl193,plain,
    ( ( memberP @ sk__54 @ sk__52 )
    | ( memberP @ sk__53 @ sk__52 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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(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_cl194,plain,
    ( ( app @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) @ sk__54 )
    = sk__47 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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

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

thf(zip_derived_cl3201,plain,
    ( ~ ( ssList @ ( cons @ sk__52 @ nil ) )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) )
    | ~ ( ssList @ sk__54 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl194,zip_derived_cl172]) ).

thf(zip_derived_cl195,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl3220,plain,
    ( ~ ( ssList @ ( cons @ sk__52 @ nil ) )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3201,zip_derived_cl195,zip_derived_cl192]) ).

thf(zip_derived_cl3687,plain,
    ( ~ ( ssList @ nil )
    | ~ ( ssItem @ sk__52 )
    | ( sk__47
      = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3220]) ).

thf(ax17,axiom,
    ssList @ nil ).

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

thf(zip_derived_cl196,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3688,plain,
    ( sk__47
    = ( app @ sk__53 @ ( app @ ( cons @ sk__52 @ nil ) @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3687,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl3755,plain,
    ( ~ ( ssList @ sk__54 )
    | ~ ( ssItem @ sk__52 )
    | ( sk__47
      = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl171,zip_derived_cl3688]) ).

thf(zip_derived_cl195_001,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl196_002,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3757,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3755,zip_derived_cl195,zip_derived_cl196]) ).

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

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

thf(zip_derived_cl3829,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__52 )
      | ~ ( ssList @ sk__54 )
      | ( sk__47 != X0 )
      | ~ ( ssList @ sk__53 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3757,zip_derived_cl8]) ).

thf(zip_derived_cl196_003,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl195_004,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl192_005,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3857,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3829,zip_derived_cl196,zip_derived_cl195,zip_derived_cl192]) ).

thf(zip_derived_cl201,plain,
    ( ( nil = sk__49 )
    | ( ssItem @ sk__51 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1529,plain,
    ( ( nil = sk__47 )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl201,zip_derived_cl197]) ).

thf(zip_derived_cl200,plain,
    ( ( nil = sk__49 )
    | ( ( cons @ sk__51 @ nil )
      = sk__49 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_006,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl197_007,plain,
    sk__47 = sk__49,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1535,plain,
    ( ( nil = sk__47 )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl197,zip_derived_cl197]) ).

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

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

thf(zip_derived_cl2281,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1535,zip_derived_cl110]) ).

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

thf(zip_derived_cl2284,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2281,zip_derived_cl83]) ).

thf(zip_derived_cl3857_009,plain,
    ! [X0: $i] :
      ( ( sk__47 != X0 )
      | ( memberP @ X0 @ sk__52 )
      | ~ ( ssList @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3829,zip_derived_cl196,zip_derived_cl195,zip_derived_cl192]) ).

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

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

thf(zip_derived_cl3867,plain,
    ( ~ ( ssList @ nil )
    | ( sk__47 != nil )
    | ~ ( ssItem @ sk__52 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3857,zip_derived_cl113]) ).

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

thf(zip_derived_cl196_011,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3871,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6258,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ( X0 = sk__51 )
      | ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2284,zip_derived_cl3871]) ).

thf(zip_derived_cl113_012,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax38]) ).

thf(zip_derived_cl6259,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 )
      | ~ ( ssItem @ sk__51 ) ),
    inference(clc,[status(thm)],[zip_derived_cl6258,zip_derived_cl113]) ).

thf(zip_derived_cl6260,plain,
    ! [X0: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1529,zip_derived_cl6259]) ).

thf(zip_derived_cl3871_013,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6262,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( X0 = sk__51 )
      | ~ ( memberP @ sk__47 @ X0 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6260,zip_derived_cl3871]) ).

thf(zip_derived_cl6263,plain,
    ( ~ ( ssList @ sk__47 )
    | ( sk__47 != sk__47 )
    | ~ ( ssItem @ sk__52 )
    | ( sk__52 = sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl3857,zip_derived_cl6262]) ).

