TSTP Solution File: SWV441^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWV441^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ReRaa6Fypr true

% Computer : n023.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 : Fri Sep  1 00:09:59 EDT 2023

% Result   : Theorem 106.88s 14.01s
% Output   : Refutation 106.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  163 (  58 unt;  27 typ;   0 def)
%            Number of atoms       :  982 (  36 equ;  90 cnn)
%            Maximal formula atoms :   44 (   7 avg)
%            Number of connectives : 2403 ( 228   ~; 213   |;   0   &;1457   @)
%                                         (   0 <=>; 271  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   9 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  146 ( 146   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  26 usr;  10 con; 0-3 aty)
%                                         ( 234  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  466 ( 294   ^; 172   !;   0   ?; 466   :)

% Comments : 
%------------------------------------------------------------------------------
thf(individuals_type,type,
    individuals: $tType ).

thf(cs4_atom_type,type,
    cs4_atom: ( $i > $o ) > $i > $o ).

thf(cs4_impl_type,type,
    cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf('#sk12_type',type,
    '#sk12': ( $i > $o ) > $i > $i ).

thf(reli_type,type,
    reli: $i > $i > $o ).

thf('#sk9_type',type,
    '#sk9': $i ).

thf('#sk3_type',type,
    '#sk3': $i > $o ).

thf(relr_type,type,
    relr: $i > $i > $o ).

thf(mimpl_type,type,
    mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk2_type',type,
    '#sk2': $i > $o ).

thf(bl_valid_type,type,
    bl_valid: ( $i > $o ) > $o ).

thf('#sk1_type',type,
    '#sk1': individuals ).

thf(cs4_box_type,type,
    cs4_box: ( $i > $o ) > $i > $o ).

thf(bl_impl_type,type,
    bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk4_type',type,
    '#sk4': $i ).

thf(bl_says_type,type,
    bl_says: individuals > ( $i > $o ) > $i > $o ).

thf(bl_princ_type,type,
    bl_princ: ( $i > $o ) > $i > $o ).

thf('#sk7_type',type,
    '#sk7': $i ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(princ_inj_type,type,
    princ_inj: individuals > $i > $o ).

thf('#sk6_type',type,
    '#sk6': $i ).

thf('#sk8_type',type,
    '#sk8': $i ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk5_type',type,
    '#sk5': $i ).

thf('#form10_type',type,
    '#form10': $i > $o ).

thf(bl_valid_def,axiom,
    bl_valid = mvalid ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [P: $i > $o] :
        ! [W: $i] : ( P @ W ) ) ) ).

thf('0',plain,
    ( mvalid
    = ( ^ [P: $i > $o] :
        ! [W: $i] : ( P @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

thf('1',plain,
    ( mvalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf('2',plain,
    bl_valid = mvalid,
    inference(simplify_rw_rule,[status(thm)],[bl_valid_def,'1']) ).

thf('3',plain,
    bl_valid = mvalid,
    define([status(thm)]) ).

thf(bl_says,axiom,
    ( bl_says
    = ( ^ [K: individuals,A: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) ) ) ).

thf(bl_princ,axiom,
    ( bl_princ
    = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ) ).

thf(cs4_atom,axiom,
    ( cs4_atom
    = ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ) ).

thf(mbox,axiom,
    ( mbox
    = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( R @ X @ Y )
         => ( P @ Y ) ) ) ) ).

thf('4',plain,
    ( mbox
    = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
        ! [Y: $i] :
          ( ( R @ X @ Y )
         => ( P @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox]) ).

thf('5',plain,
    ( mbox
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
        ! [X4: $i] :
          ( ( V_1 @ V_3 @ X4 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( cs4_atom
    = ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cs4_atom,'5']) ).

thf('7',plain,
    ( cs4_atom
    = ( ^ [V_1: $i > $o] : ( mbox @ reli @ V_1 ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( bl_princ
    = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ),
    inference(simplify_rw_rule,[status(thm)],[bl_princ,'7','5']) ).

thf('9',plain,
    ( bl_princ
    = ( ^ [V_1: $i > $o] : ( cs4_atom @ V_1 ) ) ),
    define([status(thm)]) ).

thf(cs4_box,axiom,
    ( cs4_box
    = ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ) ).

thf('10',plain,
    ( cs4_box
    = ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cs4_box,'5']) ).

thf('11',plain,
    ( cs4_box
    = ( ^ [V_1: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(cs4_impl,axiom,
    ( cs4_impl
    = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ) ).

thf(mimpl,axiom,
    ( mimpl
    = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ) ).

thf('12',plain,
    ( mor
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('13',plain,
    ( mor
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X: $i > $o,U: $i] :
          ~ ( X @ U ) ) ) ).

thf('14',plain,
    ( mnot
    = ( ^ [X: $i > $o,U: $i] :
          ~ ( X @ U ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('15',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('16',plain,
    ( mimpl
    = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimpl,'13','15']) ).

thf('17',plain,
    ( mimpl
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
    define([status(thm)]) ).

thf('18',plain,
    ( cs4_impl
    = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cs4_impl,'5','17','13','15']) ).

thf('19',plain,
    ( cs4_impl
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mbox @ reli @ ( mimpl @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf('20',plain,
    ( bl_says
    = ( ^ [K: individuals,A: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[bl_says,'9','11','19','7','5','17','13','15']) ).

