%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : SCC_Bloemen_Sequential/0000_SCC_Bloemen_Sequential/prob_01402_047662__5961522_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1388 ( 687 unt; 155 typ;   0 def)
%            Number of atoms       : 3308 (1407 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 10872 ( 360   ~;  54   |; 334   &;8927   @)
%                                         (   0 <=>;1197  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :   19 (  18 usr)
%            Number of type conns  :  501 ( 501   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  140 ( 137 usr;  22 con; 0-9 aty)
%            Number of variables   : 3580 ( 289   ^;3126   !; 165   ?;3580   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 08:53:30.160
%------------------------------------------------------------------------------
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thf(sy_c_SCC__Bloemen__Sequential_Ograph_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl8307124943676871238od_v_v: set_Product_prod_v_v > ( product_prod_v_v > set_Product_prod_v_v ) > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_001tf__v,type,
    sCC_Bloemen_graph_v: set_v > ( v > set_v ) > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ois__scc_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl6242042402218619277od_v_v: ( product_prod_v_v > set_Product_prod_v_v ) > set_Product_prod_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ois__scc_001tf__v,type,
    sCC_Bloemen_is_scc_v: ( v > set_v ) > set_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ois__subscc_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl2301996248249672505od_v_v: ( product_prod_v_v > set_Product_prod_v_v ) > set_Product_prod_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ois__subscc_001tf__v,type,
    sCC_Bl5398416737448265317bscc_v: ( v > set_v ) > set_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Opost__dfs_001tf__v_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    sCC_Bl8953792750115413617t_unit: ( v > set_v ) > v > sCC_Bl1394983891496994913t_unit > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Opost__dfss_001tf__v_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    sCC_Bl6082031138996704384t_unit: ( v > set_v ) > v > sCC_Bl1394983891496994913t_unit > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Opre__dfs_001tf__v_001t__Product____Type__Ounit,type,
    sCC_Bl36166008131615352t_unit: ( v > set_v ) > v > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Opre__dfss_001t__Product____Type__Oprod_Itf__v_Mtf__v_J_001t__Product____Type__Ounit,type,
    sCC_Bl3607325323686918683t_unit: ( product_prod_v_v > set_Product_prod_v_v ) > product_prod_v_v > sCC_Bl7326425374436813197t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Opre__dfss_001tf__v_001t__Product____Type__Ounit,type,
    sCC_Bl1748261141445803503t_unit: ( v > set_v ) > v > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl4981926079593201289od_v_v: ( product_prod_v_v > set_Product_prod_v_v ) > product_prod_v_v > product_prod_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable_001tf__v,type,
    sCC_Bl649662514949026229able_v: ( v > set_v ) > v > v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable__avoiding_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl5370300055464682748od_v_v: ( product_prod_v_v > set_Product_prod_v_v ) > product_prod_v_v > product_prod_v_v > set_Pr2149350503807050951od_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable__avoiding_001tf__v,type,
    sCC_Bl4291963740693775144ding_v: ( v > set_v ) > v > v > set_Product_prod_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable__end_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl4714988717384592488od_v_v: ( product_prod_v_v > set_Product_prod_v_v ) > product_prod_v_v > product_prod_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Oreachable__end_001tf__v,type,
    sCC_Bl770211535891879572_end_v: ( v > set_v ) > v > v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Osub__env_001t__Product____Type__Oprod_Itf__v_Mtf__v_J_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    sCC_Bl7963838319573962697t_unit: sCC_Bl7326425374436813197t_unit > sCC_Bl7326425374436813197t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Osub__env_001tf__v_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    sCC_Bl5768913643336123637t_unit: sCC_Bl1394983891496994913t_unit > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ounite_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl4702006153222411093od_v_v: product_prod_v_v > product_prod_v_v > sCC_Bl7326425374436813197t_unit > sCC_Bl7326425374436813197t_unit ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ounite_001tf__v,type,
    sCC_Bloemen_unite_v: v > v > sCC_Bl1394983891496994913t_unit > sCC_Bl1394983891496994913t_unit ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Ounvisited_001tf__v_001t__Product____Type__Ounit,type,
    sCC_Bl3123350270117520219t_unit: ( v > set_v ) > sCC_Bl1394983891496994913t_unit > v > set_Product_prod_v_v ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Owf__env_001t__Product____Type__Oprod_Itf__v_Mtf__v_J_001t__Product____Type__Ounit,type,
    sCC_Bl7798947040364291444t_unit: ( product_prod_v_v > set_Product_prod_v_v ) > sCC_Bl7326425374436813197t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Ograph_Owf__env_001tf__v_001t__Product____Type__Ounit,type,
    sCC_Bl9196236973127232072t_unit: ( v > set_v ) > sCC_Bl1394983891496994913t_unit > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Oinit__env_001tf__v,type,
    sCC_Bl7693227186847904995_env_v: v > sCC_Bl1394983891496994913t_unit ).

thf(sy_c_SCC__Bloemen__Sequential_Oprecedes_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    sCC_Bl2026170059108282219od_v_v: product_prod_v_v > product_prod_v_v > list_P7986770385144383213od_v_v > $o ).

thf(sy_c_SCC__Bloemen__Sequential_Oprecedes_001tf__v,type,
    sCC_Bl4022239298816431255edes_v: v > v > list_v > $o ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    collec140062887454715474od_v_v: ( product_prod_v_v > $o ) > set_Product_prod_v_v ).

thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_Itf__v_Mtf__v_J_J,type,
    collec8263177866097347122od_v_v: ( set_Product_prod_v_v > $o ) > set_se8455005133513928103od_v_v ).

thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__v_J,type,
    collect_set_v: ( set_v > $o ) > set_set_v ).

thf(sy_c_Set_OCollect_001tf__v,type,
    collect_v: ( v > $o ) > set_v ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    insert1338601472111419319od_v_v: product_prod_v_v > set_Product_prod_v_v > set_Product_prod_v_v ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Ounit,type,
    insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).

thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_Itf__v_Mtf__v_J_J,type,
    insert7504383016908236695od_v_v: set_Product_prod_v_v > set_se8455005133513928103od_v_v > set_se8455005133513928103od_v_v ).

thf(sy_c_Set_Oinsert_001t__Set__Oset_Itf__v_J,type,
    insert_set_v: set_v > set_set_v > set_set_v ).

thf(sy_c_Set_Oinsert_001tf__v,type,
    insert_v: v > set_v > set_v ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__v_Mtf__v_J_Mt__Product____Type__Oprod_Itf__v_Mtf__v_J_J,type,
    member3038538357316246288od_v_v: produc206430290419586791od_v_v > set_Pr2149350503807050951od_v_v > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__v_Mtf__v_J,type,
    member7453568604450474000od_v_v: product_prod_v_v > set_Product_prod_v_v > $o ).

thf(sy_c_member_001t__Product____Type__Ounit,type,
    member_Product_unit: product_unit > set_Product_unit > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_Itf__v_Mtf__v_J_J,type,
    member8406446414694345712od_v_v: set_Product_prod_v_v > set_se8455005133513928103od_v_v > $o ).

thf(sy_c_member_001t__Set__Oset_Itf__v_J,type,
    member_set_v: set_v > set_set_v > $o ).

thf(sy_c_member_001tf__v,type,
    member_v: v > set_v > $o ).

thf(sy_v_cc____,type,
    cc: set_v ).

thf(sy_v_e,type,
    e: sCC_Bl1394983891496994913t_unit ).

thf(sy_v_e_H,type,
    e2: sCC_Bl1394983891496994913t_unit ).

thf(sy_v_m____,type,
    m: v ).

thf(sy_v_n____,type,
    n: v ).

thf(sy_v_pfx____,type,
    pfx: list_v ).

thf(sy_v_successors,type,
    successors: v > set_v ).

thf(sy_v_v,type,
    v2: v ).

thf(sy_v_vertices,type,
    vertices: set_v ).

thf(sy_v_w,type,
    w: v ).

% Relevant facts (1229)
thf(fact_0__092_060open_062m_A_092_060in_062_A_092_060S_062_Ae_H_An_092_060close_062,axiom,
    member_v @ m @ ( sCC_Bl1280885523602775798t_unit @ e2 @ n ) ).

% \<open>m \<in> \<S> e' n\<close>
thf(fact_1_sub__env__trans,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit,E3: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl5768913643336123637t_unit @ E @ E2 )
     => ( ( sCC_Bl5768913643336123637t_unit @ E2 @ E3 )
       => ( sCC_Bl5768913643336123637t_unit @ E @ E3 ) ) ) ).

% sub_env_trans
thf(fact_2_calculation_I15_J,axiom,
    ! [N: v,M: v] :
      ( ( member_v @ M @ ( sCC_Bl1280885523602775798t_unit @ e2 @ N ) )
      = ( ( sCC_Bl1280885523602775798t_unit @ e2 @ N )
        = ( sCC_Bl1280885523602775798t_unit @ e2 @ M ) ) ) ).

% calculation(15)
thf(fact_3_hd__cc,axiom,
    ( ( sCC_Bl1280885523602775798t_unit @ e2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) )
    = cc ) ).

% hd_cc
thf(fact_4__092_060open_062m_A_092_060in_062_Aset_A_Icstack_Ae_H_J_092_060close_062,axiom,
    member_v @ m @ ( set_v2 @ ( sCC_Bl9201514103433284750t_unit @ e2 ) ) ).

% \<open>m \<in> set (cstack e')\<close>
thf(fact_5_Se_H,axiom,
    ! [X: v] :
      ( ( ( member_v @ X @ cc )
       => ( ( sCC_Bl1280885523602775798t_unit @ e2 @ X )
          = cc ) )
      & ( ~ ( member_v @ X @ cc )
       => ( ( sCC_Bl1280885523602775798t_unit @ e2 @ X )
          = ( sCC_Bl1280885523602775798t_unit @ e @ X ) ) ) ) ).

% Se'
thf(fact_6__092_060open_062m_A_092_060in_062_Aset_A_Icstack_Ae_J_092_060close_062,axiom,
    member_v @ m @ ( set_v2 @ ( sCC_Bl9201514103433284750t_unit @ e ) ) ).

% \<open>m \<in> set (cstack e)\<close>
thf(fact_7_graph_Opre__dfs_Ocong,axiom,
    sCC_Bl36166008131615352t_unit = sCC_Bl36166008131615352t_unit ).

% graph.pre_dfs.cong
thf(fact_8_graph_Opre__dfss_Ocong,axiom,
    sCC_Bl1748261141445803503t_unit = sCC_Bl1748261141445803503t_unit ).

% graph.pre_dfss.cong
thf(fact_9_dfss_Ocases,axiom,
    ! [X2: produc5741669702376414499t_unit] :
      ~ ! [V: v,E4: sCC_Bl1394983891496994913t_unit] :
          ( X2
         != ( produc3862955338007567901t_unit @ V @ E4 ) ) ).

% dfss.cases
thf(fact_10_True,axiom,
    ( n
    = ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) ).

% True
thf(fact_11__092_060open_062n_A_092_060in_062_Aset_A_Istack_Ae_H_J_092_060close_062,axiom,
    member_v @ n @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ).

% \<open>n \<in> set (stack e')\<close>
thf(fact_12__092_060open_062hd_A_Istack_Ae_H_J_A_092_060in_062_A_092_060S_062_Ae_A_Ihd_A_Istack_Ae_H_J_J_092_060close_062,axiom,
    member_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ ( sCC_Bl1280885523602775798t_unit @ e @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) ).

% \<open>hd (stack e') \<in> \<S> e (hd (stack e'))\<close>
thf(fact_13_pfx_I2_J,axiom,
    ( ( sCC_Bl8828226123343373779t_unit @ e2 )
   != nil_v ) ).

% pfx(2)
thf(fact_14_calculation_I13_J,axiom,
    ! [N: v,M: v] :
      ( ( sCC_Bl4022239298816431255edes_v @ N @ M @ ( sCC_Bl8828226123343373779t_unit @ e2 ) )
     => ( sCC_Bl4022239298816431255edes_v @ N @ M @ ( sCC_Bl9201514103433284750t_unit @ e2 ) ) ) ).

% calculation(13)
thf(fact_15_pfx_I1_J,axiom,
    ( ( sCC_Bl8828226123343373779t_unit @ e )
    = ( append_v @ pfx @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) ).

% pfx(1)
thf(fact_16_prod_Oinject,axiom,
    ! [X1: v,X22: sCC_Bl1394983891496994913t_unit,Y1: v,Y2: sCC_Bl1394983891496994913t_unit] :
      ( ( ( produc3862955338007567901t_unit @ X1 @ X22 )
        = ( produc3862955338007567901t_unit @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_17_prod_Oinject,axiom,
    ! [X1: v,X22: v,Y1: v,Y2: v] :
      ( ( ( product_Pair_v_v @ X1 @ X22 )
        = ( product_Pair_v_v @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_18_old_Oprod_Oinject,axiom,
    ! [A: v,B: sCC_Bl1394983891496994913t_unit,A2: v,B2: sCC_Bl1394983891496994913t_unit] :
      ( ( ( produc3862955338007567901t_unit @ A @ B )
        = ( produc3862955338007567901t_unit @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_19_old_Oprod_Oinject,axiom,
    ! [A: v,B: v,A2: v,B2: v] :
      ( ( ( product_Pair_v_v @ A @ B )
        = ( product_Pair_v_v @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_20_calculation_I2_J,axiom,
    distinct_v @ ( sCC_Bl9201514103433284750t_unit @ e2 ) ).

% calculation(2)
thf(fact_21_calculation_I12_J,axiom,
    distinct_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ).

% calculation(12)
thf(fact_22__092_060open_062_092_060And_062n_Am_O_A_092_060lbrakk_062n_A_092_060in_062_Aset_A_Itl_A_Istack_Ae_H_J_J_059_Am_A_092_060in_062_A_092_060S_062_Ae_An_A_092_060inter_062_Acc_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
    ! [N2: v,M2: v] :
      ( ( member_v @ N2 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) )
     => ~ ( member_v @ M2 @ ( inf_inf_set_v @ ( sCC_Bl1280885523602775798t_unit @ e @ N2 ) @ cc ) ) ) ).

% \<open>\<And>n m. \<lbrakk>n \<in> set (tl (stack e')); m \<in> \<S> e n \<inter> cc\<rbrakk> \<Longrightarrow> False\<close>
thf(fact_23_w_I4_J,axiom,
    ~ ( member_v @ w @ ( sCC_Bl157864678168468314t_unit @ e ) ) ).

% w(4)
thf(fact_24_e_H__def,axiom,
    ( e2
    = ( sCC_Bloemen_unite_v @ v2 @ w @ e ) ) ).

% e'_def
thf(fact_25_w_I3_J,axiom,
    member_v @ w @ ( sCC_Bl4645233313691564917t_unit @ e ) ).

% w(3)
thf(fact_26_calculation_I17_J,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) )
     => ! [Xa: v] :
          ( ( member_v @ Xa @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) )
         => ( ( X != Xa )
           => ( ( inf_inf_set_v @ ( sCC_Bl1280885523602775798t_unit @ e2 @ X ) @ ( sCC_Bl1280885523602775798t_unit @ e2 @ Xa ) )
              = bot_bot_set_v ) ) ) ) ).

% calculation(17)
thf(fact_27_tl__cc,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) )
     => ( ( inf_inf_set_v @ ( sCC_Bl1280885523602775798t_unit @ e @ X ) @ cc )
        = bot_bot_set_v ) ) ).

% tl_cc
thf(fact_28_precedes__refl,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( sCC_Bl2026170059108282219od_v_v @ X2 @ X2 @ Xs )
      = ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) ) ) ).

% precedes_refl
thf(fact_29_precedes__refl,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ X2 @ Xs )
      = ( member_v @ X2 @ ( set_v2 @ Xs ) ) ) ).

% precedes_refl
thf(fact_30_w_I2_J,axiom,
    ~ ( member_v @ w @ ( sCC_Bl3795065053823578884t_unit @ e @ v2 ) ) ).

% w(2)
thf(fact_31_precedes__append__right,axiom,
    ! [X2: v,Y: v,Xs: list_v,Ys: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( append_v @ Xs @ Ys ) ) ) ).

% precedes_append_right
thf(fact_32_precedes__append__left,axiom,
    ! [X2: v,Y: v,Xs: list_v,Ys: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( append_v @ Ys @ Xs ) ) ) ).

% precedes_append_left
thf(fact_33_precedes__antisym,axiom,
    ! [X2: v,Y: v,Xs: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( ( sCC_Bl4022239298816431255edes_v @ Y @ X2 @ Xs )
       => ( ( distinct_v @ Xs )
         => ( X2 = Y ) ) ) ) ).

% precedes_antisym
thf(fact_34_precedes__trans,axiom,
    ! [X2: v,Y: v,Xs: list_v,Z: v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( ( sCC_Bl4022239298816431255edes_v @ Y @ Z @ Xs )
       => ( ( distinct_v @ Xs )
         => ( sCC_Bl4022239298816431255edes_v @ X2 @ Z @ Xs ) ) ) ) ).

% precedes_trans
thf(fact_35_precedes__append__right__iff,axiom,
    ! [Y: product_prod_v_v,Ys: list_P7986770385144383213od_v_v,X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ Ys ) )
     => ( ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ ( append2138873909117096322od_v_v @ Xs @ Ys ) )
        = ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ Xs ) ) ) ).

% precedes_append_right_iff
thf(fact_36_precedes__append__right__iff,axiom,
    ! [Y: v,Ys: list_v,X2: v,Xs: list_v] :
      ( ~ ( member_v @ Y @ ( set_v2 @ Ys ) )
     => ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( append_v @ Xs @ Ys ) )
        = ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs ) ) ) ).

% precedes_append_right_iff
thf(fact_37_precedes__append__left__iff,axiom,
    ! [X2: product_prod_v_v,Ys: list_P7986770385144383213od_v_v,Y: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Ys ) )
     => ( ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ ( append2138873909117096322od_v_v @ Ys @ Xs ) )
        = ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ Xs ) ) ) ).

% precedes_append_left_iff
thf(fact_38_precedes__append__left__iff,axiom,
    ! [X2: v,Ys: list_v,Y: v,Xs: list_v] :
      ( ~ ( member_v @ X2 @ ( set_v2 @ Ys ) )
     => ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( append_v @ Ys @ Xs ) )
        = ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs ) ) ) ).

% precedes_append_left_iff
thf(fact_39_precedes__mem_I1_J,axiom,
    ! [X2: product_prod_v_v,Y: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ Xs )
     => ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) ) ) ).

% precedes_mem(1)
thf(fact_40_precedes__mem_I1_J,axiom,
    ! [X2: v,Y: v,Xs: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( member_v @ X2 @ ( set_v2 @ Xs ) ) ) ).

% precedes_mem(1)
thf(fact_41_precedes__mem_I2_J,axiom,
    ! [X2: product_prod_v_v,Y: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ Xs )
     => ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ Xs ) ) ) ).

% precedes_mem(2)
thf(fact_42_precedes__mem_I2_J,axiom,
    ! [X2: v,Y: v,Xs: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Xs )
     => ( member_v @ Y @ ( set_v2 @ Xs ) ) ) ).

% precedes_mem(2)
thf(fact_43_mem__Collect__eq,axiom,
    ! [A: v,P: v > $o] :
      ( ( member_v @ A @ ( collect_v @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_44_mem__Collect__eq,axiom,
    ! [A: product_prod_v_v,P: product_prod_v_v > $o] :
      ( ( member7453568604450474000od_v_v @ A @ ( collec140062887454715474od_v_v @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_45_mem__Collect__eq,axiom,
    ! [A: set_v,P: set_v > $o] :
      ( ( member_set_v @ A @ ( collect_set_v @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_46_Collect__mem__eq,axiom,
    ! [A3: set_v] :
      ( ( collect_v
        @ ^ [X3: v] : ( member_v @ X3 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_47_Collect__mem__eq,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( collec140062887454715474od_v_v
        @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_48_Collect__mem__eq,axiom,
    ! [A3: set_set_v] :
      ( ( collect_set_v
        @ ^ [X3: set_v] : ( member_set_v @ X3 @ A3 ) )
      = A3 ) ).

% Collect_mem_eq
thf(fact_49_Collect__cong,axiom,
    ! [P: set_v > $o,Q: set_v > $o] :
      ( ! [X4: set_v] :
          ( ( P @ X4 )
          = ( Q @ X4 ) )
     => ( ( collect_set_v @ P )
        = ( collect_set_v @ Q ) ) ) ).