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

thf(zip_derived_cl196_014,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6267,plain,
    ( ( sk__47 != sk__47 )
    | ( sk__52 = sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6263,zip_derived_cl190,zip_derived_cl196]) ).

thf(zip_derived_cl6268,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6268_015,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6271,plain,
    ( ( memberP @ sk__54 @ sk__51 )
    | ( memberP @ sk__53 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl193,zip_derived_cl6268,zip_derived_cl6268]) ).

thf(zip_derived_cl1535_016,plain,
    ( ( nil = sk__47 )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl197,zip_derived_cl197]) ).

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_cl2035,plain,
    ( ( nil = sk__47 )
    | ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl1535,zip_derived_cl94]) ).

thf(zip_derived_cl83_017,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl2037,plain,
    ( ( nil = sk__47 )
    | ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil ) ),
    inference(demod,[status(thm)],[zip_derived_cl2035,zip_derived_cl83]) ).

thf(zip_derived_cl1529_018,plain,
    ( ( nil = sk__47 )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl201,zip_derived_cl197]) ).

thf(zip_derived_cl2039,plain,
    ( ( ( tl @ sk__47 )
      = nil )
    | ( nil = sk__47 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2037,zip_derived_cl1529]) ).

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_cl2946,plain,
    ( ( nil = sk__47 )
    | ( nil = sk__47 )
    | ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl2039,zip_derived_cl168]) ).

thf(zip_derived_cl190_019,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2951,plain,
    ( ( nil = sk__47 )
    | ( nil = sk__47 )
    | ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2946,zip_derived_cl190]) ).

thf(zip_derived_cl2952,plain,
    ( ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2951]) ).

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

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

thf(zip_derived_cl2952_020,plain,
    ( ( ( cons @ ( hd @ sk__47 ) @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2951]) ).

thf(zip_derived_cl1529_021,plain,
    ( ( nil = sk__47 )
    | ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl201,zip_derived_cl197]) ).

thf(zip_derived_cl1535_022,plain,
    ( ( nil = sk__47 )
    | ( ( cons @ sk__51 @ nil )
      = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl200,zip_derived_cl197,zip_derived_cl197]) ).

thf(ax19,axiom,
    ! [U: $i] :
      ( ( ssList @ U )
     => ! [V: $i] :
          ( ( ssList @ V )
         => ! [W: $i] :
              ( ( ssItem @ W )
             => ! [X: $i] :
                  ( ( ssItem @ X )
                 => ( ( ( cons @ W @ U )
                      = ( cons @ X @ V ) )
                   => ( ( W = X )
                      & ( V = U ) ) ) ) ) ) ) ).

thf(zip_derived_cl85,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( X2 = X1 )
      | ( ( cons @ X2 @ X3 )
       != ( cons @ X1 @ X0 ) )
      | ~ ( ssItem @ X2 )
      | ~ ( ssList @ X3 ) ),
    inference(cnf,[status(esa)],[ax19]) ).

thf(zip_derived_cl1966,plain,
    ! [X0: $i,X1: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( sk__51 = X1 )
      | ( sk__47
       != ( cons @ X1 @ X0 ) )
      | ~ ( ssItem @ sk__51 )
      | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1535,zip_derived_cl85]) ).

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

thf(zip_derived_cl1972,plain,
    ! [X0: $i,X1: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( sk__51 = X1 )
      | ( sk__47
       != ( cons @ X1 @ X0 ) )
      | ~ ( ssItem @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1966,zip_derived_cl83]) ).

thf(zip_derived_cl3871_024,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl5997,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( sk__51 = X1 )
      | ( sk__47
       != ( cons @ X1 @ X0 ) )
      | ~ ( ssItem @ sk__51 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1972,zip_derived_cl3871]) ).

thf(zip_derived_cl5998,plain,
    ! [X0: $i,X1: $i] :
      ( ( nil = sk__47 )
      | ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( sk__51 = X1 )
      | ( sk__47
       != ( cons @ X1 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1529,zip_derived_cl5997]) ).

thf(zip_derived_cl3871_025,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6000,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( ssItem @ X1 )
      | ( sk__51 = X1 )
      | ( sk__47
       != ( cons @ X1 @ X0 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl5998,zip_derived_cl3871]) ).