thf('21',plain,
    ( bl_says
    = ( ^ [V_1: individuals,V_2: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ V_1 ) ) @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(bl_impl,axiom,
    ( bl_impl
    = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ) ).

thf('22',plain,
    ( bl_impl
    = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ),
    inference(simplify_rw_rule,[status(thm)],[bl_impl,'19','5','17','13','15']) ).

thf('23',plain,
    ( bl_impl
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( cs4_impl @ V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(bl_k,conjecture,
    ! [K: individuals,A: $i > $o,B: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ K @ ( bl_impl @ A @ B ) ) @ ( bl_impl @ ( bl_says @ K @ A ) @ ( bl_says @ K @ B ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: individuals,X6: $i > $o,X8: $i > $o,X10: $i,X12: $i] :
      ( ( reli @ X10 @ X12 )
     => ( ! [X24: $i] :
            ( ( reli @ X12 @ X24 )
           => ( ! [X34: $i] :
                  ( ( reli @ X24 @ X34 )
                 => ! [X36: $i] :
                      ( ( relr @ X34 @ X36 )
                     => ! [X38: $i] :
                          ( ( reli @ X36 @ X38 )
                         => ( ( X8 @ X38 )
                            | ~ ! [X40: $i] :
                                  ( ( reli @ X38 @ X40 )
                                 => ( princ_inj @ X4 @ X40 ) ) ) ) ) )
              | ~ ! [X26: $i] :
                    ( ( reli @ X24 @ X26 )
                   => ! [X28: $i] :
                        ( ( relr @ X26 @ X28 )
                       => ! [X30: $i] :
                            ( ( reli @ X28 @ X30 )
                           => ( ( X6 @ X30 )
                              | ~ ! [X32: $i] :
                                    ( ( reli @ X30 @ X32 )
                                   => ( princ_inj @ X4 @ X32 ) ) ) ) ) ) ) )
        | ~ ! [X14: $i] :
              ( ( reli @ X12 @ X14 )
             => ! [X16: $i] :
                  ( ( relr @ X14 @ X16 )
                 => ! [X18: $i] :
                      ( ( reli @ X16 @ X18 )
                     => ( ! [X22: $i] :
                            ( ( reli @ X18 @ X22 )
                           => ( ( X8 @ X22 )
                              | ~ ( X6 @ X22 ) ) )
                        | ~ ! [X20: $i] :
                              ( ( reli @ X18 @ X20 )
                             => ( princ_inj @ X4 @ X20 ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: individuals,X6: $i > $o,X8: $i > $o,X10: $i,X12: $i] :
        ( ( reli @ X10 @ X12 )
       => ( ! [X24: $i] :
              ( ( reli @ X12 @ X24 )
             => ( ! [X34: $i] :
                    ( ( reli @ X24 @ X34 )
                   => ! [X36: $i] :
                        ( ( relr @ X34 @ X36 )
                       => ! [X38: $i] :
                            ( ( reli @ X36 @ X38 )
                           => ( ( X8 @ X38 )
                              | ~ ! [X40: $i] :
                                    ( ( reli @ X38 @ X40 )
                                   => ( princ_inj @ X4 @ X40 ) ) ) ) ) )
                | ~ ! [X26: $i] :
                      ( ( reli @ X24 @ X26 )
                     => ! [X28: $i] :
                          ( ( relr @ X26 @ X28 )
                         => ! [X30: $i] :
                              ( ( reli @ X28 @ X30 )
                             => ( ( X6 @ X30 )
                                | ~ ! [X32: $i] :
                                      ( ( reli @ X30 @ X32 )
                                     => ( princ_inj @ X4 @ X32 ) ) ) ) ) ) ) )
          | ~ ! [X14: $i] :
                ( ( reli @ X12 @ X14 )
               => ! [X16: $i] :
                    ( ( relr @ X14 @ X16 )
                   => ! [X18: $i] :
                        ( ( reli @ X16 @ X18 )
                       => ( ! [X22: $i] :
                              ( ( reli @ X18 @ X22 )
                             => ( ( X8 @ X22 )
                                | ~ ( X6 @ X22 ) ) )
                          | ~ ! [X20: $i] :
                                ( ( reli @ X18 @ X20 )
                               => ( princ_inj @ X4 @ X20 ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6,plain,
    ~ ( !!
      @ ^ [Y0: individuals] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( !!
              @ ^ [Y2: $i > $o] :
                  ( !!
                  @ ^ [Y3: $i] :
                      ( !!
                      @ ^ [Y4: $i] :
                          ( ( reli @ Y3 @ Y4 )
                         => ( ( !!
                              @ ^ [Y5: $i] :
                                  ( ( reli @ Y4 @ Y5 )
                                 => ( ( !!
                                      @ ^ [Y6: $i] :
                                          ( ( reli @ Y5 @ Y6 )
                                         => ( !!
                                            @ ^ [Y7: $i] :
                                                ( ( relr @ Y6 @ Y7 )
                                               => ( !!
                                                  @ ^ [Y8: $i] :
                                                      ( ( reli @ Y7 @ Y8 )
                                                     => ( ( Y2 @ Y8 )
                                                        | ( (~)
                                                          @ ( !!
                                                            @ ^ [Y9: $i] :
                                                                ( ( reli @ Y8 @ Y9 )
                                                               => ( princ_inj @ Y0 @ Y9 ) ) ) ) ) ) ) ) ) ) )
                                    | ( (~)
                                      @ ( !!
                                        @ ^ [Y6: $i] :
                                            ( ( reli @ Y5 @ Y6 )
                                           => ( !!
                                              @ ^ [Y7: $i] :
                                                  ( ( relr @ Y6 @ Y7 )
                                                 => ( !!
                                                    @ ^ [Y8: $i] :
                                                        ( ( reli @ Y7 @ Y8 )
                                                       => ( ( Y1 @ Y8 )
                                                          | ( (~)
                                                            @ ( !!
                                                              @ ^ [Y9: $i] :
                                                                  ( ( reli @ Y8 @ Y9 )
                                                                 => ( princ_inj @ Y0 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                            | ( (~)
                              @ ( !!
                                @ ^ [Y5: $i] :
                                    ( ( reli @ Y4 @ Y5 )