% Collect_cong
thf(fact_50_Pair__inject,axiom,
    ! [A: v,B: sCC_Bl1394983891496994913t_unit,A2: v,B2: sCC_Bl1394983891496994913t_unit] :
      ( ( ( produc3862955338007567901t_unit @ A @ B )
        = ( produc3862955338007567901t_unit @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_51_Pair__inject,axiom,
    ! [A: v,B: v,A2: v,B2: v] :
      ( ( ( product_Pair_v_v @ A @ B )
        = ( product_Pair_v_v @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_52_prod__cases,axiom,
    ! [P: produc5741669702376414499t_unit > $o,P2: produc5741669702376414499t_unit] :
      ( ! [A4: v,B3: sCC_Bl1394983891496994913t_unit] : ( P @ ( produc3862955338007567901t_unit @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_53_prod__cases,axiom,
    ! [P: product_prod_v_v > $o,P2: product_prod_v_v] :
      ( ! [A4: v,B3: v] : ( P @ ( product_Pair_v_v @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_54_surj__pair,axiom,
    ! [P2: produc5741669702376414499t_unit] :
    ? [X4: v,Y3: sCC_Bl1394983891496994913t_unit] :
      ( P2
      = ( produc3862955338007567901t_unit @ X4 @ Y3 ) ) ).

% surj_pair
thf(fact_55_surj__pair,axiom,
    ! [P2: product_prod_v_v] :
    ? [X4: v,Y3: v] :
      ( P2
      = ( product_Pair_v_v @ X4 @ Y3 ) ) ).

% surj_pair
thf(fact_56_old_Oprod_Oexhaust,axiom,
    ! [Y: produc5741669702376414499t_unit] :
      ~ ! [A4: v,B3: sCC_Bl1394983891496994913t_unit] :
          ( Y
         != ( produc3862955338007567901t_unit @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_57_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_v_v] :
      ~ ! [A4: v,B3: v] :
          ( Y
         != ( product_Pair_v_v @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_58_distinct__append,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( distinct_v @ ( append_v @ Xs @ Ys ) )
      = ( ( distinct_v @ Xs )
        & ( distinct_v @ Ys )
        & ( ( inf_inf_set_v @ ( set_v2 @ Xs ) @ ( set_v2 @ Ys ) )
          = bot_bot_set_v ) ) ) ).

% distinct_append
thf(fact_59_distinct__append,axiom,
    ! [Xs: list_P7986770385144383213od_v_v,Ys: list_P7986770385144383213od_v_v] :
      ( ( distin6159370996967099744od_v_v @ ( append2138873909117096322od_v_v @ Xs @ Ys ) )
      = ( ( distin6159370996967099744od_v_v @ Xs )
        & ( distin6159370996967099744od_v_v @ Ys )
        & ( ( inf_in6271465464967711157od_v_v @ ( set_Product_prod_v_v2 @ Xs ) @ ( set_Product_prod_v_v2 @ Ys ) )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% distinct_append
thf(fact_60_tl__append2,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( Xs != nil_v )
     => ( ( tl_v @ ( append_v @ Xs @ Ys ) )
        = ( append_v @ ( tl_v @ Xs ) @ Ys ) ) ) ).

% tl_append2
thf(fact_61_hd__append2,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( Xs != nil_v )
     => ( ( hd_v @ ( append_v @ Xs @ Ys ) )
        = ( hd_v @ Xs ) ) ) ).

% hd_append2
thf(fact_62_set__empty,axiom,
    ! [Xs: list_v] :
      ( ( ( set_v2 @ Xs )
        = bot_bot_set_v )
      = ( Xs = nil_v ) ) ).

% set_empty
thf(fact_63_set__empty,axiom,
    ! [Xs: list_P7986770385144383213od_v_v] :
      ( ( ( set_Product_prod_v_v2 @ Xs )
        = bot_bo723834152578015283od_v_v )
      = ( Xs = nil_Product_prod_v_v ) ) ).

% set_empty
thf(fact_64_set__empty2,axiom,
    ! [Xs: list_v] :
      ( ( bot_bot_set_v
        = ( set_v2 @ Xs ) )
      = ( Xs = nil_v ) ) ).

% set_empty2
thf(fact_65_set__empty2,axiom,
    ! [Xs: list_P7986770385144383213od_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( set_Product_prod_v_v2 @ Xs ) )
      = ( Xs = nil_Product_prod_v_v ) ) ).

% set_empty2
thf(fact_66_append__is__Nil__conv,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( ( append_v @ Xs @ Ys )
        = nil_v )
      = ( ( Xs = nil_v )
        & ( Ys = nil_v ) ) ) ).

% append_is_Nil_conv
thf(fact_67_Nil__is__append__conv,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( nil_v
        = ( append_v @ Xs @ Ys ) )
      = ( ( Xs = nil_v )
        & ( Ys = nil_v ) ) ) ).

% Nil_is_append_conv
thf(fact_68_self__append__conv2,axiom,
    ! [Y: list_v,Xs: list_v] :
      ( ( Y
        = ( append_v @ Xs @ Y ) )
      = ( Xs = nil_v ) ) ).

% self_append_conv2
thf(fact_69_append__self__conv2,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( ( append_v @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_v ) ) ).

% append_self_conv2
thf(fact_70_self__append__conv,axiom,
    ! [Y: list_v,Ys: list_v] :
      ( ( Y
        = ( append_v @ Y @ Ys ) )
      = ( Ys = nil_v ) ) ).

% self_append_conv
thf(fact_71_append__self__conv,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( ( append_v @ Xs @ Ys )
        = Xs )
      = ( Ys = nil_v ) ) ).

% append_self_conv
thf(fact_72_append_Oassoc,axiom,
    ! [A: list_v,B: list_v,C: list_v] :
      ( ( append_v @ ( append_v @ A @ B ) @ C )
      = ( append_v @ A @ ( append_v @ B @ C ) ) ) ).

% append.assoc
thf(fact_73_append__assoc,axiom,
    ! [Xs: list_v,Ys: list_v,Zs: list_v] :
      ( ( append_v @ ( append_v @ Xs @ Ys ) @ Zs )
      = ( append_v @ Xs @ ( append_v @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_74_append__same__eq,axiom,
    ! [Ys: list_v,Xs: list_v,Zs: list_v] :
      ( ( ( append_v @ Ys @ Xs )
        = ( append_v @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_75_same__append__eq,axiom,
    ! [Xs: list_v,Ys: list_v,Zs: list_v] :
      ( ( ( append_v @ Xs @ Ys )
        = ( append_v @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_76_calculation_I7_J,axiom,
    ! [N: v] :
      ( ~ ( member_v @ N @ ( sCC_Bl4645233313691564917t_unit @ e2 ) )
     => ( ( sCC_Bl3795065053823578884t_unit @ e2 @ N )
        = bot_bot_set_v ) ) ).

% calculation(7)
thf(fact_77_append_Oright__neutral,axiom,
    ! [A: list_v] :
      ( ( append_v @ A @ nil_v )
      = A ) ).

% append.right_neutral
thf(fact_78_append__Nil2,axiom,
    ! [Xs: list_v] :
      ( ( append_v @ Xs @ nil_v )
      = Xs ) ).

% append_Nil2
thf(fact_79_append__eq__appendI,axiom,
    ! [Xs: list_v,Xs1: list_v,Zs: list_v,Ys: list_v,Us: list_v] :
      ( ( ( append_v @ Xs @ Xs1 )
        = Zs )
     => ( ( Ys
          = ( append_v @ Xs1 @ Us ) )
       => ( ( append_v @ Xs @ Ys )
          = ( append_v @ Zs @ Us ) ) ) ) ).

% append_eq_appendI
thf(fact_80_append__eq__append__conv2,axiom,
    ! [Xs: list_v,Ys: list_v,Zs: list_v,Ts: list_v] :
      ( ( ( append_v @ Xs @ Ys )
        = ( append_v @ Zs @ Ts ) )
      = ( ? [Us2: list_v] :
            ( ( ( Xs
                = ( append_v @ Zs @ Us2 ) )
              & ( ( append_v @ Us2 @ Ys )
                = Ts ) )
            | ( ( ( append_v @ Xs @ Us2 )
                = Zs )
              & ( Ys
                = ( append_v @ Us2 @ Ts ) ) ) ) ) ) ).

% append_eq_append_conv2
thf(fact_81_append__Nil,axiom,
    ! [Ys: list_v] :
      ( ( append_v @ nil_v @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_82_append_Oleft__neutral,axiom,
    ! [A: list_v] :
      ( ( append_v @ nil_v @ A )
      = A ) ).

% append.left_neutral
thf(fact_83_eq__Nil__appendI,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( Xs = Ys )
     => ( Xs
        = ( append_v @ nil_v @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_84_distinct_Osimps_I1_J,axiom,
    distinct_v @ nil_v ).

% distinct.simps(1)
thf(fact_85_list_Osel_I2_J,axiom,
    ( ( tl_v @ nil_v )
    = nil_v ) ).

% list.sel(2)
thf(fact_86_distinct__tl,axiom,
    ! [Xs: list_v] :
      ( ( distinct_v @ Xs )
     => ( distinct_v @ ( tl_v @ Xs ) ) ) ).

% distinct_tl
thf(fact_87_empty__set,axiom,
    ( bot_bot_set_v
    = ( set_v2 @ nil_v ) ) ).

% empty_set
thf(fact_88_empty__set,axiom,
    ( bot_bo723834152578015283od_v_v
    = ( set_Product_prod_v_v2 @ nil_Product_prod_v_v ) ) ).

% empty_set
thf(fact_89_list_Oset__sel_I1_J,axiom,
    ! [A: list_P7986770385144383213od_v_v] :
      ( ( A != nil_Product_prod_v_v )
     => ( member7453568604450474000od_v_v @ ( hd_Product_prod_v_v @ A ) @ ( set_Product_prod_v_v2 @ A ) ) ) ).

% list.set_sel(1)
thf(fact_90_list_Oset__sel_I1_J,axiom,
    ! [A: list_v] :
      ( ( A != nil_v )
     => ( member_v @ ( hd_v @ A ) @ ( set_v2 @ A ) ) ) ).

% list.set_sel(1)
thf(fact_91_hd__in__set,axiom,
    ! [Xs: list_P7986770385144383213od_v_v] :
      ( ( Xs != nil_Product_prod_v_v )
     => ( member7453568604450474000od_v_v @ ( hd_Product_prod_v_v @ Xs ) @ ( set_Product_prod_v_v2 @ Xs ) ) ) ).

% hd_in_set
thf(fact_92_hd__in__set,axiom,
    ! [Xs: list_v] :
      ( ( Xs != nil_v )
     => ( member_v @ ( hd_v @ Xs ) @ ( set_v2 @ Xs ) ) ) ).

% hd_in_set
thf(fact_93_list_Oset__sel_I2_J,axiom,
    ! [A: list_P7986770385144383213od_v_v,X2: product_prod_v_v] :
      ( ( A != nil_Product_prod_v_v )
     => ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ ( tl_Product_prod_v_v @ A ) ) )
       => ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ A ) ) ) ) ).

% list.set_sel(2)
thf(fact_94_list_Oset__sel_I2_J,axiom,
    ! [A: list_v,X2: v] :
      ( ( A != nil_v )
     => ( ( member_v @ X2 @ ( set_v2 @ ( tl_v @ A ) ) )
       => ( member_v @ X2 @ ( set_v2 @ A ) ) ) ) ).

% list.set_sel(2)
thf(fact_95_longest__common__prefix,axiom,
    ! [Xs: list_v,Ys: list_v] :
    ? [Ps: list_v,Xs2: list_v,Ys2: list_v] :
      ( ( Xs
        = ( append_v @ Ps @ Xs2 ) )
      & ( Ys
        = ( append_v @ Ps @ Ys2 ) )
      & ( ( Xs2 = nil_v )
        | ( Ys2 = nil_v )
        | ( ( hd_v @ Xs2 )
         != ( hd_v @ Ys2 ) ) ) ) ).

% longest_common_prefix
thf(fact_96_hd__append,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( ( Xs = nil_v )
       => ( ( hd_v @ ( append_v @ Xs @ Ys ) )
          = ( hd_v @ Ys ) ) )
      & ( ( Xs != nil_v )
       => ( ( hd_v @ ( append_v @ Xs @ Ys ) )
          = ( hd_v @ Xs ) ) ) ) ).

% hd_append
thf(fact_97_tl__append__if,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( ( Xs = nil_v )
       => ( ( tl_v @ ( append_v @ Xs @ Ys ) )
          = ( tl_v @ Ys ) ) )
      & ( ( Xs != nil_v )
       => ( ( tl_v @ ( append_v @ Xs @ Ys ) )
          = ( append_v @ ( tl_v @ Xs ) @ Ys ) ) ) ) ).

% tl_append_if
thf(fact_98_list_Oexpand,axiom,
    ! [List: list_v,List2: list_v] :
      ( ( ( List = nil_v )
        = ( List2 = nil_v ) )
     => ( ( ( List != nil_v )
         => ( ( List2 != nil_v )
           => ( ( ( hd_v @ List )
                = ( hd_v @ List2 ) )
              & ( ( tl_v @ List )
                = ( tl_v @ List2 ) ) ) ) )
       => ( List = List2 ) ) ) ).

% list.expand
thf(fact_99_inf__bot__left,axiom,
    ! [X2: set_v] :
      ( ( inf_inf_set_v @ bot_bot_set_v @ X2 )
      = bot_bot_set_v ) ).

% inf_bot_left
thf(fact_100_inf__bot__left,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ bot_bo723834152578015283od_v_v @ X2 )
      = bot_bo723834152578015283od_v_v ) ).

% inf_bot_left
thf(fact_101_inf__bot__left,axiom,
    ! [X2: product_unit] :
      ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X2 )
      = bot_bot_Product_unit ) ).

% inf_bot_left
thf(fact_102_inf__bot__right,axiom,
    ! [X2: set_v] :
      ( ( inf_inf_set_v @ X2 @ bot_bot_set_v )
      = bot_bot_set_v ) ).

% inf_bot_right
thf(fact_103_inf__bot__right,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ X2 @ bot_bo723834152578015283od_v_v )
      = bot_bo723834152578015283od_v_v ) ).

% inf_bot_right
thf(fact_104_inf__bot__right,axiom,
    ! [X2: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ bot_bot_Product_unit )
      = bot_bot_Product_unit ) ).

% inf_bot_right
thf(fact_105_boolean__algebra_Oconj__zero__left,axiom,
    ! [X2: set_v] :
      ( ( inf_inf_set_v @ bot_bot_set_v @ X2 )
      = bot_bot_set_v ) ).

% boolean_algebra.conj_zero_left
thf(fact_106_boolean__algebra_Oconj__zero__left,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ bot_bo723834152578015283od_v_v @ X2 )
      = bot_bo723834152578015283od_v_v ) ).

% boolean_algebra.conj_zero_left
thf(fact_107_boolean__algebra_Oconj__zero__left,axiom,
    ! [X2: product_unit] :
      ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X2 )
      = bot_bot_Product_unit ) ).

% boolean_algebra.conj_zero_left
thf(fact_108_boolean__algebra_Oconj__zero__right,axiom,
    ! [X2: set_v] :
      ( ( inf_inf_set_v @ X2 @ bot_bot_set_v )
      = bot_bot_set_v ) ).

% boolean_algebra.conj_zero_right
thf(fact_109_boolean__algebra_Oconj__zero__right,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ X2 @ bot_bo723834152578015283od_v_v )
      = bot_bo723834152578015283od_v_v ) ).

% boolean_algebra.conj_zero_right
thf(fact_110_boolean__algebra_Oconj__zero__right,axiom,
    ! [X2: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ bot_bot_Product_unit )
      = bot_bot_Product_unit ) ).

% boolean_algebra.conj_zero_right
thf(fact_111_calculation_I4_J,axiom,
    ord_less_eq_set_v @ ( set_v2 @ ( sCC_Bl9201514103433284750t_unit @ e2 ) ) @ ( sCC_Bl4645233313691564917t_unit @ e2 ) ).

% calculation(4)
thf(fact_112_calculation_I16_J,axiom,
    ! [N: v] :
      ( ~ ( member_v @ N @ ( sCC_Bl4645233313691564917t_unit @ e2 ) )
     => ( ( sCC_Bl1280885523602775798t_unit @ e2 @ N )
        = ( insert_v @ N @ bot_bot_set_v ) ) ) ).

% calculation(16)
thf(fact_113_calculation_I3_J,axiom,
    ord_less_eq_set_v @ ( sCC_Bl157864678168468314t_unit @ e2 ) @ ( sCC_Bl4645233313691564917t_unit @ e2 ) ).

% calculation(3)
thf(fact_114_w_I1_J,axiom,
    member_v @ w @ ( successors @ v2 ) ).

% w(1)
thf(fact_115_pre,axiom,
    sCC_Bl1748261141445803503t_unit @ successors @ v2 @ e ).

% pre
thf(fact_116_init__env__pre__dfs,axiom,
    ! [V2: v] : ( sCC_Bl36166008131615352t_unit @ successors @ V2 @ ( sCC_Bl7693227186847904995_env_v @ V2 ) ) ).

% init_env_pre_dfs
thf(fact_117_inf__right__idem,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ Y )
      = ( inf_inf_set_v @ X2 @ Y ) ) ).

% inf_right_idem
thf(fact_118_inf__right__idem,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ Y )
      = ( inf_inf_Product_unit @ X2 @ Y ) ) ).

% inf_right_idem
thf(fact_119_inf_Oright__idem,axiom,
    ! [A: set_v,B: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ A @ B ) @ B )
      = ( inf_inf_set_v @ A @ B ) ) ).

% inf.right_idem
thf(fact_120_inf_Oright__idem,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ A @ B ) @ B )
      = ( inf_inf_Product_unit @ A @ B ) ) ).

% inf.right_idem
thf(fact_121_inf__left__idem,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ X2 @ Y ) )
      = ( inf_inf_set_v @ X2 @ Y ) ) ).

% inf_left_idem
thf(fact_122_inf__left__idem,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ X2 @ Y ) )
      = ( inf_inf_Product_unit @ X2 @ Y ) ) ).

% inf_left_idem
thf(fact_123_inf_Oleft__idem,axiom,
    ! [A: set_v,B: set_v] :
      ( ( inf_inf_set_v @ A @ ( inf_inf_set_v @ A @ B ) )
      = ( inf_inf_set_v @ A @ B ) ) ).

% inf.left_idem
thf(fact_124_inf_Oleft__idem,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ A @ B ) )
      = ( inf_inf_Product_unit @ A @ B ) ) ).

% inf.left_idem
thf(fact_125_inf__idem,axiom,
    ! [X2: set_v] :
      ( ( inf_inf_set_v @ X2 @ X2 )
      = X2 ) ).

% inf_idem
thf(fact_126_inf__idem,axiom,
    ! [X2: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ X2 )
      = X2 ) ).

% inf_idem
thf(fact_127_inf_Oidem,axiom,
    ! [A: set_v] :
      ( ( inf_inf_set_v @ A @ A )
      = A ) ).

% inf.idem
thf(fact_128_inf_Oidem,axiom,
    ! [A: product_unit] :
      ( ( inf_inf_Product_unit @ A @ A )
      = A ) ).

% inf.idem
thf(fact_129_calculation_I8_J,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( sCC_Bl157864678168468314t_unit @ e2 ) )
     => ( ( sCC_Bl3795065053823578884t_unit @ e2 @ X )
        = ( successors @ X ) ) ) ).

% calculation(8)
thf(fact_130_inf_Obounded__iff,axiom,
    ! [A: product_unit,B: product_unit,C: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) )
      = ( ( ord_le3221252021190050221t_unit @ A @ B )
        & ( ord_le3221252021190050221t_unit @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_131_inf_Obounded__iff,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ ( inf_inf_set_v @ B @ C ) )
      = ( ( ord_less_eq_set_v @ A @ B )
        & ( ord_less_eq_set_v @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_132_inf_Obounded__iff,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ B @ C ) )
      = ( ( ord_le7336532860387713383od_v_v @ A @ B )
        & ( ord_le7336532860387713383od_v_v @ A @ C ) ) ) ).