thf(zip_derived_cl6097,plain,
    ( ( nil = sk__47 )
    | ~ ( ssList @ nil )
    | ~ ( ssItem @ ( hd @ sk__47 ) )
    | ( sk__51
      = ( hd @ sk__47 ) )
    | ( sk__47 != sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2952,zip_derived_cl6000]) ).

thf(zip_derived_cl83_026,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl6104,plain,
    ( ( nil = sk__47 )
    | ~ ( ssItem @ ( hd @ sk__47 ) )
    | ( sk__51
      = ( hd @ sk__47 ) )
    | ( sk__47 != sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6097,zip_derived_cl83]) ).

thf(zip_derived_cl6105,plain,
    ( ( sk__51
      = ( hd @ sk__47 ) )
    | ~ ( ssItem @ ( hd @ sk__47 ) )
    | ( nil = sk__47 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl6104]) ).

thf(zip_derived_cl3871_027,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6106,plain,
    ( ( sk__51
      = ( hd @ sk__47 ) )
    | ~ ( ssItem @ ( hd @ sk__47 ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6105,zip_derived_cl3871]) ).

thf(zip_derived_cl6408,plain,
    ( ~ ( ssList @ sk__47 )
    | ( nil = sk__47 )
    | ( sk__51
      = ( hd @ sk__47 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl6106]) ).

thf(zip_derived_cl190_028,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6411,plain,
    ( ( nil = sk__47 )
    | ( sk__51
      = ( hd @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl6408,zip_derived_cl190]) ).

thf(zip_derived_cl3871_029,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6412,plain,
    ( sk__51
    = ( hd @ sk__47 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6411,zip_derived_cl3871]) ).

thf(zip_derived_cl6420,plain,
    ( ( ( cons @ sk__51 @ nil )
      = sk__47 )
    | ( nil = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2952,zip_derived_cl6412]) ).

thf(zip_derived_cl3871_030,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl6421,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6420,zip_derived_cl3871]) ).

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_cl82_031,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

thf(zip_derived_cl3757_032,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__52 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3755,zip_derived_cl195,zip_derived_cl196]) ).

thf(zip_derived_cl6268_033,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6291,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__51 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3757,zip_derived_cl6268]) ).

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

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

thf(zip_derived_cl7296,plain,
    ( ~ ( ssList @ ( cons @ sk__51 @ sk__54 ) )
    | ( ( hd @ sk__47 )
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl6291,zip_derived_cl177]) ).

thf(zip_derived_cl6412_034,plain,
    ( sk__51
    = ( hd @ sk__47 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6411,zip_derived_cl3871]) ).

thf(zip_derived_cl192_035,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7355,plain,
    ( ~ ( ssList @ ( cons @ sk__51 @ sk__54 ) )
    | ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7296,zip_derived_cl6412,zip_derived_cl192]) ).

thf(zip_derived_cl7688,plain,
    ( ~ ( ssList @ sk__54 )
    | ~ ( ssItem @ sk__51 )
    | ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl7355]) ).

thf(zip_derived_cl195_036,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl196_037,plain,
    ssItem @ sk__52,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6268_038,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6273,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl7689,plain,
    ( ( sk__51
      = ( hd @ sk__53 ) )
    | ( nil = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7688,zip_derived_cl195,zip_derived_cl6273]) ).

thf(zip_derived_cl168_039,plain,
    ! [X0: $i] :
      ( ( nil = X0 )
      | ( ( cons @ ( hd @ X0 ) @ ( tl @ X0 ) )
        = X0 )
      | ~ ( ssList @ X0 ) ),
    inference(cnf,[status(esa)],[ax78]) ).

thf(zip_derived_cl7701,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 )
    | ~ ( ssList @ sk__53 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl7689,zip_derived_cl168]) ).

thf(zip_derived_cl192_040,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7711,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7701,zip_derived_cl192]) ).

thf(zip_derived_cl7712,plain,
    ( ( ( cons @ sk__51 @ ( tl @ sk__53 ) )
      = sk__53 )
    | ( nil = sk__53 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7711]) ).