                                   => ( !!
                                      @ ^ [Y6: $i] :
                                          ( ( relr @ Y5 @ Y6 )
                                         => ( !!
                                            @ ^ [Y7: $i] :
                                                ( ( reli @ Y6 @ Y7 )
                                               => ( ( !!
                                                    @ ^ [Y8: $i] :
                                                        ( ( reli @ Y7 @ Y8 )
                                                       => ( ( Y2 @ Y8 )
                                                          | ( (~) @ ( Y1 @ Y8 ) ) ) ) )
                                                  | ( (~)
                                                    @ ( !!
                                                      @ ^ [Y8: $i] :
                                                          ( ( reli @ Y7 @ Y8 )
                                                         => ( princ_inj @ Y0 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( !!
              @ ^ [Y2: $i] :
                  ( !!
                  @ ^ [Y3: $i] :
                      ( ( reli @ Y2 @ Y3 )
                     => ( ( !!
                          @ ^ [Y4: $i] :
                              ( ( reli @ Y3 @ Y4 )
                             => ( ( !!
                                  @ ^ [Y5: $i] :
                                      ( ( reli @ Y4 @ Y5 )
                                     => ( !!
                                        @ ^ [Y6: $i] :
                                            ( ( relr @ Y5 @ Y6 )
                                           => ( !!
                                              @ ^ [Y7: $i] :
                                                  ( ( reli @ Y6 @ Y7 )
                                                 => ( ( Y1 @ Y7 )
                                                    | ( (~)
                                                      @ ( !!
                                                        @ ^ [Y8: $i] :
                                                            ( ( reli @ Y7 @ Y8 )
                                                           => ( princ_inj @ '#sk1' @ Y8 ) ) ) ) ) ) ) ) ) ) )
                                | ( (~)
                                  @ ( !!
                                    @ ^ [Y5: $i] :
                                        ( ( reli @ Y4 @ Y5 )
                                       => ( !!
                                          @ ^ [Y6: $i] :
                                              ( ( relr @ Y5 @ Y6 )
                                             => ( !!
                                                @ ^ [Y7: $i] :
                                                    ( ( reli @ Y6 @ Y7 )
                                                   => ( ( Y0 @ Y7 )
                                                      | ( (~)
                                                        @ ( !!
                                                          @ ^ [Y8: $i] :
                                                              ( ( reli @ Y7 @ Y8 )
                                                             => ( princ_inj @ '#sk1' @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                        | ( (~)
                          @ ( !!
                            @ ^ [Y4: $i] :
                                ( ( reli @ Y3 @ Y4 )
                               => ( !!
                                  @ ^ [Y5: $i] :
                                      ( ( relr @ Y4 @ Y5 )
                                     => ( !!
                                        @ ^ [Y6: $i] :
                                            ( ( reli @ Y5 @ Y6 )
                                           => ( ( !!
                                                @ ^ [Y7: $i] :
                                                    ( ( reli @ Y6 @ Y7 )
                                                   => ( ( Y1 @ Y7 )
                                                      | ( (~) @ ( Y0 @ Y7 ) ) ) ) )
                                              | ( (~)
                                                @ ( !!
                                                  @ ^ [Y7: $i] :
                                                      ( ( reli @ Y6 @ Y7 )
                                                     => ( princ_inj @ '#sk1' @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl8,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( reli @ Y1 @ Y2 )
                 => ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( reli @ Y2 @ Y3 )
                         => ( ( !!
                              @ ^ [Y4: $i] :
                                  ( ( reli @ Y3 @ Y4 )
                                 => ( !!
                                    @ ^ [Y5: $i] :
                                        ( ( relr @ Y4 @ Y5 )
                                       => ( !!
                                          @ ^ [Y6: $i] :
                                              ( ( reli @ Y5 @ Y6 )
                                             => ( ( Y0 @ Y6 )
                                                | ( (~)
                                                  @ ( !!
                                                    @ ^ [Y7: $i] :
                                                        ( ( reli @ Y6 @ Y7 )
                                                       => ( princ_inj @ '#sk1' @ Y7 ) ) ) ) ) ) ) ) ) ) )
                            | ( (~)
                              @ ( !!
                                @ ^ [Y4: $i] :
                                    ( ( reli @ Y3 @ Y4 )
                                   => ( !!
                                      @ ^ [Y5: $i] :
                                          ( ( relr @ Y4 @ Y5 )
                                         => ( !!
                                            @ ^ [Y6: $i] :
                                                ( ( reli @ Y5 @ Y6 )
                                               => ( ( '#sk2' @ Y6 )
                                                  | ( (~)
                                                    @ ( !!
                                                      @ ^ [Y7: $i] :
                                                          ( ( reli @ Y6 @ Y7 )
                                                         => ( princ_inj @ '#sk1' @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( reli @ Y2 @ Y3 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( relr @ Y3 @ Y4 )
                                 => ( !!
                                    @ ^ [Y5: $i] :
                                        ( ( reli @ Y4 @ Y5 )
                                       => ( ( !!
                                            @ ^ [Y6: $i] :
                                                ( ( reli @ Y5 @ Y6 )
                                               => ( ( Y0 @ Y6 )