% inf.bounded_iff
thf(fact_133_le__inf__iff,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
      = ( ( ord_le3221252021190050221t_unit @ X2 @ Y )
        & ( ord_le3221252021190050221t_unit @ X2 @ Z ) ) ) ).

% le_inf_iff
thf(fact_134_le__inf__iff,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
      = ( ( ord_less_eq_set_v @ X2 @ Y )
        & ( ord_less_eq_set_v @ X2 @ Z ) ) ) ).

% le_inf_iff
thf(fact_135_le__inf__iff,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) )
      = ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
        & ( ord_le7336532860387713383od_v_v @ X2 @ Z ) ) ) ).

% le_inf_iff
thf(fact_136_unite__sub__env,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,W: v] :
      ( ( sCC_Bl1748261141445803503t_unit @ successors @ V2 @ E )
     => ( ( member_v @ W @ ( successors @ V2 ) )
       => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
         => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
           => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
             => ( sCC_Bl5768913643336123637t_unit @ E @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) ) ).

% unite_sub_env
thf(fact_137_calculation_I6_J,axiom,
    ! [N: v] : ( ord_less_eq_set_v @ ( sCC_Bl3795065053823578884t_unit @ e2 @ N ) @ ( inf_inf_set_v @ ( successors @ N ) @ ( sCC_Bl4645233313691564917t_unit @ e2 ) ) ) ).

% calculation(6)
thf(fact_138_sclosed,axiom,
    ! [X: v] :
      ( ( member_v @ X @ vertices )
     => ( ord_less_eq_set_v @ ( successors @ X ) @ vertices ) ) ).

% sclosed
thf(fact_139_inf_OcoboundedI2,axiom,
    ! [B: product_unit,C: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ C )
     => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_140_inf_OcoboundedI2,axiom,
    ! [B: set_v,C: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ C )
     => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_141_inf_OcoboundedI2,axiom,
    ! [B: set_Product_prod_v_v,C: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ C )
     => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ C ) ) ).

% inf.coboundedI2
thf(fact_142_inf_OcoboundedI1,axiom,
    ! [A: product_unit,C: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ C )
     => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_143_inf_OcoboundedI1,axiom,
    ! [A: set_v,C: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ C )
     => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_144_inf_OcoboundedI1,axiom,
    ! [A: set_Product_prod_v_v,C: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ C )
     => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ C ) ) ).

% inf.coboundedI1
thf(fact_145_inf_Oabsorb__iff2,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [B4: product_unit,A5: product_unit] :
          ( ( inf_inf_Product_unit @ A5 @ B4 )
          = B4 ) ) ) ).

% inf.absorb_iff2
thf(fact_146_inf_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_v
    = ( ^ [B4: set_v,A5: set_v] :
          ( ( inf_inf_set_v @ A5 @ B4 )
          = B4 ) ) ) ).

% inf.absorb_iff2
thf(fact_147_inf_Oabsorb__iff2,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [B4: set_Product_prod_v_v,A5: set_Product_prod_v_v] :
          ( ( inf_in6271465464967711157od_v_v @ A5 @ B4 )
          = B4 ) ) ) ).

% inf.absorb_iff2
thf(fact_148_inf_Oabsorb__iff1,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [A5: product_unit,B4: product_unit] :
          ( ( inf_inf_Product_unit @ A5 @ B4 )
          = A5 ) ) ) ).

% inf.absorb_iff1
thf(fact_149_inf_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A5: set_v,B4: set_v] :
          ( ( inf_inf_set_v @ A5 @ B4 )
          = A5 ) ) ) ).

% inf.absorb_iff1
thf(fact_150_inf_Oabsorb__iff1,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] :
          ( ( inf_in6271465464967711157od_v_v @ A5 @ B4 )
          = A5 ) ) ) ).

% inf.absorb_iff1
thf(fact_151_inf_Ocobounded2,axiom,
    ! [A: product_unit,B: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ B ) ).

% inf.cobounded2
thf(fact_152_inf_Ocobounded2,axiom,
    ! [A: set_v,B: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ B ) ).

% inf.cobounded2
thf(fact_153_inf_Ocobounded2,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ B ) ).

% inf.cobounded2
thf(fact_154_inf_Ocobounded1,axiom,
    ! [A: product_unit,B: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ A ) ).

% inf.cobounded1
thf(fact_155_inf_Ocobounded1,axiom,
    ! [A: set_v,B: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ A ) ).

% inf.cobounded1
thf(fact_156_inf_Ocobounded1,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ A ) ).

% inf.cobounded1
thf(fact_157_inf_Oorder__iff,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [A5: product_unit,B4: product_unit] :
          ( A5
          = ( inf_inf_Product_unit @ A5 @ B4 ) ) ) ) ).

% inf.order_iff
thf(fact_158_inf_Oorder__iff,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A5: set_v,B4: set_v] :
          ( A5
          = ( inf_inf_set_v @ A5 @ B4 ) ) ) ) ).

% inf.order_iff
thf(fact_159_inf_Oorder__iff,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] :
          ( A5
          = ( inf_in6271465464967711157od_v_v @ A5 @ B4 ) ) ) ) ).

% inf.order_iff
thf(fact_160_inf__greatest,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ Y )
     => ( ( ord_le3221252021190050221t_unit @ X2 @ Z )
       => ( ord_le3221252021190050221t_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ) ).

% inf_greatest
thf(fact_161_inf__greatest,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ Y )
     => ( ( ord_less_eq_set_v @ X2 @ Z )
       => ( ord_less_eq_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) ) ) ) ).

% inf_greatest
thf(fact_162_inf__greatest,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
     => ( ( ord_le7336532860387713383od_v_v @ X2 @ Z )
       => ( ord_le7336532860387713383od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) ) ) ) ).

% inf_greatest
thf(fact_163_inf_OboundedI,axiom,
    ! [A: product_unit,B: product_unit,C: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ B )
     => ( ( ord_le3221252021190050221t_unit @ A @ C )
       => ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ) ).

% inf.boundedI
thf(fact_164_inf_OboundedI,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ord_less_eq_set_v @ A @ C )
       => ( ord_less_eq_set_v @ A @ ( inf_inf_set_v @ B @ C ) ) ) ) ).

% inf.boundedI
thf(fact_165_inf_OboundedI,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ord_le7336532860387713383od_v_v @ A @ C )
       => ( ord_le7336532860387713383od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ B @ C ) ) ) ) ).

% inf.boundedI
thf(fact_166_inf_OboundedE,axiom,
    ! [A: product_unit,B: product_unit,C: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) )
     => ~ ( ( ord_le3221252021190050221t_unit @ A @ B )
         => ~ ( ord_le3221252021190050221t_unit @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_167_inf_OboundedE,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ ( inf_inf_set_v @ B @ C ) )
     => ~ ( ( ord_less_eq_set_v @ A @ B )
         => ~ ( ord_less_eq_set_v @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_168_inf_OboundedE,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ B @ C ) )
     => ~ ( ( ord_le7336532860387713383od_v_v @ A @ B )
         => ~ ( ord_le7336532860387713383od_v_v @ A @ C ) ) ) ).

% inf.boundedE
thf(fact_169_inf__absorb2,axiom,
    ! [Y: product_unit,X2: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ Y @ X2 )
     => ( ( inf_inf_Product_unit @ X2 @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_170_inf__absorb2,axiom,
    ! [Y: set_v,X2: set_v] :
      ( ( ord_less_eq_set_v @ Y @ X2 )
     => ( ( inf_inf_set_v @ X2 @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_171_inf__absorb2,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ Y @ X2 )
     => ( ( inf_in6271465464967711157od_v_v @ X2 @ Y )
        = Y ) ) ).

% inf_absorb2
thf(fact_172_inf__absorb1,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ Y )
     => ( ( inf_inf_Product_unit @ X2 @ Y )
        = X2 ) ) ).

% inf_absorb1
thf(fact_173_inf__absorb1,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ Y )
     => ( ( inf_inf_set_v @ X2 @ Y )
        = X2 ) ) ).

% inf_absorb1
thf(fact_174_inf__absorb1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
     => ( ( inf_in6271465464967711157od_v_v @ X2 @ Y )
        = X2 ) ) ).

% inf_absorb1
thf(fact_175_inf_Oabsorb2,axiom,
    ! [B: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ A )
     => ( ( inf_inf_Product_unit @ A @ B )
        = B ) ) ).

% inf.absorb2
thf(fact_176_inf_Oabsorb2,axiom,
    ! [B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( ( inf_inf_set_v @ A @ B )
        = B ) ) ).

% inf.absorb2
thf(fact_177_inf_Oabsorb2,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( ( inf_in6271465464967711157od_v_v @ A @ B )
        = B ) ) ).

% inf.absorb2
thf(fact_178_inf_Oabsorb1,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ B )
     => ( ( inf_inf_Product_unit @ A @ B )
        = A ) ) ).

% inf.absorb1
thf(fact_179_inf_Oabsorb1,axiom,
    ! [A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( inf_inf_set_v @ A @ B )
        = A ) ) ).

% inf.absorb1
thf(fact_180_inf_Oabsorb1,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( inf_in6271465464967711157od_v_v @ A @ B )
        = A ) ) ).

% inf.absorb1
thf(fact_181_le__iff__inf,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [X3: product_unit,Y4: product_unit] :
          ( ( inf_inf_Product_unit @ X3 @ Y4 )
          = X3 ) ) ) ).

% le_iff_inf
thf(fact_182_le__iff__inf,axiom,
    ( ord_less_eq_set_v
    = ( ^ [X3: set_v,Y4: set_v] :
          ( ( inf_inf_set_v @ X3 @ Y4 )
          = X3 ) ) ) ).

% le_iff_inf
thf(fact_183_le__iff__inf,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [X3: set_Product_prod_v_v,Y4: set_Product_prod_v_v] :
          ( ( inf_in6271465464967711157od_v_v @ X3 @ Y4 )
          = X3 ) ) ) ).

% le_iff_inf
thf(fact_184_inf__unique,axiom,
    ! [F: product_unit > product_unit > product_unit,X2: product_unit,Y: product_unit] :
      ( ! [X4: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ ( F @ X4 @ Y3 ) @ X4 )
     => ( ! [X4: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ ( F @ X4 @ Y3 ) @ Y3 )
       => ( ! [X4: product_unit,Y3: product_unit,Z2: product_unit] :
              ( ( ord_le3221252021190050221t_unit @ X4 @ Y3 )
             => ( ( ord_le3221252021190050221t_unit @ X4 @ Z2 )
               => ( ord_le3221252021190050221t_unit @ X4 @ ( F @ Y3 @ Z2 ) ) ) )
         => ( ( inf_inf_Product_unit @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_185_inf__unique,axiom,
    ! [F: set_v > set_v > set_v,X2: set_v,Y: set_v] :
      ( ! [X4: set_v,Y3: set_v] : ( ord_less_eq_set_v @ ( F @ X4 @ Y3 ) @ X4 )
     => ( ! [X4: set_v,Y3: set_v] : ( ord_less_eq_set_v @ ( F @ X4 @ Y3 ) @ Y3 )
       => ( ! [X4: set_v,Y3: set_v,Z2: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ( ord_less_eq_set_v @ X4 @ Z2 )
               => ( ord_less_eq_set_v @ X4 @ ( F @ Y3 @ Z2 ) ) ) )
         => ( ( inf_inf_set_v @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_186_inf__unique,axiom,
    ! [F: set_Product_prod_v_v > set_Product_prod_v_v > set_Product_prod_v_v,X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( F @ X4 @ Y3 ) @ X4 )
     => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( F @ X4 @ Y3 ) @ Y3 )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v,Z2: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ( ord_le7336532860387713383od_v_v @ X4 @ Z2 )
               => ( ord_le7336532860387713383od_v_v @ X4 @ ( F @ Y3 @ Z2 ) ) ) )
         => ( ( inf_in6271465464967711157od_v_v @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% inf_unique
thf(fact_187_inf_OorderI,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( A
        = ( inf_inf_Product_unit @ A @ B ) )
     => ( ord_le3221252021190050221t_unit @ A @ B ) ) ).

% inf.orderI
thf(fact_188_inf_OorderI,axiom,
    ! [A: set_v,B: set_v] :
      ( ( A
        = ( inf_inf_set_v @ A @ B ) )
     => ( ord_less_eq_set_v @ A @ B ) ) ).

% inf.orderI
thf(fact_189_inf_OorderI,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( A
        = ( inf_in6271465464967711157od_v_v @ A @ B ) )
     => ( ord_le7336532860387713383od_v_v @ A @ B ) ) ).

% inf.orderI
thf(fact_190_inf_OorderE,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ B )
     => ( A
        = ( inf_inf_Product_unit @ A @ B ) ) ) ).

% inf.orderE
thf(fact_191_inf_OorderE,axiom,
    ! [A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( A
        = ( inf_inf_set_v @ A @ B ) ) ) ).

% inf.orderE
thf(fact_192_inf_OorderE,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( A
        = ( inf_in6271465464967711157od_v_v @ A @ B ) ) ) ).

% inf.orderE
thf(fact_193_le__infI2,axiom,
    ! [B: product_unit,X2: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ X2 )
     => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X2 ) ) ).

% le_infI2
thf(fact_194_le__infI2,axiom,
    ! [B: set_v,X2: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ X2 )
     => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ X2 ) ) ).

% le_infI2
thf(fact_195_le__infI2,axiom,
    ! [B: set_Product_prod_v_v,X2: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ X2 )
     => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ X2 ) ) ).

% le_infI2
thf(fact_196_le__infI1,axiom,
    ! [A: product_unit,X2: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ X2 )
     => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X2 ) ) ).

% le_infI1
thf(fact_197_le__infI1,axiom,
    ! [A: set_v,X2: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ X2 )
     => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ X2 ) ) ).

% le_infI1
thf(fact_198_le__infI1,axiom,
    ! [A: set_Product_prod_v_v,X2: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ X2 )
     => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ X2 ) ) ).

% le_infI1
thf(fact_199_inf__mono,axiom,
    ! [A: product_unit,C: product_unit,B: product_unit,D: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ C )
     => ( ( ord_le3221252021190050221t_unit @ B @ D )
       => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ ( inf_inf_Product_unit @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_200_inf__mono,axiom,
    ! [A: set_v,C: set_v,B: set_v,D: set_v] :
      ( ( ord_less_eq_set_v @ A @ C )
     => ( ( ord_less_eq_set_v @ B @ D )
       => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A @ B ) @ ( inf_inf_set_v @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_201_inf__mono,axiom,
    ! [A: set_Product_prod_v_v,C: set_Product_prod_v_v,B: set_Product_prod_v_v,D: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ C )
     => ( ( ord_le7336532860387713383od_v_v @ B @ D )
       => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A @ B ) @ ( inf_in6271465464967711157od_v_v @ C @ D ) ) ) ) ).

% inf_mono
thf(fact_202_le__infI,axiom,
    ! [X2: product_unit,A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ A )
     => ( ( ord_le3221252021190050221t_unit @ X2 @ B )
       => ( ord_le3221252021190050221t_unit @ X2 @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).

% le_infI
thf(fact_203_le__infI,axiom,
    ! [X2: set_v,A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ A )
     => ( ( ord_less_eq_set_v @ X2 @ B )
       => ( ord_less_eq_set_v @ X2 @ ( inf_inf_set_v @ A @ B ) ) ) ) ).

% le_infI
thf(fact_204_le__infI,axiom,
    ! [X2: set_Product_prod_v_v,A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ A )
     => ( ( ord_le7336532860387713383od_v_v @ X2 @ B )
       => ( ord_le7336532860387713383od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ A @ B ) ) ) ) ).

% le_infI
thf(fact_205_le__infE,axiom,
    ! [X2: product_unit,A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ ( inf_inf_Product_unit @ A @ B ) )
     => ~ ( ( ord_le3221252021190050221t_unit @ X2 @ A )
         => ~ ( ord_le3221252021190050221t_unit @ X2 @ B ) ) ) ).

% le_infE
thf(fact_206_le__infE,axiom,
    ! [X2: set_v,A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ ( inf_inf_set_v @ A @ B ) )
     => ~ ( ( ord_less_eq_set_v @ X2 @ A )
         => ~ ( ord_less_eq_set_v @ X2 @ B ) ) ) ).

% le_infE
thf(fact_207_le__infE,axiom,
    ! [X2: set_Product_prod_v_v,A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ A @ B ) )
     => ~ ( ( ord_le7336532860387713383od_v_v @ X2 @ A )
         => ~ ( ord_le7336532860387713383od_v_v @ X2 @ B ) ) ) ).

% le_infE
thf(fact_208_inf__le2,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ Y ) ).

% inf_le2
thf(fact_209_inf__le2,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ Y ) ).

% inf_le2
thf(fact_210_inf__le2,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ Y ) ).

% inf_le2
thf(fact_211_inf__le1,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ X2 ) ).

% inf_le1
thf(fact_212_inf__le1,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ X2 ) ).

% inf_le1
thf(fact_213_inf__le1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ X2 ) ).

% inf_le1
thf(fact_214_inf__sup__ord_I1_J,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ X2 ) ).

% inf_sup_ord(1)
thf(fact_215_inf__sup__ord_I1_J,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ X2 ) ).

% inf_sup_ord(1)
thf(fact_216_inf__sup__ord_I1_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ X2 ) ).

% inf_sup_ord(1)
thf(fact_217_inf__sup__ord_I2_J,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_218_inf__sup__ord_I2_J,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_219_inf__sup__ord_I2_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ Y ) ).

% inf_sup_ord(2)
thf(fact_220_subset__code_I1_J,axiom,
    ! [Xs: list_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ ( set_v2 @ Xs ) @ B5 )
      = ( ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ Xs ) )
           => ( member_v @ X3 @ B5 ) ) ) ) ).

% subset_code(1)
thf(fact_221_subset__code_I1_J,axiom,
    ! [Xs: list_P7986770385144383213od_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( set_Product_prod_v_v2 @ Xs ) @ B5 )
      = ( ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ ( set_Product_prod_v_v2 @ Xs ) )
           => ( member7453568604450474000od_v_v @ X3 @ B5 ) ) ) ) ).

% subset_code(1)
thf(fact_222_inf__left__commute,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
      = ( inf_inf_set_v @ Y @ ( inf_inf_set_v @ X2 @ Z ) ) ) ).

% inf_left_commute
thf(fact_223_inf__left__commute,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
      = ( inf_inf_Product_unit @ Y @ ( inf_inf_Product_unit @ X2 @ Z ) ) ) ).

% inf_left_commute
thf(fact_224_inf_Oleft__commute,axiom,
    ! [B: set_v,A: set_v,C: set_v] :
      ( ( inf_inf_set_v @ B @ ( inf_inf_set_v @ A @ C ) )
      = ( inf_inf_set_v @ A @ ( inf_inf_set_v @ B @ C ) ) ) ).

% inf.left_commute
thf(fact_225_inf_Oleft__commute,axiom,
    ! [B: product_unit,A: product_unit,C: product_unit] :
      ( ( inf_inf_Product_unit @ B @ ( inf_inf_Product_unit @ A @ C ) )
      = ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ).

% inf.left_commute
thf(fact_226_boolean__algebra__cancel_Oinf2,axiom,
    ! [B5: set_v,K: set_v,B: set_v,A: set_v] :
      ( ( B5
        = ( inf_inf_set_v @ K @ B ) )
     => ( ( inf_inf_set_v @ A @ B5 )
        = ( inf_inf_set_v @ K @ ( inf_inf_set_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_227_boolean__algebra__cancel_Oinf2,axiom,
    ! [B5: product_unit,K: product_unit,B: product_unit,A: product_unit] :
      ( ( B5
        = ( inf_inf_Product_unit @ K @ B ) )
     => ( ( inf_inf_Product_unit @ A @ B5 )
        = ( inf_inf_Product_unit @ K @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf2
thf(fact_228_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: set_v,K: set_v,A: set_v,B: set_v] :
      ( ( A3
        = ( inf_inf_set_v @ K @ A ) )
     => ( ( inf_inf_set_v @ A3 @ B )
        = ( inf_inf_set_v @ K @ ( inf_inf_set_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_229_boolean__algebra__cancel_Oinf1,axiom,
    ! [A3: product_unit,K: product_unit,A: product_unit,B: product_unit] :
      ( ( A3
        = ( inf_inf_Product_unit @ K @ A ) )
     => ( ( inf_inf_Product_unit @ A3 @ B )
        = ( inf_inf_Product_unit @ K @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.inf1
thf(fact_230_inf__commute,axiom,
    ( inf_inf_set_v
    = ( ^ [X3: set_v,Y4: set_v] : ( inf_inf_set_v @ Y4 @ X3 ) ) ) ).