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

thf(zip_derived_cl2181,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl111]) ).

thf(zip_derived_cl2182,plain,
    ! [X0: $i,X1: $i] :
      ( ( memberP @ ( cons @ X0 @ X1 ) @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2181]) ).

thf(zip_derived_cl7735,plain,
    ( ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 )
    | ~ ( ssList @ ( tl @ sk__53 ) )
    | ~ ( ssItem @ sk__51 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl7712,zip_derived_cl2182]) ).

thf(zip_derived_cl6273_041,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl7851,plain,
    ( ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 )
    | ~ ( ssList @ ( tl @ sk__53 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl7735,zip_derived_cl6273]) ).

thf(zip_derived_cl8015,plain,
    ( ~ ( ssList @ sk__53 )
    | ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl7851]) ).

thf(zip_derived_cl192_042,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8016,plain,
    ( ( nil = sk__53 )
    | ( nil = sk__53 )
    | ( memberP @ sk__53 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8015,zip_derived_cl192]) ).

thf(zip_derived_cl8017,plain,
    ( ( memberP @ sk__53 @ sk__51 )
    | ( nil = sk__53 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8016]) ).

thf(zip_derived_cl6291_043,plain,
    ( sk__47
    = ( app @ sk__53 @ ( cons @ sk__51 @ sk__54 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3757,zip_derived_cl6268]) ).

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

thf(zip_derived_cl82_044,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ssList @ ( cons @ X0 @ X1 ) )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax16]) ).

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

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

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

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

thf(zip_derived_cl1495,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ X5 )
      | ~ ( ssList @ X4 )
      | ( ( app @ ( app @ X5 @ ( cons @ X3 @ X2 ) ) @ ( cons @ X1 @ X4 ) )
       != ( cons @ X0 @ nil ) )
      | ( X3 != X1 )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl159,zip_derived_cl72]) ).

thf(zip_derived_cl3934,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ( ( app @ ( app @ X3 @ ( cons @ X0 @ X1 ) ) @ ( cons @ X0 @ X2 ) )
       != ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X3 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ ( cons @ X4 @ nil ) )
      | ~ ( ssItem @ X4 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl1495]) ).

thf(zip_derived_cl3935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X4 )
      | ~ ( ssList @ ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X3 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X3 @ ( cons @ X0 @ X1 ) ) @ ( cons @ X0 @ X2 ) )
       != ( cons @ X4 @ nil ) )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3934]) ).

thf(zip_derived_cl4042,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ X0 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X4 )
      | ~ ( ssItem @ X3 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl3935]) ).

thf(zip_derived_cl83_045,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl4046,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssItem @ X0 )
      | ~ ( ssList @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X4 )
      | ~ ( ssItem @ X3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl4042,zip_derived_cl83]) ).

thf(zip_derived_cl4047,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( ssItem @ X3 )
      | ~ ( ssList @ X4 )
      | ( ( app @ ( app @ X1 @ ( cons @ X3 @ X4 ) ) @ ( cons @ X3 @ X2 ) )
       != ( cons @ X0 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ X1 )
      | ~ ( ssItem @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4046]) ).

thf(zip_derived_cl4193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssList @ ( sk__2 @ X3 @ X0 ) )
      | ~ ( ssItem @ X1 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl4047]) ).

thf(zip_derived_cl4213,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X1 )
      | ~ ( ssList @ ( sk__2 @ X3 @ X0 ) )
      | ~ ( ssList @ X2 )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ~ ( ssItem @ X3 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssList @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl4193]) ).

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

thf(zip_derived_cl7430,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssList @ X0 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssItem @ X3 )
      | ~ ( ssList @ ( sk__3 @ X3 @ X0 ) )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssList @ X2 )
      | ~ ( ssItem @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl4213,zip_derived_cl7]) ).