                                                  | ( (~) @ ( '#sk2' @ Y6 ) ) ) ) )
                                          | ( (~)
                                            @ ( !!
                                              @ ^ [Y6: $i] :
                                                  ( ( reli @ Y5 @ Y6 )
                                                 => ( princ_inj @ '#sk1' @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl9,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( reli @ Y0 @ Y1 )
             => ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( reli @ Y1 @ Y2 )
                     => ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( reli @ Y2 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( relr @ Y3 @ Y4 )
                                   => ( !!
                                      @ ^ [Y5: $i] :
                                          ( ( reli @ Y4 @ Y5 )
                                         => ( ( '#sk3' @ Y5 )
                                            | ( (~)
                                              @ ( !!
                                                @ ^ [Y6: $i] :
                                                    ( ( reli @ Y5 @ Y6 )
                                                   => ( princ_inj @ '#sk1' @ Y6 ) ) ) ) ) ) ) ) ) ) )
                        | ( (~)
                          @ ( !!
                            @ ^ [Y3: $i] :
                                ( ( reli @ Y2 @ Y3 )
                               => ( !!
                                  @ ^ [Y4: $i] :
                                      ( ( relr @ Y3 @ Y4 )
                                     => ( !!
                                        @ ^ [Y5: $i] :
                                            ( ( reli @ Y4 @ Y5 )
                                           => ( ( '#sk2' @ Y5 )
                                              | ( (~)
                                                @ ( !!
                                                  @ ^ [Y6: $i] :
                                                      ( ( reli @ Y5 @ Y6 )
                                                     => ( princ_inj @ '#sk1' @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y2: $i] :
                        ( ( reli @ Y1 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( relr @ Y2 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( reli @ Y3 @ Y4 )
                                   => ( ( !!
                                        @ ^ [Y5: $i] :
                                            ( ( reli @ Y4 @ Y5 )
                                           => ( ( '#sk3' @ Y5 )
                                              | ( (~) @ ( '#sk2' @ Y5 ) ) ) ) )
                                      | ( (~)
                                        @ ( !!
                                          @ ^ [Y5: $i] :
                                              ( ( reli @ Y4 @ Y5 )
                                             => ( princ_inj @ '#sk1' @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( reli @ '#sk4' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( relr @ Y2 @ Y3 )
                               => ( !!
                                  @ ^ [Y4: $i] :
                                      ( ( reli @ Y3 @ Y4 )
                                     => ( ( '#sk3' @ Y4 )
                                        | ( (~)
                                          @ ( !!
                                            @ ^ [Y5: $i] :
                                                ( ( reli @ Y4 @ Y5 )
                                               => ( princ_inj @ '#sk1' @ Y5 ) ) ) ) ) ) ) ) ) ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( !!
                              @ ^ [Y3: $i] :
                                  ( ( relr @ Y2 @ Y3 )
                                 => ( !!
                                    @ ^ [Y4: $i] :
                                        ( ( reli @ Y3 @ Y4 )
                                       => ( ( '#sk2' @ Y4 )
                                          | ( (~)
                                            @ ( !!
                                              @ ^ [Y5: $i] :
                                                  ( ( reli @ Y4 @ Y5 )
                                                 => ( princ_inj @ '#sk1' @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( reli @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( relr @ Y1 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( reli @ Y2 @ Y3 )
                               => ( ( !!
                                    @ ^ [Y4: $i] :
                                        ( ( reli @ Y3 @ Y4 )
                                       => ( ( '#sk3' @ Y4 )
                                          | ( (~) @ ( '#sk2' @ Y4 ) ) ) ) )
                                  | ( (~)
                                    @ ( !!
                                      @ ^ [Y4: $i] :
                                          ( ( reli @ Y3 @ Y4 )
                                         => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl11,plain,
    ~ ( ( reli @ '#sk4' @ '#sk5' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ '#sk5' @ Y0 )
             => ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( relr @ Y1 @ Y2 )
                           => ( !!
                              @ ^ [Y3: $i] :
                                  ( ( reli @ Y2 @ Y3 )
                                 => ( ( '#sk3' @ Y3 )
                                    | ( (~)
                                      @ ( !!
                                        @ ^ [Y4: $i] :
                                            ( ( reli @ Y3 @ Y4 )
                                           => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( reli @ Y0 @ Y1 )
                       => ( !!
                          @ ^ [Y2: $i] :
                              ( ( relr @ Y1 @ Y2 )
                             => ( !!
                                @ ^ [Y3: $i] :
                                    ( ( reli @ Y2 @ Y3 )
                                   => ( ( '#sk2' @ Y3 )
                                      | ( (~)
                                        @ ( !!
                                          @ ^ [Y4: $i] :
                                              ( ( reli @ Y3 @ Y4 )
                                             => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( reli @ '#sk5' @ Y0 )
               => ( !!
                  @ ^ [Y1: $i] :
                      ( ( relr @ Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( ( !!
                                @ ^ [Y3: $i] :
                                    ( ( reli @ Y2 @ Y3 )
                                   => ( ( '#sk3' @ Y3 )
                                      | ( (~) @ ( '#sk2' @ Y3 ) ) ) ) )
                              | ( (~)
                                @ ( !!