% inf_commute
thf(fact_231_inf__commute,axiom,
    ( inf_inf_Product_unit
    = ( ^ [X3: product_unit,Y4: product_unit] : ( inf_inf_Product_unit @ Y4 @ X3 ) ) ) ).

% inf_commute
thf(fact_232_inf_Ocommute,axiom,
    ( inf_inf_set_v
    = ( ^ [A5: set_v,B4: set_v] : ( inf_inf_set_v @ B4 @ A5 ) ) ) ).

% inf.commute
thf(fact_233_inf_Ocommute,axiom,
    ( inf_inf_Product_unit
    = ( ^ [A5: product_unit,B4: product_unit] : ( inf_inf_Product_unit @ B4 @ A5 ) ) ) ).

% inf.commute
thf(fact_234_inf__assoc,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ Z )
      = ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) ) ) ).

% inf_assoc
thf(fact_235_inf__assoc,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ Z )
      = ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ).

% inf_assoc
thf(fact_236_inf_Oassoc,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ A @ B ) @ C )
      = ( inf_inf_set_v @ A @ ( inf_inf_set_v @ B @ C ) ) ) ).

% inf.assoc
thf(fact_237_inf_Oassoc,axiom,
    ! [A: product_unit,B: product_unit,C: product_unit] :
      ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ A @ B ) @ C )
      = ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ).

% inf.assoc
thf(fact_238_inf__sup__aci_I1_J,axiom,
    ( inf_inf_set_v
    = ( ^ [X3: set_v,Y4: set_v] : ( inf_inf_set_v @ Y4 @ X3 ) ) ) ).

% inf_sup_aci(1)
thf(fact_239_inf__sup__aci_I1_J,axiom,
    ( inf_inf_Product_unit
    = ( ^ [X3: product_unit,Y4: product_unit] : ( inf_inf_Product_unit @ Y4 @ X3 ) ) ) ).

% inf_sup_aci(1)
thf(fact_240_inf__sup__aci_I2_J,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ Z )
      = ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) ) ) ).

% inf_sup_aci(2)
thf(fact_241_inf__sup__aci_I2_J,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ Z )
      = ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ).

% inf_sup_aci(2)
thf(fact_242_inf__sup__aci_I3_J,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
      = ( inf_inf_set_v @ Y @ ( inf_inf_set_v @ X2 @ Z ) ) ) ).

% inf_sup_aci(3)
thf(fact_243_inf__sup__aci_I3_J,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
      = ( inf_inf_Product_unit @ Y @ ( inf_inf_Product_unit @ X2 @ Z ) ) ) ).

% inf_sup_aci(3)
thf(fact_244_inf__sup__aci_I4_J,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( inf_inf_set_v @ X2 @ Y ) )
      = ( inf_inf_set_v @ X2 @ Y ) ) ).

% inf_sup_aci(4)
thf(fact_245_inf__sup__aci_I4_J,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( inf_inf_Product_unit @ X2 @ Y ) )
      = ( inf_inf_Product_unit @ X2 @ Y ) ) ).

% inf_sup_aci(4)
thf(fact_246_dfs__S__tl__stack_I2_J,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl8953792750115413617t_unit @ successors @ V2 @ E @ E2 )
     => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
         != nil_v )
       => ! [X: v] :
            ( ( member_v @ X @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
           => ( ( sCC_Bl1280885523602775798t_unit @ E2 @ X )
              = ( sCC_Bl1280885523602775798t_unit @ E @ X ) ) ) ) ) ).

% dfs_S_tl_stack(2)
thf(fact_247_scc__partition,axiom,
    ! [S: set_v,S2: set_v,X2: v] :
      ( ( sCC_Bloemen_is_scc_v @ successors @ S )
     => ( ( sCC_Bloemen_is_scc_v @ successors @ S2 )
       => ( ( member_v @ X2 @ ( inf_inf_set_v @ S @ S2 ) )
         => ( S = S2 ) ) ) ) ).

% scc_partition
thf(fact_248_unite__subscc,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,W: v] :
      ( ( sCC_Bl1748261141445803503t_unit @ successors @ V2 @ E )
     => ( ( member_v @ W @ ( successors @ V2 ) )
       => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
         => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
           => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
             => ( sCC_Bl5398416737448265317bscc_v @ successors @ ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) ) ) ) ) ).

% unite_subscc
thf(fact_249_dfs__S__tl__stack_I1_J,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl8953792750115413617t_unit @ successors @ V2 @ E @ E2 )
     => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
         != nil_v )
       => ( ( sCC_Bl8828226123343373779t_unit @ E2 )
         != nil_v ) ) ) ).

% dfs_S_tl_stack(1)
thf(fact_250_unite__S__tl,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,W: v,V2: v,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ W @ ( successors @ V2 ) )
       => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
         => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
           => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
             => ( ( member_v @ N2 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) )
               => ( ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ N2 )
                  = ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) ) ) ) ) ) ) ) ).

% unite_S_tl
thf(fact_251_visited__unexplored,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,M2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ M2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
       => ( ~ ( member_v @ M2 @ ( sCC_Bl157864678168468314t_unit @ E ) )
         => ~ ! [N3: v] :
                ( ( member_v @ N3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
               => ~ ( member_v @ M2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N3 ) ) ) ) ) ) ).

% visited_unexplored
thf(fact_252_insert__disjoint_I1_J,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ( ( inf_inf_set_v @ ( insert_v @ A @ A3 ) @ B5 )
        = bot_bot_set_v )
      = ( ~ ( member_v @ A @ B5 )
        & ( ( inf_inf_set_v @ A3 @ B5 )
          = bot_bot_set_v ) ) ) ).

% insert_disjoint(1)
thf(fact_253_insert__disjoint_I1_J,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ A3 ) @ B5 )
        = bot_bo723834152578015283od_v_v )
      = ( ~ ( member7453568604450474000od_v_v @ A @ B5 )
        & ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% insert_disjoint(1)
thf(fact_254_insert__disjoint_I2_J,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ( bot_bot_set_v
        = ( inf_inf_set_v @ ( insert_v @ A @ A3 ) @ B5 ) )
      = ( ~ ( member_v @ A @ B5 )
        & ( bot_bot_set_v
          = ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_255_insert__disjoint_I2_J,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ A3 ) @ B5 ) )
      = ( ~ ( member7453568604450474000od_v_v @ A @ B5 )
        & ( bot_bo723834152578015283od_v_v
          = ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_256_disjoint__insert_I1_J,axiom,
    ! [B5: set_v,A: v,A3: set_v] :
      ( ( ( inf_inf_set_v @ B5 @ ( insert_v @ A @ A3 ) )
        = bot_bot_set_v )
      = ( ~ ( member_v @ A @ B5 )
        & ( ( inf_inf_set_v @ B5 @ A3 )
          = bot_bot_set_v ) ) ) ).

% disjoint_insert(1)
thf(fact_257_disjoint__insert_I1_J,axiom,
    ! [B5: set_Product_prod_v_v,A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ B5 @ ( insert1338601472111419319od_v_v @ A @ A3 ) )
        = bot_bo723834152578015283od_v_v )
      = ( ~ ( member7453568604450474000od_v_v @ A @ B5 )
        & ( ( inf_in6271465464967711157od_v_v @ B5 @ A3 )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% disjoint_insert(1)
thf(fact_258_disjoint__insert_I2_J,axiom,
    ! [A3: set_v,B: v,B5: set_v] :
      ( ( bot_bot_set_v
        = ( inf_inf_set_v @ A3 @ ( insert_v @ B @ B5 ) ) )
      = ( ~ ( member_v @ B @ A3 )
        & ( bot_bot_set_v
          = ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_259_disjoint__insert_I2_J,axiom,
    ! [A3: set_Product_prod_v_v,B: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( inf_in6271465464967711157od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ B @ B5 ) ) )
      = ( ~ ( member7453568604450474000od_v_v @ B @ A3 )
        & ( bot_bo723834152578015283od_v_v
          = ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_260_S__reflexive,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) ) ) ).

% S_reflexive
thf(fact_261_empty__iff,axiom,
    ! [C: v] :
      ~ ( member_v @ C @ bot_bot_set_v ) ).

% empty_iff
thf(fact_262_empty__iff,axiom,
    ! [C: product_prod_v_v] :
      ~ ( member7453568604450474000od_v_v @ C @ bot_bo723834152578015283od_v_v ) ).

% empty_iff
thf(fact_263_all__not__in__conv,axiom,
    ! [A3: set_v] :
      ( ( ! [X3: v] :
            ~ ( member_v @ X3 @ A3 ) )
      = ( A3 = bot_bot_set_v ) ) ).

% all_not_in_conv
thf(fact_264_all__not__in__conv,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( ! [X3: product_prod_v_v] :
            ~ ( member7453568604450474000od_v_v @ X3 @ A3 ) )
      = ( A3 = bot_bo723834152578015283od_v_v ) ) ).

% all_not_in_conv
thf(fact_265_Collect__empty__eq,axiom,
    ! [P: set_v > $o] :
      ( ( ( collect_set_v @ P )
        = bot_bot_set_set_v )
      = ( ! [X3: set_v] :
            ~ ( P @ X3 ) ) ) ).

% Collect_empty_eq
thf(fact_266_Collect__empty__eq,axiom,
    ! [P: v > $o] :
      ( ( ( collect_v @ P )
        = bot_bot_set_v )
      = ( ! [X3: v] :
            ~ ( P @ X3 ) ) ) ).

% Collect_empty_eq
thf(fact_267_Collect__empty__eq,axiom,
    ! [P: product_prod_v_v > $o] :
      ( ( ( collec140062887454715474od_v_v @ P )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: product_prod_v_v] :
            ~ ( P @ X3 ) ) ) ).

% Collect_empty_eq
thf(fact_268_empty__Collect__eq,axiom,
    ! [P: set_v > $o] :
      ( ( bot_bot_set_set_v
        = ( collect_set_v @ P ) )
      = ( ! [X3: set_v] :
            ~ ( P @ X3 ) ) ) ).

% empty_Collect_eq
thf(fact_269_empty__Collect__eq,axiom,
    ! [P: v > $o] :
      ( ( bot_bot_set_v
        = ( collect_v @ P ) )
      = ( ! [X3: v] :
            ~ ( P @ X3 ) ) ) ).

% empty_Collect_eq
thf(fact_270_empty__Collect__eq,axiom,
    ! [P: product_prod_v_v > $o] :
      ( ( bot_bo723834152578015283od_v_v
        = ( collec140062887454715474od_v_v @ P ) )
      = ( ! [X3: product_prod_v_v] :
            ~ ( P @ X3 ) ) ) ).

% empty_Collect_eq
thf(fact_271_subsetI,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ! [X4: v] :
          ( ( member_v @ X4 @ A3 )
         => ( member_v @ X4 @ B5 ) )
     => ( ord_less_eq_set_v @ A3 @ B5 ) ) ).

% subsetI
thf(fact_272_subsetI,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ! [X4: product_prod_v_v] :
          ( ( member7453568604450474000od_v_v @ X4 @ A3 )
         => ( member7453568604450474000od_v_v @ X4 @ B5 ) )
     => ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ).

% subsetI
thf(fact_273_subset__antisym,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( ord_less_eq_set_v @ B5 @ A3 )
       => ( A3 = B5 ) ) ) ).

% subset_antisym
thf(fact_274_subset__antisym,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ A3 )
       => ( A3 = B5 ) ) ) ).

% subset_antisym
thf(fact_275_insertCI,axiom,
    ! [A: v,B5: set_v,B: v] :
      ( ( ~ ( member_v @ A @ B5 )
       => ( A = B ) )
     => ( member_v @ A @ ( insert_v @ B @ B5 ) ) ) ).

% insertCI
thf(fact_276_insertCI,axiom,
    ! [A: product_prod_v_v,B5: set_Product_prod_v_v,B: product_prod_v_v] :
      ( ( ~ ( member7453568604450474000od_v_v @ A @ B5 )
       => ( A = B ) )
     => ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ B @ B5 ) ) ) ).

% insertCI
thf(fact_277_insert__iff,axiom,
    ! [A: v,B: v,A3: set_v] :
      ( ( member_v @ A @ ( insert_v @ B @ A3 ) )
      = ( ( A = B )
        | ( member_v @ A @ A3 ) ) ) ).

% insert_iff
thf(fact_278_insert__iff,axiom,
    ! [A: product_prod_v_v,B: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ B @ A3 ) )
      = ( ( A = B )
        | ( member7453568604450474000od_v_v @ A @ A3 ) ) ) ).

% insert_iff
thf(fact_279_insert__absorb2,axiom,
    ! [X2: v,A3: set_v] :
      ( ( insert_v @ X2 @ ( insert_v @ X2 @ A3 ) )
      = ( insert_v @ X2 @ A3 ) ) ).

% insert_absorb2
thf(fact_280_insert__absorb2,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( insert1338601472111419319od_v_v @ X2 @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) )
      = ( insert1338601472111419319od_v_v @ X2 @ A3 ) ) ).

% insert_absorb2
thf(fact_281_IntI,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ A3 )
     => ( ( member7453568604450474000od_v_v @ C @ B5 )
       => ( member7453568604450474000od_v_v @ C @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% IntI
thf(fact_282_IntI,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ A3 )
     => ( ( member_v @ C @ B5 )
       => ( member_v @ C @ ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% IntI
thf(fact_283_Int__iff,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
      = ( ( member7453568604450474000od_v_v @ C @ A3 )
        & ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_284_Int__iff,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( inf_inf_set_v @ A3 @ B5 ) )
      = ( ( member_v @ C @ A3 )
        & ( member_v @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_285_local_Owf,axiom,
    sCC_Bl9196236973127232072t_unit @ successors @ e ).

% local.wf
thf(fact_286_stack__visited,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
       => ( member_v @ N2 @ ( sCC_Bl4645233313691564917t_unit @ E ) ) ) ) ).

% stack_visited
thf(fact_287_stack__unexplored,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
       => ~ ( member_v @ N2 @ ( sCC_Bl157864678168468314t_unit @ E ) ) ) ) ).

% stack_unexplored
thf(fact_288_is__scc__def,axiom,
    ! [S: set_v] :
      ( ( sCC_Bloemen_is_scc_v @ successors @ S )
      = ( ( S != bot_bot_set_v )
        & ( sCC_Bl5398416737448265317bscc_v @ successors @ S )
        & ! [S3: set_v] :
            ( ( ( ord_less_eq_set_v @ S @ S3 )
              & ( sCC_Bl5398416737448265317bscc_v @ successors @ S3 ) )
           => ( S3 = S ) ) ) ) ).

% is_scc_def
thf(fact_289_subset__empty,axiom,
    ! [A3: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ bot_bot_set_v )
      = ( A3 = bot_bot_set_v ) ) ).

% subset_empty
thf(fact_290_subset__empty,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ bot_bo723834152578015283od_v_v )
      = ( A3 = bot_bo723834152578015283od_v_v ) ) ).

% subset_empty
thf(fact_291_empty__subsetI,axiom,
    ! [A3: set_v] : ( ord_less_eq_set_v @ bot_bot_set_v @ A3 ) ).

% empty_subsetI
thf(fact_292_empty__subsetI,axiom,
    ! [A3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ bot_bo723834152578015283od_v_v @ A3 ) ).

% empty_subsetI
thf(fact_293_singletonI,axiom,
    ! [A: v] : ( member_v @ A @ ( insert_v @ A @ bot_bot_set_v ) ) ).

% singletonI
thf(fact_294_singletonI,axiom,
    ! [A: product_prod_v_v] : ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) ).

% singletonI
thf(fact_295_insert__subset,axiom,
    ! [X2: v,A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ ( insert_v @ X2 @ A3 ) @ B5 )
      = ( ( member_v @ X2 @ B5 )
        & ( ord_less_eq_set_v @ A3 @ B5 ) ) ) ).

% insert_subset
thf(fact_296_insert__subset,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) @ B5 )
      = ( ( member7453568604450474000od_v_v @ X2 @ B5 )
        & ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ) ).

% insert_subset
thf(fact_297_Int__subset__iff,axiom,
    ! [C2: set_v,A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ C2 @ ( inf_inf_set_v @ A3 @ B5 ) )
      = ( ( ord_less_eq_set_v @ C2 @ A3 )
        & ( ord_less_eq_set_v @ C2 @ B5 ) ) ) ).

% Int_subset_iff
thf(fact_298_Int__subset__iff,axiom,
    ! [C2: set_Product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C2 @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
      = ( ( ord_le7336532860387713383od_v_v @ C2 @ A3 )
        & ( ord_le7336532860387713383od_v_v @ C2 @ B5 ) ) ) ).

% Int_subset_iff
thf(fact_299_Int__insert__left__if0,axiom,
    ! [A: product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ A @ C2 )
     => ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ B5 ) @ C2 )
        = ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_300_Int__insert__left__if0,axiom,
    ! [A: v,C2: set_v,B5: set_v] :
      ( ~ ( member_v @ A @ C2 )
     => ( ( inf_inf_set_v @ ( insert_v @ A @ B5 ) @ C2 )
        = ( inf_inf_set_v @ B5 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_301_Int__insert__left__if1,axiom,
    ! [A: product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ C2 )
     => ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ B5 ) @ C2 )
        = ( insert1338601472111419319od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_302_Int__insert__left__if1,axiom,
    ! [A: v,C2: set_v,B5: set_v] :
      ( ( member_v @ A @ C2 )
     => ( ( inf_inf_set_v @ ( insert_v @ A @ B5 ) @ C2 )
        = ( insert_v @ A @ ( inf_inf_set_v @ B5 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_303_insert__inter__insert,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ A3 ) @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
      = ( insert1338601472111419319od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ).

% insert_inter_insert
thf(fact_304_insert__inter__insert,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ( inf_inf_set_v @ ( insert_v @ A @ A3 ) @ ( insert_v @ A @ B5 ) )
      = ( insert_v @ A @ ( inf_inf_set_v @ A3 @ B5 ) ) ) ).

% insert_inter_insert
thf(fact_305_Int__insert__right__if0,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ A @ A3 )
     => ( ( inf_in6271465464967711157od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
        = ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ).

% Int_insert_right_if0
thf(fact_306_Int__insert__right__if0,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ~ ( member_v @ A @ A3 )
     => ( ( inf_inf_set_v @ A3 @ ( insert_v @ A @ B5 ) )
        = ( inf_inf_set_v @ A3 @ B5 ) ) ) ).

% Int_insert_right_if0
thf(fact_307_Int__insert__right__if1,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ A3 )
     => ( ( inf_in6271465464967711157od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
        = ( insert1338601472111419319od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_308_Int__insert__right__if1,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ( member_v @ A @ A3 )
     => ( ( inf_inf_set_v @ A3 @ ( insert_v @ A @ B5 ) )
        = ( insert_v @ A @ ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_309_dfs__S__hd__stack_I2_J,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,V2: v,E2: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( sCC_Bl8953792750115413617t_unit @ successors @ V2 @ E @ E2 )
       => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
           != nil_v )
         => ( ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
           => ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) ) ) ) ) ) ).

% dfs_S_hd_stack(2)
thf(fact_310_dfs__S__hd__stack_I1_J,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,V2: v,E2: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( sCC_Bl8953792750115413617t_unit @ successors @ V2 @ E @ E2 )
       => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
           != nil_v )
         => ( ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
           => ( ( sCC_Bl8828226123343373779t_unit @ E2 )
             != nil_v ) ) ) ) ) ).