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

thf(zip_derived_cl7431,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( ssItem @ X1 )
      | ~ ( ssList @ X2 )
      | ( ( app @ X0 @ ( cons @ X3 @ X2 ) )
       != ( cons @ X1 @ nil ) )
      | ~ ( ssItem @ X3 )
      | ~ ( memberP @ X0 @ X3 )
      | ~ ( ssList @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl7430,zip_derived_cl5]) ).

thf(zip_derived_cl7440,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ~ ( ssList @ sk__54 )
      | ( sk__47
       != ( cons @ X0 @ nil ) )
      | ~ ( ssItem @ sk__51 )
      | ~ ( memberP @ sk__53 @ sk__51 )
      | ~ ( ssList @ sk__53 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6291,zip_derived_cl7431]) ).

thf(zip_derived_cl195_046,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6273_047,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl192_048,plain,
    ssList @ sk__53,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7448,plain,
    ! [X0: $i] :
      ( ~ ( ssItem @ X0 )
      | ( sk__47
       != ( cons @ X0 @ nil ) )
      | ~ ( memberP @ sk__53 @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7440,zip_derived_cl195,zip_derived_cl6273,zip_derived_cl192]) ).

thf(zip_derived_cl8024,plain,
    ! [X0: $i] :
      ( ( nil = sk__53 )
      | ~ ( ssItem @ X0 )
      | ( sk__47
       != ( cons @ X0 @ nil ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl8017,zip_derived_cl7448]) ).

thf(zip_derived_cl8026,plain,
    ( ( nil = sk__53 )
    | ~ ( ssItem @ sk__51 )
    | ( sk__47 != sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl6421,zip_derived_cl8024]) ).

thf(zip_derived_cl6273_049,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl8027,plain,
    ( ( nil = sk__53 )
    | ( sk__47 != sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8026,zip_derived_cl6273]) ).

thf(zip_derived_cl8028,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl8027]) ).

thf(zip_derived_cl8030,plain,
    ( ( memberP @ sk__54 @ sk__51 )
    | ( memberP @ nil @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6271,zip_derived_cl8028]) ).

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

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

thf(zip_derived_cl194_050,plain,
    ( ( app @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) @ sk__54 )
    = sk__47 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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(zip_derived_cl3351,plain,
    ( ~ ( ssList @ sk__54 )
    | ( ( tl @ sk__47 )
      = ( app @ ( tl @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) ) @ sk__54 ) )
    | ( nil
      = ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) )
    | ~ ( ssList @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl194,zip_derived_cl178]) ).

thf(zip_derived_cl195_051,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3365,plain,
    ( ( ( tl @ sk__47 )
      = ( app @ ( tl @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) ) @ sk__54 ) )
    | ( nil
      = ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) )
    | ~ ( ssList @ ( app @ sk__53 @ ( cons @ sk__52 @ nil ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3351,zip_derived_cl195]) ).

thf(zip_derived_cl6421_052,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6420,zip_derived_cl3871]) ).

thf(zip_derived_cl94_053,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ssItem @ X0 )
      | ( ( tl @ ( cons @ X0 @ X1 ) )
        = X1 )
      | ~ ( ssList @ X1 ) ),
    inference(cnf,[status(esa)],[ax25]) ).

thf(zip_derived_cl6451,plain,
    ( ~ ( ssItem @ sk__51 )
    | ( ( tl @ sk__47 )
      = nil )
    | ~ ( ssList @ nil ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl6421,zip_derived_cl94]) ).

thf(zip_derived_cl6273_054,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl83_055,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl6568,plain,
    ( ( tl @ sk__47 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl6451,zip_derived_cl6273,zip_derived_cl83]) ).

thf(zip_derived_cl8028_056,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl8027]) ).

thf(zip_derived_cl6268_057,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6421_058,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6420,zip_derived_cl3871]) ).

thf(zip_derived_cl8028_059,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl8027]) ).

thf(zip_derived_cl6268_060,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6421_061,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6420,zip_derived_cl3871]) ).

thf(zip_derived_cl8028_062,plain,
    nil = sk__53,
    inference(simplify,[status(thm)],[zip_derived_cl8027]) ).

thf(zip_derived_cl6268_063,plain,
    sk__52 = sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl6267]) ).

thf(zip_derived_cl6421_064,plain,
    ( ( cons @ sk__51 @ nil )
    = sk__47 ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl6420,zip_derived_cl3871]) ).