                                  @ ^ [Y3: $i] :
                                      ( ( reli @ Y2 @ Y3 )
                                     => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl13,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ '#sk5' @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( reli @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( relr @ Y1 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( reli @ Y2 @ Y3 )
                               => ( ( '#sk3' @ Y3 )
                                  | ( (~)
                                    @ ( !!
                                      @ ^ [Y4: $i] :
                                          ( ( reli @ Y3 @ Y4 )
                                         => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( relr @ Y1 @ Y2 )
                           => ( !!
                              @ ^ [Y3: $i] :
                                  ( ( reli @ Y2 @ Y3 )
                                 => ( ( '#sk2' @ Y3 )
                                    | ( (~)
                                      @ ( !!
                                        @ ^ [Y4: $i] :
                                            ( ( reli @ Y3 @ Y4 )
                                           => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ '#sk5' @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( relr @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( ( !!
                              @ ^ [Y3: $i] :
                                  ( ( reli @ Y2 @ Y3 )
                                 => ( ( '#sk3' @ Y3 )
                                    | ( (~) @ ( '#sk2' @ Y3 ) ) ) ) )
                            | ( (~)
                              @ ( !!
                                @ ^ [Y3: $i] :
                                    ( ( reli @ Y2 @ Y3 )
                                   => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl14,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( reli @ '#sk5' @ Y0 )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( relr @ Y1 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( reli @ Y2 @ Y3 )
                             => ( ( '#sk3' @ Y3 )
                                | ( (~)
                                  @ ( !!
                                    @ ^ [Y4: $i] :
                                        ( ( reli @ Y3 @ Y4 )
                                       => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( reli @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( relr @ Y1 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( reli @ Y2 @ Y3 )
                               => ( ( '#sk2' @ Y3 )
                                  | ( (~)
                                    @ ( !!
                                      @ ^ [Y4: $i] :
                                          ( ( reli @ Y3 @ Y4 )
                                         => ( princ_inj @ '#sk1' @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl16,plain,
    ~ ( ( reli @ '#sk5' @ '#sk6' )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ '#sk6' @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( relr @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( ( '#sk3' @ Y2 )
                            | ( (~)
                              @ ( !!
                                @ ^ [Y3: $i] :
                                    ( ( reli @ Y2 @ Y3 )
                                   => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( reli @ '#sk6' @ Y0 )
               => ( !!
                  @ ^ [Y1: $i] :
                      ( ( relr @ Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( ( '#sk2' @ Y2 )
                              | ( (~)
                                @ ( !!
                                  @ ^ [Y3: $i] :
                                      ( ( reli @ Y2 @ Y3 )
                                     => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl18,plain,
    reli @ '#sk5' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl19,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ '#sk6' @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( relr @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( reli @ Y1 @ Y2 )
                       => ( ( '#sk3' @ Y2 )
                          | ( (~)
                            @ ( !!
                              @ ^ [Y3: $i] :
                                  ( ( reli @ Y2 @ Y3 )
                                 => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ '#sk6' @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( relr @ Y0 @ Y1 )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( ( '#sk2' @ Y2 )
                            | ( (~)
                              @ ( !!
                                @ ^ [Y3: $i] :
                                    ( ( reli @ Y2 @ Y3 )
                                   => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl21,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( reli @ '#sk6' @ Y0 )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( relr @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( reli @ Y1 @ Y2 )
                     => ( ( '#sk3' @ Y2 )
                        | ( (~)
                          @ ( !!
                            @ ^ [Y3: $i] :
                                ( ( reli @ Y2 @ Y3 )
                               => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl24,plain,
    ~ ( ( reli @ '#sk6' @ '#sk7' )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( relr @ '#sk7' @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( '#sk3' @ Y1 )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    reli @ '#sk6' @ '#sk7',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(trans_axiom_i,axiom,
    ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i > $o,X6: $i] :
      ( ! [X10: $i] :
          ( ( reli @ X6 @ X10 )
         => ! [X12: $i] :
              ( ( reli @ X10 @ X12 )
             => ( X4 @ X12 ) ) )
      | ~ ! [X8: $i] :
            ( ( reli @ X6 @ X8 )
           => ( X4 @ X8 ) ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( reli @ Y1 @ Y2 )
                 => ( !!
                    @ ^ [Y3: $i] :
                        ( ( reli @ Y2 @ Y3 )
                       => ( Y0 @ Y3 ) ) ) ) )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( reli @ Y1 @ Y2 )
                   => ( Y0 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl112,plain,
    ! [X2: $i > $o] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( reli @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( reli @ Y1 @ Y2 )
                     => ( X2 @ Y2 ) ) ) ) )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( X2 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl113,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X4 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( X2 @ Y1 ) ) ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl112]) ).