% dfs_S_hd_stack(1)
thf(fact_311_singleton__insert__inj__eq,axiom,
    ! [B: v,A: v,A3: set_v] :
      ( ( ( insert_v @ B @ bot_bot_set_v )
        = ( insert_v @ A @ A3 ) )
      = ( ( A = B )
        & ( ord_less_eq_set_v @ A3 @ ( insert_v @ B @ bot_bot_set_v ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_312_singleton__insert__inj__eq,axiom,
    ! [B: product_prod_v_v,A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v )
        = ( insert1338601472111419319od_v_v @ A @ A3 ) )
      = ( ( A = B )
        & ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_313_singleton__insert__inj__eq_H,axiom,
    ! [A: v,A3: set_v,B: v] :
      ( ( ( insert_v @ A @ A3 )
        = ( insert_v @ B @ bot_bot_set_v ) )
      = ( ( A = B )
        & ( ord_less_eq_set_v @ A3 @ ( insert_v @ B @ bot_bot_set_v ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_314_singleton__insert__inj__eq_H,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B: product_prod_v_v] :
      ( ( ( insert1338601472111419319od_v_v @ A @ A3 )
        = ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v ) )
      = ( ( A = B )
        & ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_315_graph__axioms,axiom,
    sCC_Bloemen_graph_v @ vertices @ successors ).

% graph_axioms
thf(fact_316_calculation_I10_J,axiom,
    ! [X: set_v] :
      ( ( member_set_v @ X @ ( sCC_Bl2536197123907397897t_unit @ e2 ) )
     => ( sCC_Bloemen_is_scc_v @ successors @ X ) ) ).

% calculation(10)
thf(fact_317_graph_Ois__subscc_Ocong,axiom,
    sCC_Bl5398416737448265317bscc_v = sCC_Bl5398416737448265317bscc_v ).

% graph.is_subscc.cong
thf(fact_318_graph_Owf__env_Ocong,axiom,
    sCC_Bl9196236973127232072t_unit = sCC_Bl9196236973127232072t_unit ).

% graph.wf_env.cong
thf(fact_319_graph_Ois__scc_Ocong,axiom,
    sCC_Bloemen_is_scc_v = sCC_Bloemen_is_scc_v ).

% graph.is_scc.cong
thf(fact_320_emptyE,axiom,
    ! [A: v] :
      ~ ( member_v @ A @ bot_bot_set_v ) ).

% emptyE
thf(fact_321_emptyE,axiom,
    ! [A: product_prod_v_v] :
      ~ ( member7453568604450474000od_v_v @ A @ bot_bo723834152578015283od_v_v ) ).

% emptyE
thf(fact_322_equals0D,axiom,
    ! [A3: set_v,A: v] :
      ( ( A3 = bot_bot_set_v )
     => ~ ( member_v @ A @ A3 ) ) ).

% equals0D
thf(fact_323_equals0D,axiom,
    ! [A3: set_Product_prod_v_v,A: product_prod_v_v] :
      ( ( A3 = bot_bo723834152578015283od_v_v )
     => ~ ( member7453568604450474000od_v_v @ A @ A3 ) ) ).

% equals0D
thf(fact_324_equals0I,axiom,
    ! [A3: set_v] :
      ( ! [Y3: v] :
          ~ ( member_v @ Y3 @ A3 )
     => ( A3 = bot_bot_set_v ) ) ).

% equals0I
thf(fact_325_equals0I,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ! [Y3: product_prod_v_v] :
          ~ ( member7453568604450474000od_v_v @ Y3 @ A3 )
     => ( A3 = bot_bo723834152578015283od_v_v ) ) ).

% equals0I
thf(fact_326_ex__in__conv,axiom,
    ! [A3: set_v] :
      ( ( ? [X3: v] : ( member_v @ X3 @ A3 ) )
      = ( A3 != bot_bot_set_v ) ) ).

% ex_in_conv
thf(fact_327_ex__in__conv,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( ? [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A3 ) )
      = ( A3 != bot_bo723834152578015283od_v_v ) ) ).

% ex_in_conv
thf(fact_328_bot__set__def,axiom,
    ( bot_bot_set_set_v
    = ( collect_set_v @ bot_bot_set_v_o ) ) ).

% bot_set_def
thf(fact_329_bot__set__def,axiom,
    ( bot_bot_set_v
    = ( collect_v @ bot_bot_v_o ) ) ).

% bot_set_def
thf(fact_330_bot__set__def,axiom,
    ( bot_bo723834152578015283od_v_v
    = ( collec140062887454715474od_v_v @ bot_bo8461541820394803818_v_v_o ) ) ).

% bot_set_def
thf(fact_331_in__mono,axiom,
    ! [A3: set_v,B5: set_v,X2: v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( member_v @ X2 @ A3 )
       => ( member_v @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_332_in__mono,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,X2: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( member7453568604450474000od_v_v @ X2 @ A3 )
       => ( member7453568604450474000od_v_v @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_333_subsetD,axiom,
    ! [A3: set_v,B5: set_v,C: v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( member_v @ C @ A3 )
       => ( member_v @ C @ B5 ) ) ) ).

% subsetD
thf(fact_334_subsetD,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( member7453568604450474000od_v_v @ C @ A3 )
       => ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% subsetD
thf(fact_335_equalityE,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( A3 = B5 )
     => ~ ( ( ord_less_eq_set_v @ A3 @ B5 )
         => ~ ( ord_less_eq_set_v @ B5 @ A3 ) ) ) ).

% equalityE
thf(fact_336_equalityE,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( A3 = B5 )
     => ~ ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
         => ~ ( ord_le7336532860387713383od_v_v @ B5 @ A3 ) ) ) ).

% equalityE
thf(fact_337_subset__eq,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A6: set_v,B6: set_v] :
        ! [X3: v] :
          ( ( member_v @ X3 @ A6 )
         => ( member_v @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_338_subset__eq,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
        ! [X3: product_prod_v_v] :
          ( ( member7453568604450474000od_v_v @ X3 @ A6 )
         => ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_339_equalityD1,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( A3 = B5 )
     => ( ord_less_eq_set_v @ A3 @ B5 ) ) ).

% equalityD1
thf(fact_340_equalityD1,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( A3 = B5 )
     => ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ).

% equalityD1
thf(fact_341_equalityD2,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( A3 = B5 )
     => ( ord_less_eq_set_v @ B5 @ A3 ) ) ).

% equalityD2
thf(fact_342_equalityD2,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( A3 = B5 )
     => ( ord_le7336532860387713383od_v_v @ B5 @ A3 ) ) ).

% equalityD2
thf(fact_343_subset__iff,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A6: set_v,B6: set_v] :
        ! [T: v] :
          ( ( member_v @ T @ A6 )
         => ( member_v @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_344_subset__iff,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
        ! [T: product_prod_v_v] :
          ( ( member7453568604450474000od_v_v @ T @ A6 )
         => ( member7453568604450474000od_v_v @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_345_subset__refl,axiom,
    ! [A3: set_v] : ( ord_less_eq_set_v @ A3 @ A3 ) ).

% subset_refl
thf(fact_346_subset__refl,axiom,
    ! [A3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ A3 @ A3 ) ).

% subset_refl
thf(fact_347_Collect__mono,axiom,
    ! [P: set_v > $o,Q: set_v > $o] :
      ( ! [X4: set_v] :
          ( ( P @ X4 )
         => ( Q @ X4 ) )
     => ( ord_le5216385588623774835_set_v @ ( collect_set_v @ P ) @ ( collect_set_v @ Q ) ) ) ).

% Collect_mono
thf(fact_348_Collect__mono,axiom,
    ! [P: v > $o,Q: v > $o] :
      ( ! [X4: v] :
          ( ( P @ X4 )
         => ( Q @ X4 ) )
     => ( ord_less_eq_set_v @ ( collect_v @ P ) @ ( collect_v @ Q ) ) ) ).

% Collect_mono
thf(fact_349_Collect__mono,axiom,
    ! [P: product_prod_v_v > $o,Q: product_prod_v_v > $o] :
      ( ! [X4: product_prod_v_v] :
          ( ( P @ X4 )
         => ( Q @ X4 ) )
     => ( ord_le7336532860387713383od_v_v @ ( collec140062887454715474od_v_v @ P ) @ ( collec140062887454715474od_v_v @ Q ) ) ) ).

% Collect_mono
thf(fact_350_subset__trans,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( ord_less_eq_set_v @ B5 @ C2 )
       => ( ord_less_eq_set_v @ A3 @ C2 ) ) ) ).

% subset_trans
thf(fact_351_subset__trans,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ C2 )
       => ( ord_le7336532860387713383od_v_v @ A3 @ C2 ) ) ) ).

% subset_trans
thf(fact_352_set__eq__subset,axiom,
    ( ( ^ [Y5: set_v,Z3: set_v] : ( Y5 = Z3 ) )
    = ( ^ [A6: set_v,B6: set_v] :
          ( ( ord_less_eq_set_v @ A6 @ B6 )
          & ( ord_less_eq_set_v @ B6 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_353_set__eq__subset,axiom,
    ( ( ^ [Y5: set_Product_prod_v_v,Z3: set_Product_prod_v_v] : ( Y5 = Z3 ) )
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( ( ord_le7336532860387713383od_v_v @ A6 @ B6 )
          & ( ord_le7336532860387713383od_v_v @ B6 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_354_Collect__mono__iff,axiom,
    ! [P: set_v > $o,Q: set_v > $o] :
      ( ( ord_le5216385588623774835_set_v @ ( collect_set_v @ P ) @ ( collect_set_v @ Q ) )
      = ( ! [X3: set_v] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_355_Collect__mono__iff,axiom,
    ! [P: v > $o,Q: v > $o] :
      ( ( ord_less_eq_set_v @ ( collect_v @ P ) @ ( collect_v @ Q ) )
      = ( ! [X3: v] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_356_Collect__mono__iff,axiom,
    ! [P: product_prod_v_v > $o,Q: product_prod_v_v > $o] :
      ( ( ord_le7336532860387713383od_v_v @ ( collec140062887454715474od_v_v @ P ) @ ( collec140062887454715474od_v_v @ Q ) )
      = ( ! [X3: product_prod_v_v] :
            ( ( P @ X3 )
           => ( Q @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_357_insertE,axiom,
    ! [A: v,B: v,A3: set_v] :
      ( ( member_v @ A @ ( insert_v @ B @ A3 ) )
     => ( ( A != B )
       => ( member_v @ A @ A3 ) ) ) ).

% insertE
thf(fact_358_insertE,axiom,
    ! [A: product_prod_v_v,B: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ B @ A3 ) )
     => ( ( A != B )
       => ( member7453568604450474000od_v_v @ A @ A3 ) ) ) ).

% insertE
thf(fact_359_insertI1,axiom,
    ! [A: v,B5: set_v] : ( member_v @ A @ ( insert_v @ A @ B5 ) ) ).

% insertI1
thf(fact_360_insertI1,axiom,
    ! [A: product_prod_v_v,B5: set_Product_prod_v_v] : ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ A @ B5 ) ) ).

% insertI1
thf(fact_361_insertI2,axiom,
    ! [A: v,B5: set_v,B: v] :
      ( ( member_v @ A @ B5 )
     => ( member_v @ A @ ( insert_v @ B @ B5 ) ) ) ).

% insertI2
thf(fact_362_insertI2,axiom,
    ! [A: product_prod_v_v,B5: set_Product_prod_v_v,B: product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ B5 )
     => ( member7453568604450474000od_v_v @ A @ ( insert1338601472111419319od_v_v @ B @ B5 ) ) ) ).

% insertI2
thf(fact_363_Set_Oset__insert,axiom,
    ! [X2: v,A3: set_v] :
      ( ( member_v @ X2 @ A3 )
     => ~ ! [B7: set_v] :
            ( ( A3
              = ( insert_v @ X2 @ B7 ) )
           => ( member_v @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_364_Set_Oset__insert,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ A3 )
     => ~ ! [B7: set_Product_prod_v_v] :
            ( ( A3
              = ( insert1338601472111419319od_v_v @ X2 @ B7 ) )
           => ( member7453568604450474000od_v_v @ X2 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_365_insert__ident,axiom,
    ! [X2: v,A3: set_v,B5: set_v] :
      ( ~ ( member_v @ X2 @ A3 )
     => ( ~ ( member_v @ X2 @ B5 )
       => ( ( ( insert_v @ X2 @ A3 )
            = ( insert_v @ X2 @ B5 ) )
          = ( A3 = B5 ) ) ) ) ).

% insert_ident
thf(fact_366_insert__ident,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ A3 )
     => ( ~ ( member7453568604450474000od_v_v @ X2 @ B5 )
       => ( ( ( insert1338601472111419319od_v_v @ X2 @ A3 )
            = ( insert1338601472111419319od_v_v @ X2 @ B5 ) )
          = ( A3 = B5 ) ) ) ) ).

% insert_ident
thf(fact_367_insert__absorb,axiom,
    ! [A: v,A3: set_v] :
      ( ( member_v @ A @ A3 )
     => ( ( insert_v @ A @ A3 )
        = A3 ) ) ).

% insert_absorb
thf(fact_368_insert__absorb,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ A3 )
     => ( ( insert1338601472111419319od_v_v @ A @ A3 )
        = A3 ) ) ).

% insert_absorb
thf(fact_369_insert__eq__iff,axiom,
    ! [A: v,A3: set_v,B: v,B5: set_v] :
      ( ~ ( member_v @ A @ A3 )
     => ( ~ ( member_v @ B @ B5 )
       => ( ( ( insert_v @ A @ A3 )
            = ( insert_v @ B @ B5 ) )
          = ( ( ( A = B )
             => ( A3 = B5 ) )
            & ( ( A != B )
             => ? [C3: set_v] :
                  ( ( A3
                    = ( insert_v @ B @ C3 ) )
                  & ~ ( member_v @ B @ C3 )
                  & ( B5
                    = ( insert_v @ A @ C3 ) )
                  & ~ ( member_v @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_370_insert__eq__iff,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ A @ A3 )
     => ( ~ ( member7453568604450474000od_v_v @ B @ B5 )
       => ( ( ( insert1338601472111419319od_v_v @ A @ A3 )
            = ( insert1338601472111419319od_v_v @ B @ B5 ) )
          = ( ( ( A = B )
             => ( A3 = B5 ) )
            & ( ( A != B )
             => ? [C3: set_Product_prod_v_v] :
                  ( ( A3
                    = ( insert1338601472111419319od_v_v @ B @ C3 ) )
                  & ~ ( member7453568604450474000od_v_v @ B @ C3 )
                  & ( B5
                    = ( insert1338601472111419319od_v_v @ A @ C3 ) )
                  & ~ ( member7453568604450474000od_v_v @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_371_insert__commute,axiom,
    ! [X2: v,Y: v,A3: set_v] :
      ( ( insert_v @ X2 @ ( insert_v @ Y @ A3 ) )
      = ( insert_v @ Y @ ( insert_v @ X2 @ A3 ) ) ) ).

% insert_commute
thf(fact_372_insert__commute,axiom,
    ! [X2: product_prod_v_v,Y: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( insert1338601472111419319od_v_v @ X2 @ ( insert1338601472111419319od_v_v @ Y @ A3 ) )
      = ( insert1338601472111419319od_v_v @ Y @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) ) ) ).

% insert_commute
thf(fact_373_mk__disjoint__insert,axiom,
    ! [A: v,A3: set_v] :
      ( ( member_v @ A @ A3 )
     => ? [B7: set_v] :
          ( ( A3
            = ( insert_v @ A @ B7 ) )
          & ~ ( member_v @ A @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_374_mk__disjoint__insert,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ A3 )
     => ? [B7: set_Product_prod_v_v] :
          ( ( A3
            = ( insert1338601472111419319od_v_v @ A @ B7 ) )
          & ~ ( member7453568604450474000od_v_v @ A @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_375_IntE,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
     => ~ ( ( member7453568604450474000od_v_v @ C @ A3 )
         => ~ ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% IntE
thf(fact_376_IntE,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( inf_inf_set_v @ A3 @ B5 ) )
     => ~ ( ( member_v @ C @ A3 )
         => ~ ( member_v @ C @ B5 ) ) ) ).

% IntE
thf(fact_377_IntD1,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
     => ( member7453568604450474000od_v_v @ C @ A3 ) ) ).

% IntD1
thf(fact_378_IntD1,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( inf_inf_set_v @ A3 @ B5 ) )
     => ( member_v @ C @ A3 ) ) ).

% IntD1
thf(fact_379_IntD2,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
     => ( member7453568604450474000od_v_v @ C @ B5 ) ) ).

% IntD2
thf(fact_380_IntD2,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( inf_inf_set_v @ A3 @ B5 ) )
     => ( member_v @ C @ B5 ) ) ).

% IntD2
thf(fact_381_Int__assoc,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ C2 )
      = ( inf_inf_set_v @ A3 @ ( inf_inf_set_v @ B5 @ C2 ) ) ) ).

% Int_assoc
thf(fact_382_Int__absorb,axiom,
    ! [A3: set_v] :
      ( ( inf_inf_set_v @ A3 @ A3 )
      = A3 ) ).

% Int_absorb
thf(fact_383_Int__commute,axiom,
    ( inf_inf_set_v
    = ( ^ [A6: set_v,B6: set_v] : ( inf_inf_set_v @ B6 @ A6 ) ) ) ).

% Int_commute
thf(fact_384_Int__left__absorb,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( inf_inf_set_v @ A3 @ ( inf_inf_set_v @ A3 @ B5 ) )
      = ( inf_inf_set_v @ A3 @ B5 ) ) ).

% Int_left_absorb
thf(fact_385_Int__left__commute,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( inf_inf_set_v @ A3 @ ( inf_inf_set_v @ B5 @ C2 ) )
      = ( inf_inf_set_v @ B5 @ ( inf_inf_set_v @ A3 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_386_singletonD,axiom,
    ! [B: v,A: v] :
      ( ( member_v @ B @ ( insert_v @ A @ bot_bot_set_v ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_387_singletonD,axiom,
    ! [B: product_prod_v_v,A: product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ B @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_388_singleton__iff,axiom,
    ! [B: v,A: v] :
      ( ( member_v @ B @ ( insert_v @ A @ bot_bot_set_v ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_389_singleton__iff,axiom,
    ! [B: product_prod_v_v,A: product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ B @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_390_doubleton__eq__iff,axiom,
    ! [A: v,B: v,C: v,D: v] :
      ( ( ( insert_v @ A @ ( insert_v @ B @ bot_bot_set_v ) )
        = ( insert_v @ C @ ( insert_v @ D @ bot_bot_set_v ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_391_doubleton__eq__iff,axiom,
    ! [A: product_prod_v_v,B: product_prod_v_v,C: product_prod_v_v,D: product_prod_v_v] :
      ( ( ( insert1338601472111419319od_v_v @ A @ ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v ) )
        = ( insert1338601472111419319od_v_v @ C @ ( insert1338601472111419319od_v_v @ D @ bot_bo723834152578015283od_v_v ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_392_insert__not__empty,axiom,
    ! [A: v,A3: set_v] :
      ( ( insert_v @ A @ A3 )
     != bot_bot_set_v ) ).

% insert_not_empty
thf(fact_393_insert__not__empty,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( insert1338601472111419319od_v_v @ A @ A3 )
     != bot_bo723834152578015283od_v_v ) ).

% insert_not_empty
thf(fact_394_singleton__inject,axiom,
    ! [A: v,B: v] :
      ( ( ( insert_v @ A @ bot_bot_set_v )
        = ( insert_v @ B @ bot_bot_set_v ) )
     => ( A = B ) ) ).

% singleton_inject
thf(fact_395_singleton__inject,axiom,
    ! [A: product_prod_v_v,B: product_prod_v_v] :
      ( ( ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v )
        = ( insert1338601472111419319od_v_v @ B @ bot_bo723834152578015283od_v_v ) )
     => ( A = B ) ) ).

% singleton_inject
thf(fact_396_insert__mono,axiom,
    ! [C2: set_v,D2: set_v,A: v] :
      ( ( ord_less_eq_set_v @ C2 @ D2 )
     => ( ord_less_eq_set_v @ ( insert_v @ A @ C2 ) @ ( insert_v @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_397_insert__mono,axiom,
    ! [C2: set_Product_prod_v_v,D2: set_Product_prod_v_v,A: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C2 @ D2 )
     => ( ord_le7336532860387713383od_v_v @ ( insert1338601472111419319od_v_v @ A @ C2 ) @ ( insert1338601472111419319od_v_v @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_398_subset__insert,axiom,
    ! [X2: v,A3: set_v,B5: set_v] :
      ( ~ ( member_v @ X2 @ A3 )
     => ( ( ord_less_eq_set_v @ A3 @ ( insert_v @ X2 @ B5 ) )
        = ( ord_less_eq_set_v @ A3 @ B5 ) ) ) ).