thf(zip_derived_cl8276,plain,
    ( ( nil
      = ( app @ ( tl @ ( app @ nil @ sk__47 ) ) @ sk__54 ) )
    | ( nil
      = ( app @ nil @ sk__47 ) )
    | ~ ( ssList @ ( app @ nil @ sk__47 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3365,zip_derived_cl6568,zip_derived_cl8028,zip_derived_cl6268,zip_derived_cl6421,zip_derived_cl8028,zip_derived_cl6268,zip_derived_cl6421,zip_derived_cl8028,zip_derived_cl6268,zip_derived_cl6421]) ).

thf(zip_derived_cl8279,plain,
    ( ~ ( ssList @ sk__47 )
    | ( nil
      = ( app @ ( tl @ sk__47 ) @ sk__54 ) )
    | ( nil = sk__47 )
    | ~ ( ssList @ sk__47 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl97,zip_derived_cl8276]) ).

thf(zip_derived_cl190_065,plain,
    ssList @ sk__47,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6568_066,plain,
    ( ( tl @ sk__47 )
    = nil ),
    inference(demod,[status(thm)],[zip_derived_cl6451,zip_derived_cl6273,zip_derived_cl83]) ).

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

thf(zip_derived_cl8283,plain,
    ( ( nil
      = ( app @ nil @ sk__54 ) )
    | ( nil = sk__47 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8279,zip_derived_cl190,zip_derived_cl6568,zip_derived_cl190]) ).

thf(zip_derived_cl3871_068,plain,
    sk__47 != nil,
    inference(demod,[status(thm)],[zip_derived_cl3867,zip_derived_cl83,zip_derived_cl196]) ).

thf(zip_derived_cl8284,plain,
    ( nil
    = ( app @ nil @ sk__54 ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl8283,zip_derived_cl3871]) ).

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

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_cl8314,plain,
    ( ~ ( ssList @ sk__54 )
    | ( nil != nil )
    | ( nil = sk__54 )
    | ~ ( ssList @ nil ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl8284,zip_derived_cl173]) ).

thf(zip_derived_cl195_069,plain,
    ssList @ sk__54,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl83_070,plain,
    ssList @ nil,
    inference(cnf,[status(esa)],[ax17]) ).

thf(zip_derived_cl8343,plain,
    ( ( nil != nil )
    | ( nil = sk__54 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8314,zip_derived_cl195,zip_derived_cl83]) ).

thf(zip_derived_cl8344,plain,
    nil = sk__54,
    inference(simplify,[status(thm)],[zip_derived_cl8343]) ).

thf(zip_derived_cl8375,plain,
    ( ( memberP @ nil @ sk__51 )
    | ( memberP @ nil @ sk__51 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8030,zip_derived_cl8344]) ).

thf(zip_derived_cl8376,plain,
    memberP @ nil @ sk__51,
    inference(simplify,[status(thm)],[zip_derived_cl8375]) ).

thf(zip_derived_cl113_071,plain,
    ! [X0: $i] :
      ( ~ ( memberP @ nil @ X0 )
      | ~ ( ssItem @ X0 ) ),
    inference(cnf,[status(esa)],[ax38]) ).

thf(zip_derived_cl8420,plain,
    ~ ( ssItem @ sk__51 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl8376,zip_derived_cl113]) ).

thf(zip_derived_cl6273_072,plain,
    ssItem @ sk__51,
    inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl6268]) ).

thf(zip_derived_cl8422,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl8420,zip_derived_cl6273]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC183+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6dYi5wuuC6 true
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 17:48:39 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in FO mode
% 0.21/0.65  % Total configuration time : 435
% 0.21/0.65  % Estimated wc time : 1092
% 0.21/0.65  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.94/0.74  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.94/0.75  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.94/0.75  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.94/0.75  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.94/0.75  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.94/0.75  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 12.03/2.32  % Solved by fo/fo6_bce.sh.
% 12.03/2.32  % BCE start: 209
% 12.03/2.32  % BCE eliminated: 6
% 12.03/2.32  % PE start: 203
% 12.03/2.32  logic: eq
% 12.03/2.32  % PE eliminated: 6
% 12.03/2.32  % done 1019 iterations in 1.545s
% 12.03/2.32  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 12.03/2.32  % SZS output start Refutation
% See solution above
% 12.03/2.32  
% 12.03/2.32  
% 12.03/2.32  % Terminating...
% 12.18/2.38  % Runner terminated.
% 12.18/2.39  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------