thf(zip_derived_cl114,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X4 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( X2 @ Y1 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl113]) ).

thf(zip_derived_cl115,plain,
    ! [X2: $i > $o,X4: $i,X6: $i] :
      ( ( ( reli @ X4 @ X6 )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( X2 @ Y0 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl116,plain,
    ! [X2: $i > $o,X4: $i,X6: $i] :
      ( ~ ( reli @ X4 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X6 @ Y0 )
           => ( X2 @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl115]) ).

thf(zip_derived_cl117,plain,
    ! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
      ( ( ( reli @ X6 @ X8 )
       => ( X2 @ X8 ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl116]) ).

thf(zip_derived_cl118,plain,
    ! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
      ( ~ ( reli @ X6 @ X8 )
      | ( X2 @ X8 )
      | ~ ( reli @ X4 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl117]) ).

thf(zip_derived_cl119,plain,
    ! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
      ( ~ ( ( reli @ X4 @ ( '#sk12' @ X2 @ X4 ) )
         => ( X2 @ ( '#sk12' @ X2 @ X4 ) ) )
      | ~ ( reli @ X4 @ X6 )
      | ( X2 @ X8 )
      | ~ ( reli @ X6 @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl118]) ).

thf(zip_derived_cl120,plain,
    ! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
      ( ( reli @ X4 @ ( '#sk12' @ X2 @ X4 ) )
      | ~ ( reli @ X6 @ X8 )
      | ( X2 @ X8 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl126,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( reli @ X0 @ '#sk6' )
      | ( X1 @ '#sk7' )
      | ( reli @ X0 @ ( '#sk12' @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl120]) ).

thf(zip_derived_cl651,plain,
    ! [X0: $i > $o] :
      ( ( reli @ '#sk5' @ ( '#sk12' @ X0 @ '#sk5' ) )
      | ( X0 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl126]) ).

thf(zip_derived_cl18_001,plain,
    reli @ '#sk5' @ '#sk6',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl27_002,plain,
    reli @ '#sk6' @ '#sk7',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl121,plain,
    ! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
      ( ~ ( X2 @ ( '#sk12' @ X2 @ X4 ) )
      | ~ ( reli @ X6 @ X8 )
      | ( X2 @ X8 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl135,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( reli @ X0 @ '#sk6' )
      | ( X1 @ '#sk7' )
      | ~ ( X1 @ ( '#sk12' @ X1 @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl121]) ).

thf(zip_derived_cl704,plain,
    ! [X0: $i > $o] :
      ( ~ ( X0 @ ( '#sk12' @ X0 @ '#sk5' ) )
      | ( X0 @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl135]) ).

thf(zip_derived_cl4229,plain,
    ( ( reli @ '#sk5' @ '#sk7' )
    | ( reli @ '#sk5' @ '#sk7' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl651,zip_derived_cl704]) ).

thf(zip_derived_cl4248,plain,
    reli @ '#sk5' @ '#sk7',
    inference(simplify,[status(thm)],[zip_derived_cl4229]) ).

thf(zip_derived_cl28,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( relr @ '#sk7' @ Y0 )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( reli @ Y0 @ Y1 )
               => ( ( '#sk3' @ Y1 )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl31,plain,
    ~ ( ( relr @ '#sk7' @ '#sk8' )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ '#sk8' @ Y0 )
           => ( ( '#sk3' @ Y0 )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl35,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( reli @ '#sk8' @ Y0 )
         => ( ( '#sk3' @ Y0 )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( reli @ Y0 @ Y1 )
                   => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl38,plain,
    ~ ( ( reli @ '#sk8' @ '#sk9' )
     => ( ( '#sk3' @ '#sk9' )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( reli @ '#sk9' @ Y0 )
               => ( princ_inj @ '#sk1' @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl41,plain,
    reli @ '#sk8' @ '#sk9',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(refl_axiom_i,axiom,
    ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i > $o,X6: $i] :
      ( ( X4 @ X6 )
      | ~ ! [X8: $i] :
            ( ( reli @ X6 @ X8 )
           => ( X4 @ X8 ) ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( Y0 @ Y1 )
            | ( (~)
              @ ( !!
                @ ^ [Y2: $i] :
                    ( ( reli @ Y1 @ Y2 )
                   => ( Y0 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl62,plain,
    ! [X2: $i > $o] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( X2 @ Y0 )
          | ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( X2 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl63,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( X2 @ X4 )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl64,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( X2 @ X4 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( X2 @ Y0 ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl65,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( ( reli @ X4 @ ( '#sk12' @ X2 @ X4 ) )
         => ( X2 @ ( '#sk12' @ X2 @ X4 ) ) )
      | ( X2 @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl66,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( reli @ X4 @ ( '#sk12' @ X2 @ X4 ) )
      | ( X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl67,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( X2 @ ( '#sk12' @ X2 @ X4 ) )
      | ( X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl79,plain,
    ! [X0: $i] :
      ( ( reli @ X0 @ X0 )
      | ( reli @ X0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl67]) ).