% subset_insert
thf(fact_399_subset__insert,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ A3 )
     => ( ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ B5 ) )
        = ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ) ).

% subset_insert
thf(fact_400_subset__insertI,axiom,
    ! [B5: set_v,A: v] : ( ord_less_eq_set_v @ B5 @ ( insert_v @ A @ B5 ) ) ).

% subset_insertI
thf(fact_401_subset__insertI,axiom,
    ! [B5: set_Product_prod_v_v,A: product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ B5 @ ( insert1338601472111419319od_v_v @ A @ B5 ) ) ).

% subset_insertI
thf(fact_402_subset__insertI2,axiom,
    ! [A3: set_v,B5: set_v,B: v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ord_less_eq_set_v @ A3 @ ( insert_v @ B @ B5 ) ) ) ).

% subset_insertI2
thf(fact_403_subset__insertI2,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,B: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ B @ B5 ) ) ) ).

% subset_insertI2
thf(fact_404_Int__emptyI,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ! [X4: v] :
          ( ( member_v @ X4 @ A3 )
         => ~ ( member_v @ X4 @ B5 ) )
     => ( ( inf_inf_set_v @ A3 @ B5 )
        = bot_bot_set_v ) ) ).

% Int_emptyI
thf(fact_405_Int__emptyI,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ! [X4: product_prod_v_v] :
          ( ( member7453568604450474000od_v_v @ X4 @ A3 )
         => ~ ( member7453568604450474000od_v_v @ X4 @ B5 ) )
     => ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v ) ) ).

% Int_emptyI
thf(fact_406_disjoint__iff,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ( inf_inf_set_v @ A3 @ B5 )
        = bot_bot_set_v )
      = ( ! [X3: v] :
            ( ( member_v @ X3 @ A3 )
           => ~ ( member_v @ X3 @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_407_disjoint__iff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ A3 )
           => ~ ( member7453568604450474000od_v_v @ X3 @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_408_Int__empty__left,axiom,
    ! [B5: set_v] :
      ( ( inf_inf_set_v @ bot_bot_set_v @ B5 )
      = bot_bot_set_v ) ).

% Int_empty_left
thf(fact_409_Int__empty__left,axiom,
    ! [B5: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ bot_bo723834152578015283od_v_v @ B5 )
      = bot_bo723834152578015283od_v_v ) ).

% Int_empty_left
thf(fact_410_Int__empty__right,axiom,
    ! [A3: set_v] :
      ( ( inf_inf_set_v @ A3 @ bot_bot_set_v )
      = bot_bot_set_v ) ).

% Int_empty_right
thf(fact_411_Int__empty__right,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ A3 @ bot_bo723834152578015283od_v_v )
      = bot_bo723834152578015283od_v_v ) ).

% Int_empty_right
thf(fact_412_disjoint__iff__not__equal,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ( inf_inf_set_v @ A3 @ B5 )
        = bot_bot_set_v )
      = ( ! [X3: v] :
            ( ( member_v @ X3 @ A3 )
           => ! [Y4: v] :
                ( ( member_v @ Y4 @ B5 )
               => ( X3 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_413_disjoint__iff__not__equal,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ A3 )
           => ! [Y4: product_prod_v_v] :
                ( ( member7453568604450474000od_v_v @ Y4 @ B5 )
               => ( X3 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_414_Int__mono,axiom,
    ! [A3: set_v,C2: set_v,B5: set_v,D2: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ C2 )
     => ( ( ord_less_eq_set_v @ B5 @ D2 )
       => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ ( inf_inf_set_v @ C2 @ D2 ) ) ) ) ).

% Int_mono
thf(fact_415_Int__mono,axiom,
    ! [A3: set_Product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v,D2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ C2 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ D2 )
       => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ ( inf_in6271465464967711157od_v_v @ C2 @ D2 ) ) ) ) ).

% Int_mono
thf(fact_416_Int__lower1,axiom,
    ! [A3: set_v,B5: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ A3 ) ).

% Int_lower1
thf(fact_417_Int__lower1,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ A3 ) ).

% Int_lower1
thf(fact_418_Int__lower2,axiom,
    ! [A3: set_v,B5: set_v] : ( ord_less_eq_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ B5 ) ).

% Int_lower2
thf(fact_419_Int__lower2,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ B5 ) ).

% Int_lower2
thf(fact_420_Int__absorb1,axiom,
    ! [B5: set_v,A3: set_v] :
      ( ( ord_less_eq_set_v @ B5 @ A3 )
     => ( ( inf_inf_set_v @ A3 @ B5 )
        = B5 ) ) ).

% Int_absorb1
thf(fact_421_Int__absorb1,axiom,
    ! [B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B5 @ A3 )
     => ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = B5 ) ) ).

% Int_absorb1
thf(fact_422_Int__absorb2,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( inf_inf_set_v @ A3 @ B5 )
        = A3 ) ) ).

% Int_absorb2
thf(fact_423_Int__absorb2,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = A3 ) ) ).

% Int_absorb2
thf(fact_424_Int__greatest,axiom,
    ! [C2: set_v,A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ C2 @ A3 )
     => ( ( ord_less_eq_set_v @ C2 @ B5 )
       => ( ord_less_eq_set_v @ C2 @ ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% Int_greatest
thf(fact_425_Int__greatest,axiom,
    ! [C2: set_Product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C2 @ A3 )
     => ( ( ord_le7336532860387713383od_v_v @ C2 @ B5 )
       => ( ord_le7336532860387713383od_v_v @ C2 @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% Int_greatest
thf(fact_426_Int__Collect__mono,axiom,
    ! [A3: set_set_v,B5: set_set_v,P: set_v > $o,Q: set_v > $o] :
      ( ( ord_le5216385588623774835_set_v @ A3 @ B5 )
     => ( ! [X4: set_v] :
            ( ( member_set_v @ X4 @ A3 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le5216385588623774835_set_v @ ( inf_inf_set_set_v @ A3 @ ( collect_set_v @ P ) ) @ ( inf_inf_set_set_v @ B5 @ ( collect_set_v @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_427_Int__Collect__mono,axiom,
    ! [A3: set_v,B5: set_v,P: v > $o,Q: v > $o] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ! [X4: v] :
            ( ( member_v @ X4 @ A3 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_less_eq_set_v @ ( inf_inf_set_v @ A3 @ ( collect_v @ P ) ) @ ( inf_inf_set_v @ B5 @ ( collect_v @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_428_Int__Collect__mono,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,P: product_prod_v_v > $o,Q: product_prod_v_v > $o] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ! [X4: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X4 @ A3 )
           => ( ( P @ X4 )
             => ( Q @ X4 ) ) )
       => ( ord_le7336532860387713383od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ ( collec140062887454715474od_v_v @ P ) ) @ ( inf_in6271465464967711157od_v_v @ B5 @ ( collec140062887454715474od_v_v @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_429_Int__insert__left,axiom,
    ! [A: product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( member7453568604450474000od_v_v @ A @ C2 )
       => ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ B5 ) @ C2 )
          = ( insert1338601472111419319od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) ) ) )
      & ( ~ ( member7453568604450474000od_v_v @ A @ C2 )
       => ( ( inf_in6271465464967711157od_v_v @ ( insert1338601472111419319od_v_v @ A @ B5 ) @ C2 )
          = ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_430_Int__insert__left,axiom,
    ! [A: v,C2: set_v,B5: set_v] :
      ( ( ( member_v @ A @ C2 )
       => ( ( inf_inf_set_v @ ( insert_v @ A @ B5 ) @ C2 )
          = ( insert_v @ A @ ( inf_inf_set_v @ B5 @ C2 ) ) ) )
      & ( ~ ( member_v @ A @ C2 )
       => ( ( inf_inf_set_v @ ( insert_v @ A @ B5 ) @ C2 )
          = ( inf_inf_set_v @ B5 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_431_Int__insert__right,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( member7453568604450474000od_v_v @ A @ A3 )
       => ( ( inf_in6271465464967711157od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
          = ( insert1338601472111419319od_v_v @ A @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) )
      & ( ~ ( member7453568604450474000od_v_v @ A @ A3 )
       => ( ( inf_in6271465464967711157od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
          = ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) ) ) ) ).

% Int_insert_right
thf(fact_432_Int__insert__right,axiom,
    ! [A: v,A3: set_v,B5: set_v] :
      ( ( ( member_v @ A @ A3 )
       => ( ( inf_inf_set_v @ A3 @ ( insert_v @ A @ B5 ) )
          = ( insert_v @ A @ ( inf_inf_set_v @ A3 @ B5 ) ) ) )
      & ( ~ ( member_v @ A @ A3 )
       => ( ( inf_inf_set_v @ A3 @ ( insert_v @ A @ B5 ) )
          = ( inf_inf_set_v @ A3 @ B5 ) ) ) ) ).

% Int_insert_right
thf(fact_433_subset__singletonD,axiom,
    ! [A3: set_v,X2: v] :
      ( ( ord_less_eq_set_v @ A3 @ ( insert_v @ X2 @ bot_bot_set_v ) )
     => ( ( A3 = bot_bot_set_v )
        | ( A3
          = ( insert_v @ X2 @ bot_bot_set_v ) ) ) ) ).

% subset_singletonD
thf(fact_434_subset__singletonD,axiom,
    ! [A3: set_Product_prod_v_v,X2: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
     => ( ( A3 = bot_bo723834152578015283od_v_v )
        | ( A3
          = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) ) ) ).

% subset_singletonD
thf(fact_435_subset__singleton__iff,axiom,
    ! [X5: set_v,A: v] :
      ( ( ord_less_eq_set_v @ X5 @ ( insert_v @ A @ bot_bot_set_v ) )
      = ( ( X5 = bot_bot_set_v )
        | ( X5
          = ( insert_v @ A @ bot_bot_set_v ) ) ) ) ).

% subset_singleton_iff
thf(fact_436_subset__singleton__iff,axiom,
    ! [X5: set_Product_prod_v_v,A: product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X5 @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) )
      = ( ( X5 = bot_bo723834152578015283od_v_v )
        | ( X5
          = ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) ) ) ).

% subset_singleton_iff
thf(fact_437_post__dfs__def,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl8953792750115413617t_unit @ successors @ V2 @ E @ E2 )
      = ( ( sCC_Bl9196236973127232072t_unit @ successors @ E2 )
        & ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E2 ) )
        & ( sCC_Bl5768913643336123637t_unit @ E @ E2 )
        & ( ( sCC_Bl3795065053823578884t_unit @ E2 @ V2 )
          = ( successors @ V2 ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
           => ( ( sCC_Bl3795065053823578884t_unit @ E2 @ X3 )
              = ( sCC_Bl3795065053823578884t_unit @ E @ X3 ) ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) )
           => ( sCC_Bl649662514949026229able_v @ successors @ X3 @ V2 ) )
        & ? [Ns: list_v] :
            ( ( sCC_Bl8828226123343373779t_unit @ E )
            = ( append_v @ Ns @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) )
        & ( ( ( member_v @ V2 @ ( sCC_Bl157864678168468314t_unit @ E2 ) )
            & ( ( sCC_Bl8828226123343373779t_unit @ E2 )
              = ( sCC_Bl8828226123343373779t_unit @ E ) )
            & ! [X3: v] :
                ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) )
               => ( ( sCC_Bl1280885523602775798t_unit @ E2 @ X3 )
                  = ( sCC_Bl1280885523602775798t_unit @ E @ X3 ) ) ) )
          | ( ( ( sCC_Bl8828226123343373779t_unit @ E2 )
             != nil_v )
            & ( member_v @ V2 @ ( sCC_Bl1280885523602775798t_unit @ E2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
            & ! [X3: v] :
                ( ( member_v @ X3 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
               => ( ( sCC_Bl1280885523602775798t_unit @ E2 @ X3 )
                  = ( sCC_Bl1280885523602775798t_unit @ E @ X3 ) ) ) ) )
        & ( ( sCC_Bl9201514103433284750t_unit @ E2 )
          = ( sCC_Bl9201514103433284750t_unit @ E ) ) ) ) ).

% post_dfs_def
thf(fact_438_stack__class,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,N2: v,M2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
       => ( ( member_v @ M2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) )
         => ( member_v @ M2 @ ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ E ) @ ( sCC_Bl157864678168468314t_unit @ E ) ) ) ) ) ) ).

% stack_class
thf(fact_439_calculation_I9_J,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ e2 ) @ ( set_v2 @ ( sCC_Bl9201514103433284750t_unit @ e2 ) ) ) )
     => ( ( sCC_Bl3795065053823578884t_unit @ e2 @ X )
        = ( successors @ X ) ) ) ).

% calculation(9)
thf(fact_440_calculation_I14_J,axiom,
    ! [N: v,M: v] :
      ( ( sCC_Bl4022239298816431255edes_v @ N @ M @ ( sCC_Bl8828226123343373779t_unit @ e2 ) )
     => ( sCC_Bl649662514949026229able_v @ successors @ M @ N ) ) ).

% calculation(14)
thf(fact_441_graph_Ounite__subscc,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,V2: product_prod_v_v,E: sCC_Bl7326425374436813197t_unit,W: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl3607325323686918683t_unit @ Successors @ V2 @ E )
       => ( ( member7453568604450474000od_v_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl3878977043676959280t_unit @ E @ V2 ) )
           => ( ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5498988629518860705t_unit @ E ) )
             => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5094201334446601350t_unit @ E ) )
               => ( sCC_Bl2301996248249672505od_v_v @ Successors @ ( sCC_Bl8440648026628373538t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) @ ( hd_Product_prod_v_v @ ( sCC_Bl2021302119412358655t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) ) ) ) ) ) ) ) ) ) ) ).

% graph.unite_subscc
thf(fact_442_graph_Ounite__subscc,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit,W: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl1748261141445803503t_unit @ Successors @ V2 @ E )
       => ( ( member_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
           => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
             => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
               => ( sCC_Bl5398416737448265317bscc_v @ Successors @ ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) ) ) ) ) ) ).

% graph.unite_subscc
thf(fact_443_graph_Ounite__S__tl,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,E: sCC_Bl7326425374436813197t_unit,W: product_prod_v_v,V2: product_prod_v_v,N2: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl7798947040364291444t_unit @ Successors @ E )
       => ( ( member7453568604450474000od_v_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl3878977043676959280t_unit @ E @ V2 ) )
           => ( ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5498988629518860705t_unit @ E ) )
             => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5094201334446601350t_unit @ E ) )
               => ( ( member7453568604450474000od_v_v @ N2 @ ( set_Product_prod_v_v2 @ ( tl_Product_prod_v_v @ ( sCC_Bl2021302119412358655t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) ) ) ) )
                 => ( ( sCC_Bl8440648026628373538t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) @ N2 )
                    = ( sCC_Bl8440648026628373538t_unit @ E @ N2 ) ) ) ) ) ) ) ) ) ).

% graph.unite_S_tl
thf(fact_444_graph_Ounite__S__tl,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,W: v,V2: v,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
           => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
             => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
               => ( ( member_v @ N2 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) )
                 => ( ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ N2 )
                    = ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) ) ) ) ) ) ) ) ) ).

% graph.unite_S_tl
thf(fact_445_pre__dfs__def,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl36166008131615352t_unit @ successors @ V2 @ E )
      = ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
        & ~ ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
        & ( sCC_Bl649662514949026229able_v @ successors @ ( sCC_Bl1090238580953940555t_unit @ E ) @ V2 )
        & ( ( sCC_Bl3795065053823578884t_unit @ E @ V2 )
          = bot_bot_set_v )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
           => ( sCC_Bl649662514949026229able_v @ successors @ X3 @ V2 ) ) ) ) ).

% pre_dfs_def
thf(fact_446_calculation_I5_J,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( sCC_Bl157864678168468314t_unit @ e2 ) )
     => ! [M: v] :
          ( ( sCC_Bl649662514949026229able_v @ successors @ X @ M )
         => ( member_v @ M @ ( sCC_Bl157864678168468314t_unit @ e2 ) ) ) ) ).

% calculation(5)
thf(fact_447_succ__reachable,axiom,
    ! [X2: v,Y: v,Z: v] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
     => ( ( member_v @ Z @ ( successors @ Y ) )
       => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Z ) ) ) ).

% succ_reachable
thf(fact_448_reachable__trans,axiom,
    ! [X2: v,Y: v,Z: v] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
     => ( ( sCC_Bl649662514949026229able_v @ successors @ Y @ Z )
       => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Z ) ) ) ).

% reachable_trans
thf(fact_449_reachable__end__induct,axiom,
    ! [X2: v,Y: v,P: v > v > $o] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
     => ( ! [X4: v] : ( P @ X4 @ X4 )
       => ( ! [X4: v,Y3: v,Z2: v] :
              ( ( P @ X4 @ Y3 )
             => ( ( member_v @ Z2 @ ( successors @ Y3 ) )
               => ( P @ X4 @ Z2 ) ) )
         => ( P @ X2 @ Y ) ) ) ) ).

% reachable_end_induct
thf(fact_450_reachable__edge,axiom,
    ! [Y: v,X2: v] :
      ( ( member_v @ Y @ ( successors @ X2 ) )
     => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y ) ) ).

% reachable_edge
thf(fact_451_reachable_Osimps,axiom,
    ! [A1: v,A22: v] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ A1 @ A22 )
      = ( ? [X3: v] :
            ( ( A1 = X3 )
            & ( A22 = X3 ) )
        | ? [X3: v,Y4: v,Z4: v] :
            ( ( A1 = X3 )
            & ( A22 = Z4 )
            & ( member_v @ Y4 @ ( successors @ X3 ) )
            & ( sCC_Bl649662514949026229able_v @ successors @ Y4 @ Z4 ) ) ) ) ).

% reachable.simps
thf(fact_452_reachable__succ,axiom,
    ! [Y: v,X2: v,Z: v] :
      ( ( member_v @ Y @ ( successors @ X2 ) )
     => ( ( sCC_Bl649662514949026229able_v @ successors @ Y @ Z )
       => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Z ) ) ) ).

% reachable_succ
thf(fact_453_reachable__refl,axiom,
    ! [X2: v] : ( sCC_Bl649662514949026229able_v @ successors @ X2 @ X2 ) ).

% reachable_refl
thf(fact_454_reachable_Ocases,axiom,
    ! [A1: v,A22: v] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ A1 @ A22 )
     => ( ( A22 != A1 )
       => ~ ! [Y3: v] :
              ( ( member_v @ Y3 @ ( successors @ A1 ) )
             => ~ ( sCC_Bl649662514949026229able_v @ successors @ Y3 @ A22 ) ) ) ) ).

% reachable.cases
thf(fact_455_is__subscc__def,axiom,
    ! [S: set_v] :
      ( ( sCC_Bl5398416737448265317bscc_v @ successors @ S )
      = ( ! [X3: v] :
            ( ( member_v @ X3 @ S )
           => ! [Y4: v] :
                ( ( member_v @ Y4 @ S )
               => ( sCC_Bl649662514949026229able_v @ successors @ X3 @ Y4 ) ) ) ) ) ).

% is_subscc_def
thf(fact_456_sccE,axiom,
    ! [S: set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_is_scc_v @ successors @ S )
     => ( ( member_v @ X2 @ S )
       => ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
         => ( ( sCC_Bl649662514949026229able_v @ successors @ Y @ X2 )
           => ( member_v @ Y @ S ) ) ) ) ) ).

% sccE
thf(fact_457_DiffI,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ A3 )
     => ( ~ ( member7453568604450474000od_v_v @ C @ B5 )
       => ( member7453568604450474000od_v_v @ C @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) ) ) ) ).

% DiffI
thf(fact_458_DiffI,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ A3 )
     => ( ~ ( member_v @ C @ B5 )
       => ( member_v @ C @ ( minus_minus_set_v @ A3 @ B5 ) ) ) ) ).

% DiffI
thf(fact_459_Diff__iff,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
      = ( ( member7453568604450474000od_v_v @ C @ A3 )
        & ~ ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_460_Diff__iff,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( minus_minus_set_v @ A3 @ B5 ) )
      = ( ( member_v @ C @ A3 )
        & ~ ( member_v @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_461_Diff__idemp,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( minus_minus_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ B5 )
      = ( minus_minus_set_v @ A3 @ B5 ) ) ).