thf(zip_derived_cl80,plain,
    ! [X0: $i] : ( reli @ X0 @ X0 ),
    inference(simplify,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl15,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( reli @ '#sk5' @ Y0 )
       => ( !!
          @ ^ [Y1: $i] :
              ( ( relr @ Y0 @ Y1 )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( reli @ Y1 @ Y2 )
                   => ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( reli @ Y2 @ Y3 )
                           => ( ( '#sk3' @ Y3 )
                              | ( (~) @ ( '#sk2' @ Y3 ) ) ) ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( reli @ Y2 @ Y3 )
                             => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i] :
      ( ( reli @ '#sk5' @ X2 )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( relr @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( ( '#sk3' @ Y2 )
                            | ( (~) @ ( '#sk2' @ Y2 ) ) ) ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i] :
      ( ~ ( reli @ '#sk5' @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( relr @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( reli @ Y1 @ Y2 )
                         => ( ( '#sk3' @ Y2 )
                            | ( (~) @ ( '#sk2' @ Y2 ) ) ) ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( relr @ X2 @ X4 )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( ( '#sk3' @ Y1 )
                        | ( (~) @ ( '#sk2' @ Y1 ) ) ) ) )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( reli @ Y0 @ Y1 )
                       => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) ) )
      | ~ ( reli @ '#sk5' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( relr @ X2 @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X4 @ Y0 )
           => ( ( !!
                @ ^ [Y1: $i] :
                    ( ( reli @ Y0 @ Y1 )
                   => ( ( '#sk3' @ Y1 )
                      | ( (~) @ ( '#sk2' @ Y1 ) ) ) ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) )
      | ~ ( reli @ '#sk5' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( reli @ X4 @ X6 )
       => ( ( !!
            @ ^ [Y0: $i] :
                ( ( reli @ X6 @ Y0 )
               => ( ( '#sk3' @ Y0 )
                  | ( (~) @ ( '#sk2' @ Y0 ) ) ) ) )
          | ( (~)
            @ ( !!
              @ ^ [Y0: $i] :
                  ( ( reli @ X6 @ Y0 )
                 => ( princ_inj @ '#sk1' @ Y0 ) ) ) ) ) )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( relr @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( reli @ X4 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X6 @ Y0 )
           => ( ( '#sk3' @ Y0 )
              | ( (~) @ ( '#sk2' @ Y0 ) ) ) ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ '#sk5' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl37,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X6 @ Y0 )
           => ( ( '#sk3' @ Y0 )
              | ( (~) @ ( '#sk2' @ Y0 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( ( reli @ X6 @ X8 )
       => ( ( '#sk3' @ X8 )
          | ( (~) @ ( '#sk2' @ X8 ) ) ) )
      | ~ ( reli @ X4 @ X6 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( reli @ X6 @ X8 )
      | ( '#sk3' @ X8 )
      | ( (~) @ ( '#sk2' @ X8 ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl44_003,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( reli @ X6 @ X8 )
      | ( '#sk3' @ X8 )
      | ( (~) @ ( '#sk2' @ X8 ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl48,plain,
    ! [X6: $i] :
      ( ( '#form10' @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ~ ( '#form10' @ X6 )
      | ~ ( reli @ X4 @ X6 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ '#sk5' @ X2 )
      | ( '#sk3' @ X8 )
      | ( (~) @ ( '#sk2' @ X8 ) )
      | ~ ( reli @ X6 @ X8 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl48]) ).

thf(zip_derived_cl55,plain,
    ! [X2: $i,X4: $i,X6: $i,X8: $i] :
      ( ( '#sk3' @ X8 )
      | ~ ( '#sk2' @ X8 )
      | ~ ( reli @ X6 @ X8 )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ X4 @ X6 )
      | ~ ( '#form10' @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl83,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( '#form10' @ X0 )
      | ~ ( reli @ X1 @ X0 )
      | ~ ( relr @ X2 @ X1 )
      | ~ ( reli @ '#sk5' @ X2 )
      | ~ ( '#sk2' @ X0 )
      | ( '#sk3' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl55]) ).

thf(zip_derived_cl595,plain,
    ! [X0: $i] :
      ( ( '#sk3' @ '#sk9' )
      | ~ ( '#sk2' @ '#sk9' )
      | ~ ( reli @ '#sk5' @ X0 )
      | ~ ( relr @ X0 @ '#sk8' )
      | ~ ( '#form10' @ '#sk9' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl83]) ).

thf(zip_derived_cl42,plain,
    ~ ( ( '#sk3' @ '#sk9' )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ '#sk9' @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl45,plain,
    ~ ( '#sk3' @ '#sk9' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl27_004,plain,
    reli @ '#sk6' @ '#sk7',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl41_005,plain,
    reli @ '#sk8' @ '#sk9',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl22,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( reli @ '#sk6' @ Y0 )
       => ( !!
          @ ^ [Y1: $i] :
              ( ( relr @ Y0 @ Y1 )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( reli @ Y1 @ Y2 )
                   => ( ( '#sk2' @ Y2 )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( reli @ Y2 @ Y3 )
                             => ( princ_inj @ '#sk1' @ Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i] :
      ( ( reli @ '#sk6' @ X2 )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( relr @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( '#sk2' @ Y1 )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i] :
      ( ~ ( reli @ '#sk6' @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( relr @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( reli @ Y0 @ Y1 )
                 => ( ( '#sk2' @ Y1 )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y2: $i] :
                            ( ( reli @ Y1 @ Y2 )
                           => ( princ_inj @ '#sk1' @ Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( relr @ X2 @ X4 )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X4 @ Y0 )
             => ( ( '#sk2' @ Y0 )
                | ( (~)
                  @ ( !!
                    @ ^ [Y1: $i] :
                        ( ( reli @ Y0 @ Y1 )
                       => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) ) )
      | ~ ( reli @ '#sk6' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( relr @ X2 @ X4 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X4 @ Y0 )
           => ( ( '#sk2' @ Y0 )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( reli @ Y0 @ Y1 )
                     => ( princ_inj @ '#sk1' @ Y1 ) ) ) ) ) ) )
      | ~ ( reli @ '#sk6' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( reli @ X4 @ X6 )
       => ( ( '#sk2' @ X6 )
          | ( (~)
            @ ( !!
              @ ^ [Y0: $i] :
                  ( ( reli @ X6 @ Y0 )
                 => ( princ_inj @ '#sk1' @ Y0 ) ) ) ) ) )
      | ~ ( reli @ '#sk6' @ X2 )
      | ~ ( relr @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( reli @ X4 @ X6 )
      | ( '#sk2' @ X6 )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ '#sk6' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl47,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( '#sk2' @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) )
      | ~ ( reli @ '#sk6' @ X2 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl46,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( reli @ '#sk9' @ Y0 )
       => ( princ_inj @ '#sk1' @ Y0 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl51,plain,
    ! [X6: $i] :
      ( ~ ( '#form10' @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X6 @ Y0 )
           => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl48_006,plain,
    ! [X6: $i] :
      ( ( '#form10' @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl54,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#form10' @ X6 )
      | ~ ( reli @ X4 @ X6 )
      | ~ ( relr @ X2 @ X4 )
      | ~ ( reli @ '#sk6' @ X2 )
      | ( '#sk2' @ X6 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl47,zip_derived_cl51,zip_derived_cl48]) ).

thf(zip_derived_cl74,plain,
    ! [X0: $i] :
      ( ( '#sk2' @ '#sk9' )
      | ~ ( reli @ '#sk6' @ X0 )
      | ~ ( relr @ X0 @ '#sk8' )
      | ~ ( '#form10' @ '#sk9' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl54]) ).

thf(zip_derived_cl46_007,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( reli @ '#sk9' @ Y0 )
       => ( princ_inj @ '#sk1' @ Y0 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl51_008,plain,
    ! [X6: $i] :
      ( ~ ( '#form10' @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( reli @ X6 @ Y0 )
           => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl48_009,plain,
    ! [X6: $i] :
      ( ( '#form10' @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( reli @ X6 @ Y0 )
             => ( princ_inj @ '#sk1' @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl53,plain,
    '#form10' @ '#sk9',
    inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl51,zip_derived_cl48]) ).

thf(zip_derived_cl76,plain,
    ! [X0: $i] :
      ( ( '#sk2' @ '#sk9' )
      | ~ ( reli @ '#sk6' @ X0 )
      | ~ ( relr @ X0 @ '#sk8' ) ),
    inference(demod,[status(thm)],[zip_derived_cl74,zip_derived_cl53]) ).

thf(zip_derived_cl166,plain,
    ( ~ ( relr @ '#sk7' @ '#sk8' )
    | ( '#sk2' @ '#sk9' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl76]) ).

thf(zip_derived_cl34,plain,
    relr @ '#sk7' @ '#sk8',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl167,plain,
    '#sk2' @ '#sk9',
    inference(demod,[status(thm)],[zip_derived_cl166,zip_derived_cl34]) ).

thf(zip_derived_cl53_010,plain,
    '#form10' @ '#sk9',
    inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl51,zip_derived_cl48]) ).

thf(zip_derived_cl596,plain,
    ! [X0: $i] :
      ( ~ ( reli @ '#sk5' @ X0 )
      | ~ ( relr @ X0 @ '#sk8' ) ),
    inference(demod,[status(thm)],[zip_derived_cl595,zip_derived_cl45,zip_derived_cl167,zip_derived_cl53]) ).

thf(zip_derived_cl4294,plain,
    ~ ( relr @ '#sk7' @ '#sk8' ),
    inference('sup-',[status(thm)],[zip_derived_cl4248,zip_derived_cl596]) ).

thf(zip_derived_cl34_011,plain,
    relr @ '#sk7' @ '#sk8',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl4298,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl4294,zip_derived_cl34]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SWV441^1 : TPTP v8.1.2. Released v3.7.0.
% 0.04/0.10  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ReRaa6Fypr true
% 0.09/0.30  % Computer : n023.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue Aug 29 05:35:10 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Running portfolio for 300 s
% 0.09/0.30  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.30  % Number of cores: 8
% 0.09/0.31  % Python version: Python 3.6.8
% 0.09/0.31  % Running in HO mode
% 0.42/0.59  % Total configuration time : 828
% 0.42/0.59  % Estimated wc time : 1656
% 0.42/0.59  % Estimated cpu time (8 cpus) : 207.0
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.43/0.66  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.43/0.67  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.43/0.67  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.44/0.71  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.45/0.79  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 0.45/0.81  % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 0.45/0.85  % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s
% 106.88/14.01  % Solved by lams/15_lifting3.sh.
% 106.88/14.01  % done 586 iterations in 13.081s
% 106.88/14.01  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 106.88/14.01  % SZS output start Refutation
% See solution above
% 106.88/14.01  
% 106.88/14.01  
% 106.88/14.01  % Terminating...
% 107.56/14.13  % Runner terminated.
% 107.56/14.14  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------