% Diff_idemp
thf(fact_462_subscc__add,axiom,
    ! [S: set_v,X2: v,Y: v] :
      ( ( sCC_Bl5398416737448265317bscc_v @ successors @ S )
     => ( ( member_v @ X2 @ S )
       => ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
         => ( ( sCC_Bl649662514949026229able_v @ successors @ Y @ X2 )
           => ( sCC_Bl5398416737448265317bscc_v @ successors @ ( insert_v @ Y @ S ) ) ) ) ) ) ).

% subscc_add
thf(fact_463_calculation_I1_J,axiom,
    ! [X: v] :
      ( ( member_v @ X @ ( sCC_Bl4645233313691564917t_unit @ e2 ) )
     => ( sCC_Bl649662514949026229able_v @ successors @ ( sCC_Bl1090238580953940555t_unit @ e2 ) @ X ) ) ).

% calculation(1)
thf(fact_464_reachable__visited,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,V2: v,W: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
       => ( ( sCC_Bl649662514949026229able_v @ successors @ V2 @ W )
         => ( ! [X4: v] :
                ( ( member_v @ X4 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
               => ! [Xa2: v] :
                    ( ( member_v @ Xa2 @ ( minus_minus_set_v @ ( successors @ X4 ) @ ( sCC_Bl3795065053823578884t_unit @ E @ X4 ) ) )
                   => ( ( sCC_Bl649662514949026229able_v @ successors @ V2 @ X4 )
                     => ~ ( sCC_Bl649662514949026229able_v @ successors @ Xa2 @ W ) ) ) )
           => ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) ) ) ) ) ) ).

% reachable_visited
thf(fact_465_Diff__cancel,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ A3 )
      = bot_bo723834152578015283od_v_v ) ).

% Diff_cancel
thf(fact_466_Diff__cancel,axiom,
    ! [A3: set_v] :
      ( ( minus_minus_set_v @ A3 @ A3 )
      = bot_bot_set_v ) ).

% Diff_cancel
thf(fact_467_empty__Diff,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ bot_bo723834152578015283od_v_v @ A3 )
      = bot_bo723834152578015283od_v_v ) ).

% empty_Diff
thf(fact_468_empty__Diff,axiom,
    ! [A3: set_v] :
      ( ( minus_minus_set_v @ bot_bot_set_v @ A3 )
      = bot_bot_set_v ) ).

% empty_Diff
thf(fact_469_Diff__empty,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ bot_bo723834152578015283od_v_v )
      = A3 ) ).

% Diff_empty
thf(fact_470_Diff__empty,axiom,
    ! [A3: set_v] :
      ( ( minus_minus_set_v @ A3 @ bot_bot_set_v )
      = A3 ) ).

% Diff_empty
thf(fact_471_insert__Diff1,axiom,
    ! [X2: product_prod_v_v,B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ B5 )
     => ( ( minus_4183494784930505774od_v_v @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) @ B5 )
        = ( minus_4183494784930505774od_v_v @ A3 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_472_insert__Diff1,axiom,
    ! [X2: v,B5: set_v,A3: set_v] :
      ( ( member_v @ X2 @ B5 )
     => ( ( minus_minus_set_v @ ( insert_v @ X2 @ A3 ) @ B5 )
        = ( minus_minus_set_v @ A3 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_473_Diff__insert0,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ A3 )
     => ( ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ B5 ) )
        = ( minus_4183494784930505774od_v_v @ A3 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_474_Diff__insert0,axiom,
    ! [X2: v,A3: set_v,B5: set_v] :
      ( ~ ( member_v @ X2 @ A3 )
     => ( ( minus_minus_set_v @ A3 @ ( insert_v @ X2 @ B5 ) )
        = ( minus_minus_set_v @ A3 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_475_Diff__eq__empty__iff,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ( minus_minus_set_v @ A3 @ B5 )
        = bot_bot_set_v )
      = ( ord_less_eq_set_v @ A3 @ B5 ) ) ).

% Diff_eq_empty_iff
thf(fact_476_Diff__eq__empty__iff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( minus_4183494784930505774od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v )
      = ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ).

% Diff_eq_empty_iff
thf(fact_477_insert__Diff__single,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( insert1338601472111419319od_v_v @ A @ ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) )
      = ( insert1338601472111419319od_v_v @ A @ A3 ) ) ).

% insert_Diff_single
thf(fact_478_insert__Diff__single,axiom,
    ! [A: v,A3: set_v] :
      ( ( insert_v @ A @ ( minus_minus_set_v @ A3 @ ( insert_v @ A @ bot_bot_set_v ) ) )
      = ( insert_v @ A @ A3 ) ) ).

% insert_Diff_single
thf(fact_479_Diff__disjoint,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ A3 @ ( minus_4183494784930505774od_v_v @ B5 @ A3 ) )
      = bot_bo723834152578015283od_v_v ) ).

% Diff_disjoint
thf(fact_480_Diff__disjoint,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( inf_inf_set_v @ A3 @ ( minus_minus_set_v @ B5 @ A3 ) )
      = bot_bot_set_v ) ).

% Diff_disjoint
thf(fact_481_DiffE,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
     => ~ ( ( member7453568604450474000od_v_v @ C @ A3 )
         => ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% DiffE
thf(fact_482_DiffE,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( minus_minus_set_v @ A3 @ B5 ) )
     => ~ ( ( member_v @ C @ A3 )
         => ( member_v @ C @ B5 ) ) ) ).

% DiffE
thf(fact_483_DiffD1,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
     => ( member7453568604450474000od_v_v @ C @ A3 ) ) ).

% DiffD1
thf(fact_484_DiffD1,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( minus_minus_set_v @ A3 @ B5 ) )
     => ( member_v @ C @ A3 ) ) ).

% DiffD1
thf(fact_485_DiffD2,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
     => ~ ( member7453568604450474000od_v_v @ C @ B5 ) ) ).

% DiffD2
thf(fact_486_DiffD2,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( minus_minus_set_v @ A3 @ B5 ) )
     => ~ ( member_v @ C @ B5 ) ) ).

% DiffD2
thf(fact_487_graph_Oreachable__succ,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,Y: product_prod_v_v,X2: product_prod_v_v,Z: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( member7453568604450474000od_v_v @ Y @ ( Successors @ X2 ) )
       => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ Y @ Z )
         => ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.reachable_succ
thf(fact_488_graph_Oreachable__succ,axiom,
    ! [Vertices: set_v,Successors: v > set_v,Y: v,X2: v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( member_v @ Y @ ( Successors @ X2 ) )
       => ( ( sCC_Bl649662514949026229able_v @ Successors @ Y @ Z )
         => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.reachable_succ
thf(fact_489_graph_Oreachable__refl,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ X2 ) ) ).

% graph.reachable_refl
thf(fact_490_graph_Oreachable__end__induct,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v,P: product_prod_v_v > product_prod_v_v > $o] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Y )
       => ( ! [X4: product_prod_v_v] : ( P @ X4 @ X4 )
         => ( ! [X4: product_prod_v_v,Y3: product_prod_v_v,Z2: product_prod_v_v] :
                ( ( P @ X4 @ Y3 )
               => ( ( member7453568604450474000od_v_v @ Z2 @ ( Successors @ Y3 ) )
                 => ( P @ X4 @ Z2 ) ) )
           => ( P @ X2 @ Y ) ) ) ) ) ).

% graph.reachable_end_induct
thf(fact_491_graph_Oreachable__end__induct,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,P: v > v > $o] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
       => ( ! [X4: v] : ( P @ X4 @ X4 )
         => ( ! [X4: v,Y3: v,Z2: v] :
                ( ( P @ X4 @ Y3 )
               => ( ( member_v @ Z2 @ ( Successors @ Y3 ) )
                 => ( P @ X4 @ Z2 ) ) )
           => ( P @ X2 @ Y ) ) ) ) ) ).

% graph.reachable_end_induct
thf(fact_492_graph_Oreachable__trans,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
       => ( ( sCC_Bl649662514949026229able_v @ Successors @ Y @ Z )
         => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.reachable_trans
thf(fact_493_graph_Oreachable_Osimps,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ A1 @ A22 )
        = ( ? [X3: product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = X3 ) )
          | ? [X3: product_prod_v_v,Y4: product_prod_v_v,Z4: product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( member7453568604450474000od_v_v @ Y4 @ ( Successors @ X3 ) )
              & ( sCC_Bl4981926079593201289od_v_v @ Successors @ Y4 @ Z4 ) ) ) ) ) ).

% graph.reachable.simps
thf(fact_494_graph_Oreachable_Osimps,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ A1 @ A22 )
        = ( ? [X3: v] :
              ( ( A1 = X3 )
              & ( A22 = X3 ) )
          | ? [X3: v,Y4: v,Z4: v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( member_v @ Y4 @ ( Successors @ X3 ) )
              & ( sCC_Bl649662514949026229able_v @ Successors @ Y4 @ Z4 ) ) ) ) ) ).

% graph.reachable.simps
thf(fact_495_graph_Oreachable_Ocases,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ A1 @ A22 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: product_prod_v_v] :
                ( ( member7453568604450474000od_v_v @ Y3 @ ( Successors @ A1 ) )
               => ~ ( sCC_Bl4981926079593201289od_v_v @ Successors @ Y3 @ A22 ) ) ) ) ) ).

% graph.reachable.cases
thf(fact_496_graph_Oreachable_Ocases,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ A1 @ A22 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: v] :
                ( ( member_v @ Y3 @ ( Successors @ A1 ) )
               => ~ ( sCC_Bl649662514949026229able_v @ Successors @ Y3 @ A22 ) ) ) ) ) ).

% graph.reachable.cases
thf(fact_497_graph_Osucc__reachable,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v,Z: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Y )
       => ( ( member7453568604450474000od_v_v @ Z @ ( Successors @ Y ) )
         => ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.succ_reachable
thf(fact_498_graph_Osucc__reachable,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
       => ( ( member_v @ Z @ ( Successors @ Y ) )
         => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.succ_reachable
thf(fact_499_graph_Oreachable__edge,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,Y: product_prod_v_v,X2: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( member7453568604450474000od_v_v @ Y @ ( Successors @ X2 ) )
       => ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Y ) ) ) ).

% graph.reachable_edge
thf(fact_500_graph_Oreachable__edge,axiom,
    ! [Vertices: set_v,Successors: v > set_v,Y: v,X2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( member_v @ Y @ ( Successors @ X2 ) )
       => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y ) ) ) ).

% graph.reachable_edge
thf(fact_501_graph_Oreachable_Ocong,axiom,
    sCC_Bl649662514949026229able_v = sCC_Bl649662514949026229able_v ).

% graph.reachable.cong
thf(fact_502_graph_Ois__subscc__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,S: set_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl5398416737448265317bscc_v @ Successors @ S )
        = ( ! [X3: v] :
              ( ( member_v @ X3 @ S )
             => ! [Y4: v] :
                  ( ( member_v @ Y4 @ S )
                 => ( sCC_Bl649662514949026229able_v @ Successors @ X3 @ Y4 ) ) ) ) ) ) ).

% graph.is_subscc_def
thf(fact_503_graph_OsccE,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,S: set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl6242042402218619277od_v_v @ Successors @ S )
       => ( ( member7453568604450474000od_v_v @ X2 @ S )
         => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Y )
           => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ Y @ X2 )
             => ( member7453568604450474000od_v_v @ Y @ S ) ) ) ) ) ) ).

% graph.sccE
thf(fact_504_graph_OsccE,axiom,
    ! [Vertices: set_v,Successors: v > set_v,S: set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bloemen_is_scc_v @ Successors @ S )
       => ( ( member_v @ X2 @ S )
         => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
           => ( ( sCC_Bl649662514949026229able_v @ Successors @ Y @ X2 )
             => ( member_v @ Y @ S ) ) ) ) ) ) ).

% graph.sccE
thf(fact_505_graph_Osclosed,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ! [X: product_prod_v_v] :
          ( ( member7453568604450474000od_v_v @ X @ Vertices )
         => ( ord_le7336532860387713383od_v_v @ ( Successors @ X ) @ Vertices ) ) ) ).

% graph.sclosed
thf(fact_506_graph_Osclosed,axiom,
    ! [Vertices: set_v,Successors: v > set_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ! [X: v] :
          ( ( member_v @ X @ Vertices )
         => ( ord_less_eq_set_v @ ( Successors @ X ) @ Vertices ) ) ) ).

% graph.sclosed
thf(fact_507_graph_Oreachable__visited,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,V2: v,W: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
         => ( ( sCC_Bl649662514949026229able_v @ Successors @ V2 @ W )
           => ( ! [X4: v] :
                  ( ( member_v @ X4 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
                 => ! [Xa2: v] :
                      ( ( member_v @ Xa2 @ ( minus_minus_set_v @ ( Successors @ X4 ) @ ( sCC_Bl3795065053823578884t_unit @ E @ X4 ) ) )
                     => ( ( sCC_Bl649662514949026229able_v @ Successors @ V2 @ X4 )
                       => ~ ( sCC_Bl649662514949026229able_v @ Successors @ Xa2 @ W ) ) ) )
             => ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) ) ) ) ) ) ) ).

% graph.reachable_visited
thf(fact_508_double__diff,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( ord_less_eq_set_v @ B5 @ C2 )
       => ( ( minus_minus_set_v @ B5 @ ( minus_minus_set_v @ C2 @ A3 ) )
          = A3 ) ) ) ).

% double_diff
thf(fact_509_double__diff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ C2 )
       => ( ( minus_4183494784930505774od_v_v @ B5 @ ( minus_4183494784930505774od_v_v @ C2 @ A3 ) )
          = A3 ) ) ) ).

% double_diff
thf(fact_510_Diff__subset,axiom,
    ! [A3: set_v,B5: set_v] : ( ord_less_eq_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ A3 ) ).

% Diff_subset
thf(fact_511_Diff__subset,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ A3 ) ).

% Diff_subset
thf(fact_512_Diff__mono,axiom,
    ! [A3: set_v,C2: set_v,D2: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ C2 )
     => ( ( ord_less_eq_set_v @ D2 @ B5 )
       => ( ord_less_eq_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ ( minus_minus_set_v @ C2 @ D2 ) ) ) ) ).

% Diff_mono
thf(fact_513_Diff__mono,axiom,
    ! [A3: set_Product_prod_v_v,C2: set_Product_prod_v_v,D2: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ C2 )
     => ( ( ord_le7336532860387713383od_v_v @ D2 @ B5 )
       => ( ord_le7336532860387713383od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ ( minus_4183494784930505774od_v_v @ C2 @ D2 ) ) ) ) ).

% Diff_mono
thf(fact_514_insert__Diff__if,axiom,
    ! [X2: product_prod_v_v,B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ( member7453568604450474000od_v_v @ X2 @ B5 )
       => ( ( minus_4183494784930505774od_v_v @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) @ B5 )
          = ( minus_4183494784930505774od_v_v @ A3 @ B5 ) ) )
      & ( ~ ( member7453568604450474000od_v_v @ X2 @ B5 )
       => ( ( minus_4183494784930505774od_v_v @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) @ B5 )
          = ( insert1338601472111419319od_v_v @ X2 @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_515_insert__Diff__if,axiom,
    ! [X2: v,B5: set_v,A3: set_v] :
      ( ( ( member_v @ X2 @ B5 )
       => ( ( minus_minus_set_v @ ( insert_v @ X2 @ A3 ) @ B5 )
          = ( minus_minus_set_v @ A3 @ B5 ) ) )
      & ( ~ ( member_v @ X2 @ B5 )
       => ( ( minus_minus_set_v @ ( insert_v @ X2 @ A3 ) @ B5 )
          = ( insert_v @ X2 @ ( minus_minus_set_v @ A3 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_516_graph_Osubscc__add,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,S: set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl2301996248249672505od_v_v @ Successors @ S )
       => ( ( member7453568604450474000od_v_v @ X2 @ S )
         => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ X2 @ Y )
           => ( ( sCC_Bl4981926079593201289od_v_v @ Successors @ Y @ X2 )
             => ( sCC_Bl2301996248249672505od_v_v @ Successors @ ( insert1338601472111419319od_v_v @ Y @ S ) ) ) ) ) ) ) ).

% graph.subscc_add
thf(fact_517_graph_Osubscc__add,axiom,
    ! [Vertices: set_v,Successors: v > set_v,S: set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl5398416737448265317bscc_v @ Successors @ S )
       => ( ( member_v @ X2 @ S )
         => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
           => ( ( sCC_Bl649662514949026229able_v @ Successors @ Y @ X2 )
             => ( sCC_Bl5398416737448265317bscc_v @ Successors @ ( insert_v @ Y @ S ) ) ) ) ) ) ) ).

% graph.subscc_add
thf(fact_518_Diff__Int__distrib2,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( inf_inf_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ C2 )
      = ( minus_minus_set_v @ ( inf_inf_set_v @ A3 @ C2 ) @ ( inf_inf_set_v @ B5 @ C2 ) ) ) ).

% Diff_Int_distrib2
thf(fact_519_Diff__Int__distrib,axiom,
    ! [C2: set_v,A3: set_v,B5: set_v] :
      ( ( inf_inf_set_v @ C2 @ ( minus_minus_set_v @ A3 @ B5 ) )
      = ( minus_minus_set_v @ ( inf_inf_set_v @ C2 @ A3 ) @ ( inf_inf_set_v @ C2 @ B5 ) ) ) ).

% Diff_Int_distrib
thf(fact_520_Diff__Diff__Int,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( minus_minus_set_v @ A3 @ ( minus_minus_set_v @ A3 @ B5 ) )
      = ( inf_inf_set_v @ A3 @ B5 ) ) ).

% Diff_Diff_Int
thf(fact_521_Diff__Int2,axiom,
    ! [A3: set_v,C2: set_v,B5: set_v] :
      ( ( minus_minus_set_v @ ( inf_inf_set_v @ A3 @ C2 ) @ ( inf_inf_set_v @ B5 @ C2 ) )
      = ( minus_minus_set_v @ ( inf_inf_set_v @ A3 @ C2 ) @ B5 ) ) ).

% Diff_Int2
thf(fact_522_Int__Diff,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( minus_minus_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ C2 )
      = ( inf_inf_set_v @ A3 @ ( minus_minus_set_v @ B5 @ C2 ) ) ) ).

% Int_Diff
thf(fact_523_graph_Osub__env__trans,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit,E3: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl5768913643336123637t_unit @ E @ E2 )
       => ( ( sCC_Bl5768913643336123637t_unit @ E2 @ E3 )
         => ( sCC_Bl5768913643336123637t_unit @ E @ E3 ) ) ) ) ).

% graph.sub_env_trans
thf(fact_524_graph_Odfss_Ocases,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: produc5741669702376414499t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ~ ! [V: v,E4: sCC_Bl1394983891496994913t_unit] :
            ( X2
           != ( produc3862955338007567901t_unit @ V @ E4 ) ) ) ).

% graph.dfss.cases
thf(fact_525_diff__shunt__var,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( ( minus_3524152463667985524t_unit @ X2 @ Y )
        = bot_bot_Product_unit )
      = ( ord_le3221252021190050221t_unit @ X2 @ Y ) ) ).

% diff_shunt_var
thf(fact_526_diff__shunt__var,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( ( minus_minus_set_v @ X2 @ Y )
        = bot_bot_set_v )
      = ( ord_less_eq_set_v @ X2 @ Y ) ) ).

% diff_shunt_var
thf(fact_527_diff__shunt__var,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( ( minus_4183494784930505774od_v_v @ X2 @ Y )
        = bot_bo723834152578015283od_v_v )
      = ( ord_le7336532860387713383od_v_v @ X2 @ Y ) ) ).

% diff_shunt_var
thf(fact_528_Diff__insert__absorb,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ A3 )
     => ( ( minus_4183494784930505774od_v_v @ ( insert1338601472111419319od_v_v @ X2 @ A3 ) @ ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
        = A3 ) ) ).

% Diff_insert_absorb
thf(fact_529_Diff__insert__absorb,axiom,
    ! [X2: v,A3: set_v] :
      ( ~ ( member_v @ X2 @ A3 )
     => ( ( minus_minus_set_v @ ( insert_v @ X2 @ A3 ) @ ( insert_v @ X2 @ bot_bot_set_v ) )
        = A3 ) ) ).

% Diff_insert_absorb
thf(fact_530_Diff__insert2,axiom,
    ! [A3: set_Product_prod_v_v,A: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
      = ( minus_4183494784930505774od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_531_Diff__insert2,axiom,
    ! [A3: set_v,A: v,B5: set_v] :
      ( ( minus_minus_set_v @ A3 @ ( insert_v @ A @ B5 ) )
      = ( minus_minus_set_v @ ( minus_minus_set_v @ A3 @ ( insert_v @ A @ bot_bot_set_v ) ) @ B5 ) ) ).

% Diff_insert2
thf(fact_532_insert__Diff,axiom,
    ! [A: product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ A @ A3 )
     => ( ( insert1338601472111419319od_v_v @ A @ ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) )
        = A3 ) ) ).

% insert_Diff
thf(fact_533_insert__Diff,axiom,
    ! [A: v,A3: set_v] :
      ( ( member_v @ A @ A3 )
     => ( ( insert_v @ A @ ( minus_minus_set_v @ A3 @ ( insert_v @ A @ bot_bot_set_v ) ) )
        = A3 ) ) ).

% insert_Diff
thf(fact_534_Diff__insert,axiom,
    ! [A3: set_Product_prod_v_v,A: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
      = ( minus_4183494784930505774od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) ) ).

% Diff_insert
thf(fact_535_Diff__insert,axiom,
    ! [A3: set_v,A: v,B5: set_v] :
      ( ( minus_minus_set_v @ A3 @ ( insert_v @ A @ B5 ) )
      = ( minus_minus_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ ( insert_v @ A @ bot_bot_set_v ) ) ) ).

% Diff_insert
thf(fact_536_subset__Diff__insert,axiom,
    ! [A3: set_v,B5: set_v,X2: v,C2: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ ( minus_minus_set_v @ B5 @ ( insert_v @ X2 @ C2 ) ) )
      = ( ( ord_less_eq_set_v @ A3 @ ( minus_minus_set_v @ B5 @ C2 ) )
        & ~ ( member_v @ X2 @ A3 ) ) ) ).

% subset_Diff_insert
thf(fact_537_subset__Diff__insert,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,X2: product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ ( minus_4183494784930505774od_v_v @ B5 @ ( insert1338601472111419319od_v_v @ X2 @ C2 ) ) )
      = ( ( ord_le7336532860387713383od_v_v @ A3 @ ( minus_4183494784930505774od_v_v @ B5 @ C2 ) )
        & ~ ( member7453568604450474000od_v_v @ X2 @ A3 ) ) ) ).

% subset_Diff_insert
thf(fact_538_Int__Diff__disjoint,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
      = bot_bo723834152578015283od_v_v ) ).

% Int_Diff_disjoint
thf(fact_539_Int__Diff__disjoint,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( inf_inf_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ ( minus_minus_set_v @ A3 @ B5 ) )
      = bot_bot_set_v ) ).

% Int_Diff_disjoint
thf(fact_540_Diff__triv,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v )
     => ( ( minus_4183494784930505774od_v_v @ A3 @ B5 )
        = A3 ) ) ).

% Diff_triv
thf(fact_541_Diff__triv,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ( inf_inf_set_v @ A3 @ B5 )
        = bot_bot_set_v )
     => ( ( minus_minus_set_v @ A3 @ B5 )
        = A3 ) ) ).

% Diff_triv
thf(fact_542_graph_OS__reflexive,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) ) ) ) ).

% graph.S_reflexive
thf(fact_543_graph_Oscc__partition,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,S: set_Product_prod_v_v,S2: set_Product_prod_v_v,X2: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl6242042402218619277od_v_v @ Successors @ S )
       => ( ( sCC_Bl6242042402218619277od_v_v @ Successors @ S2 )
         => ( ( member7453568604450474000od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ S @ S2 ) )
           => ( S = S2 ) ) ) ) ) ).

% graph.scc_partition
thf(fact_544_graph_Oscc__partition,axiom,
    ! [Vertices: set_v,Successors: v > set_v,S: set_v,S2: set_v,X2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bloemen_is_scc_v @ Successors @ S )
       => ( ( sCC_Bloemen_is_scc_v @ Successors @ S2 )
         => ( ( member_v @ X2 @ ( inf_inf_set_v @ S @ S2 ) )
           => ( S = S2 ) ) ) ) ) ).

% graph.scc_partition
thf(fact_545_graph_Opre__dfs__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl36166008131615352t_unit @ Successors @ V2 @ E )
        = ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
          & ~ ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
          & ( sCC_Bl649662514949026229able_v @ Successors @ ( sCC_Bl1090238580953940555t_unit @ E ) @ V2 )
          & ( ( sCC_Bl3795065053823578884t_unit @ E @ V2 )
            = bot_bot_set_v )
          & ! [X3: v] :
              ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
             => ( sCC_Bl649662514949026229able_v @ Successors @ X3 @ V2 ) ) ) ) ) ).

% graph.pre_dfs_def
thf(fact_546_Diff__single__insert,axiom,
    ! [A3: set_v,X2: v,B5: set_v] :
      ( ( ord_less_eq_set_v @ ( minus_minus_set_v @ A3 @ ( insert_v @ X2 @ bot_bot_set_v ) ) @ B5 )
     => ( ord_less_eq_set_v @ A3 @ ( insert_v @ X2 @ B5 ) ) ) ).

% Diff_single_insert
thf(fact_547_Diff__single__insert,axiom,
    ! [A3: set_Product_prod_v_v,X2: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) @ B5 )
     => ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ B5 ) ) ) ).

% Diff_single_insert
thf(fact_548_subset__insert__iff,axiom,
    ! [A3: set_v,X2: v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ ( insert_v @ X2 @ B5 ) )
      = ( ( ( member_v @ X2 @ A3 )
         => ( ord_less_eq_set_v @ ( minus_minus_set_v @ A3 @ ( insert_v @ X2 @ bot_bot_set_v ) ) @ B5 ) )
        & ( ~ ( member_v @ X2 @ A3 )
         => ( ord_less_eq_set_v @ A3 @ B5 ) ) ) ) ).

% subset_insert_iff
thf(fact_549_subset__insert__iff,axiom,
    ! [A3: set_Product_prod_v_v,X2: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ B5 ) )
      = ( ( ( member7453568604450474000od_v_v @ X2 @ A3 )
         => ( ord_le7336532860387713383od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) @ B5 ) )
        & ( ~ ( member7453568604450474000od_v_v @ X2 @ A3 )
         => ( ord_le7336532860387713383od_v_v @ A3 @ B5 ) ) ) ) ).

% subset_insert_iff
thf(fact_550_graph_Ostack__class,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,N2: v,M2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
         => ( ( member_v @ M2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N2 ) )
           => ( member_v @ M2 @ ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ E ) @ ( sCC_Bl157864678168468314t_unit @ E ) ) ) ) ) ) ) ).

% graph.stack_class
thf(fact_551_graph_Odfs__S__tl__stack_I1_J,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl8953792750115413617t_unit @ Successors @ V2 @ E @ E2 )
       => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
           != nil_v )
         => ( ( sCC_Bl8828226123343373779t_unit @ E2 )
           != nil_v ) ) ) ) ).

% graph.dfs_S_tl_stack(1)
thf(fact_552_graph_Oinit__env__pre__dfs,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( sCC_Bl36166008131615352t_unit @ Successors @ V2 @ ( sCC_Bl7693227186847904995_env_v @ V2 ) ) ) ).

% graph.init_env_pre_dfs
thf(fact_553_graph_Ostack__visited,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
         => ( member_v @ N2 @ ( sCC_Bl4645233313691564917t_unit @ E ) ) ) ) ) ).

% graph.stack_visited
thf(fact_554_graph_Ostack__unexplored,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ N2 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
         => ~ ( member_v @ N2 @ ( sCC_Bl157864678168468314t_unit @ E ) ) ) ) ) ).

% graph.stack_unexplored
thf(fact_555_graph_Ois__scc__def,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,S: set_Product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl6242042402218619277od_v_v @ Successors @ S )
        = ( ( S != bot_bo723834152578015283od_v_v )
          & ( sCC_Bl2301996248249672505od_v_v @ Successors @ S )
          & ! [S3: set_Product_prod_v_v] :
              ( ( ( ord_le7336532860387713383od_v_v @ S @ S3 )
                & ( sCC_Bl2301996248249672505od_v_v @ Successors @ S3 ) )
             => ( S3 = S ) ) ) ) ) ).

% graph.is_scc_def
thf(fact_556_graph_Ois__scc__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,S: set_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bloemen_is_scc_v @ Successors @ S )
        = ( ( S != bot_bot_set_v )
          & ( sCC_Bl5398416737448265317bscc_v @ Successors @ S )
          & ! [S3: set_v] :
              ( ( ( ord_less_eq_set_v @ S @ S3 )
                & ( sCC_Bl5398416737448265317bscc_v @ Successors @ S3 ) )
             => ( S3 = S ) ) ) ) ) ).

% graph.is_scc_def
thf(fact_557_graph_Odfs__S__tl__stack_I2_J,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl8953792750115413617t_unit @ Successors @ V2 @ E @ E2 )
       => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
           != nil_v )
         => ! [X: v] :
              ( ( member_v @ X @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
             => ( ( sCC_Bl1280885523602775798t_unit @ E2 @ X )
                = ( sCC_Bl1280885523602775798t_unit @ E @ X ) ) ) ) ) ) ).

% graph.dfs_S_tl_stack(2)
thf(fact_558_graph_Ovisited__unexplored,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,M2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ M2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
         => ( ~ ( member_v @ M2 @ ( sCC_Bl157864678168468314t_unit @ E ) )
           => ~ ! [N3: v] :
                  ( ( member_v @ N3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
                 => ~ ( member_v @ M2 @ ( sCC_Bl1280885523602775798t_unit @ E @ N3 ) ) ) ) ) ) ) ).

% graph.visited_unexplored
thf(fact_559_graph_Odfs__S__hd__stack_I1_J,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,V2: v,E2: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( sCC_Bl8953792750115413617t_unit @ Successors @ V2 @ E @ E2 )
         => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
             != nil_v )
           => ( ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
             => ( ( sCC_Bl8828226123343373779t_unit @ E2 )
               != nil_v ) ) ) ) ) ) ).

% graph.dfs_S_hd_stack(1)
thf(fact_560_graph_Odfs__S__hd__stack_I2_J,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,V2: v,E2: sCC_Bl1394983891496994913t_unit,N2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( sCC_Bl8953792750115413617t_unit @ Successors @ V2 @ E @ E2 )
         => ( ( ( sCC_Bl8828226123343373779t_unit @ E )
             != nil_v )
           => ( ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
             => ( member_v @ N2 @ ( sCC_Bl1280885523602775798t_unit @ E2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) ) ) ) ) ) ) ).

% graph.dfs_S_hd_stack(2)
thf(fact_561_graph_Ounite__sub__env,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,V2: product_prod_v_v,E: sCC_Bl7326425374436813197t_unit,W: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl3607325323686918683t_unit @ Successors @ V2 @ E )
       => ( ( member7453568604450474000od_v_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl3878977043676959280t_unit @ E @ V2 ) )
           => ( ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5498988629518860705t_unit @ E ) )
             => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5094201334446601350t_unit @ E ) )
               => ( sCC_Bl7963838319573962697t_unit @ E @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) ) ) ) ) ) ) ) ).

% graph.unite_sub_env
thf(fact_562_graph_Ounite__sub__env,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit,W: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl1748261141445803503t_unit @ Successors @ V2 @ E )
       => ( ( member_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
           => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
             => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
               => ( sCC_Bl5768913643336123637t_unit @ E @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) ) ) ).

% graph.unite_sub_env
thf(fact_563_post__dfss__def,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl6082031138996704384t_unit @ successors @ V2 @ E @ E2 )
      = ( ( sCC_Bl9196236973127232072t_unit @ successors @ E2 )
        & ( ( sCC_Bl3795065053823578884t_unit @ E2 @ V2 )
          = ( successors @ V2 ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ E ) @ ( insert_v @ V2 @ bot_bot_set_v ) ) )
           => ( ( sCC_Bl3795065053823578884t_unit @ E2 @ X3 )
              = ( sCC_Bl3795065053823578884t_unit @ E @ X3 ) ) )
        & ( sCC_Bl5768913643336123637t_unit @ E @ E2 )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( successors @ V2 ) )
           => ( member_v @ X3 @ ( sup_sup_set_v @ ( sCC_Bl157864678168468314t_unit @ E2 ) @ ( sCC_Bl1280885523602775798t_unit @ E2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) ) ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) )
           => ( sCC_Bl649662514949026229able_v @ successors @ X3 @ V2 ) )
        & ( ( sCC_Bl8828226123343373779t_unit @ E2 )
         != nil_v )
        & ? [Ns: list_v] :
            ( ( sCC_Bl8828226123343373779t_unit @ E )
            = ( append_v @ Ns @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) )
        & ( member_v @ V2 @ ( sCC_Bl1280885523602775798t_unit @ E2 @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
           => ( ( sCC_Bl1280885523602775798t_unit @ E2 @ X3 )
              = ( sCC_Bl1280885523602775798t_unit @ E @ X3 ) ) )
        & ( ( ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) )
            = V2 )
         => ! [X3: v] :
              ( ( member_v @ X3 @ ( set_v2 @ ( tl_v @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) )
             => ~ ( sCC_Bl649662514949026229able_v @ successors @ V2 @ X3 ) ) )
        & ( ( sCC_Bl9201514103433284750t_unit @ E2 )
          = ( sCC_Bl9201514103433284750t_unit @ E ) ) ) ) ).

% post_dfss_def
thf(fact_564_equality,axiom,
    ! [R: sCC_Bl1394983891496994913t_unit,R2: sCC_Bl1394983891496994913t_unit] :
      ( ( ( sCC_Bl1090238580953940555t_unit @ R )
        = ( sCC_Bl1090238580953940555t_unit @ R2 ) )
     => ( ( ( sCC_Bl1280885523602775798t_unit @ R )
          = ( sCC_Bl1280885523602775798t_unit @ R2 ) )
       => ( ( ( sCC_Bl157864678168468314t_unit @ R )
            = ( sCC_Bl157864678168468314t_unit @ R2 ) )
         => ( ( ( sCC_Bl4645233313691564917t_unit @ R )
              = ( sCC_Bl4645233313691564917t_unit @ R2 ) )
           => ( ( ( sCC_Bl3795065053823578884t_unit @ R )
                = ( sCC_Bl3795065053823578884t_unit @ R2 ) )
             => ( ( ( sCC_Bl2536197123907397897t_unit @ R )
                  = ( sCC_Bl2536197123907397897t_unit @ R2 ) )
               => ( ( ( sCC_Bl8828226123343373779t_unit @ R )
                    = ( sCC_Bl8828226123343373779t_unit @ R2 ) )
                 => ( ( ( sCC_Bl9201514103433284750t_unit @ R )
                      = ( sCC_Bl9201514103433284750t_unit @ R2 ) )
                   => ( ( ( sCC_Bl3567736435408124606t_unit @ R )
                        = ( sCC_Bl3567736435408124606t_unit @ R2 ) )
                     => ( R = R2 ) ) ) ) ) ) ) ) ) ) ).

% equality
thf(fact_565_reachable__re,axiom,
    ! [X2: v,Y: v] :
      ( ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y )
     => ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ Y ) ) ).

% reachable_re
thf(fact_566_re__reachable,axiom,
    ! [X2: v,Y: v] :
      ( ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ Y )
     => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y ) ) ).

% re_reachable
thf(fact_567_calculation_I11_J,axiom,
    ( ( comple2307003700295860064_set_v @ ( sCC_Bl2536197123907397897t_unit @ e2 ) )
    = ( sCC_Bl157864678168468314t_unit @ e2 ) ) ).

% calculation(11)
thf(fact_568_reachable__end_Ocases,axiom,
    ! [A1: v,A22: v] :
      ( ( sCC_Bl770211535891879572_end_v @ successors @ A1 @ A22 )
     => ( ( A22 != A1 )
       => ~ ! [Y3: v] :
              ( ( sCC_Bl770211535891879572_end_v @ successors @ A1 @ Y3 )
             => ~ ( member_v @ A22 @ ( successors @ Y3 ) ) ) ) ) ).

% reachable_end.cases
thf(fact_569_re__refl,axiom,
    ! [X2: v] : ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ X2 ) ).

% re_refl
thf(fact_570_re__succ,axiom,
    ! [X2: v,Y: v,Z: v] :
      ( ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ Y )
     => ( ( member_v @ Z @ ( successors @ Y ) )
       => ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ Z ) ) ) ).

% re_succ
thf(fact_571_reachable__end_Osimps,axiom,
    ! [A1: v,A22: v] :
      ( ( sCC_Bl770211535891879572_end_v @ successors @ A1 @ A22 )
      = ( ? [X3: v] :
            ( ( A1 = X3 )
            & ( A22 = X3 ) )
        | ? [X3: v,Y4: v,Z4: v] :
            ( ( A1 = X3 )
            & ( A22 = Z4 )
            & ( sCC_Bl770211535891879572_end_v @ successors @ X3 @ Y4 )
            & ( member_v @ Z4 @ ( successors @ Y4 ) ) ) ) ) ).

% reachable_end.simps
thf(fact_572_succ__re,axiom,
    ! [Y: v,X2: v,Z: v] :
      ( ( member_v @ Y @ ( successors @ X2 ) )
     => ( ( sCC_Bl770211535891879572_end_v @ successors @ Y @ Z )
       => ( sCC_Bl770211535891879572_end_v @ successors @ X2 @ Z ) ) ) ).

% succ_re
thf(fact_573_order__refl,axiom,
    ! [X2: set_v] : ( ord_less_eq_set_v @ X2 @ X2 ) ).

% order_refl
thf(fact_574_order__refl,axiom,
    ! [X2: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ X2 @ X2 ) ).

% order_refl
thf(fact_575_dual__order_Orefl,axiom,
    ! [A: set_v] : ( ord_less_eq_set_v @ A @ A ) ).

% dual_order.refl
thf(fact_576_dual__order_Orefl,axiom,
    ! [A: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ A @ A ) ).

% dual_order.refl
thf(fact_577_sup_Oright__idem,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ A @ B ) @ B )
      = ( sup_su414716646722978715od_v_v @ A @ B ) ) ).

% sup.right_idem
thf(fact_578_sup_Oright__idem,axiom,
    ! [A: set_v,B: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ A @ B ) @ B )
      = ( sup_sup_set_v @ A @ B ) ) ).

% sup.right_idem
thf(fact_579_sup_Oright__idem,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ A @ B ) @ B )
      = ( sup_sup_Product_unit @ A @ B ) ) ).

% sup.right_idem
thf(fact_580_sup__left__idem,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) )
      = ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% sup_left_idem
thf(fact_581_sup__left__idem,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ X2 @ Y ) )
      = ( sup_sup_set_v @ X2 @ Y ) ) ).

% sup_left_idem
thf(fact_582_sup__left__idem,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ X2 @ Y ) )
      = ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% sup_left_idem
thf(fact_583_sup_Oleft__idem,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A @ ( sup_su414716646722978715od_v_v @ A @ B ) )
      = ( sup_su414716646722978715od_v_v @ A @ B ) ) ).

% sup.left_idem
thf(fact_584_sup_Oleft__idem,axiom,
    ! [A: set_v,B: set_v] :
      ( ( sup_sup_set_v @ A @ ( sup_sup_set_v @ A @ B ) )
      = ( sup_sup_set_v @ A @ B ) ) ).

% sup.left_idem
thf(fact_585_sup_Oleft__idem,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( sup_sup_Product_unit @ A @ ( sup_sup_Product_unit @ A @ B ) )
      = ( sup_sup_Product_unit @ A @ B ) ) ).

% sup.left_idem
thf(fact_586_sup__idem,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ X2 )
      = X2 ) ).

% sup_idem
thf(fact_587_sup__idem,axiom,
    ! [X2: set_v] :
      ( ( sup_sup_set_v @ X2 @ X2 )
      = X2 ) ).

% sup_idem
thf(fact_588_sup__idem,axiom,
    ! [X2: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ X2 )
      = X2 ) ).

% sup_idem
thf(fact_589_sup_Oidem,axiom,
    ! [A: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A @ A )
      = A ) ).

% sup.idem
thf(fact_590_sup_Oidem,axiom,
    ! [A: set_v] :
      ( ( sup_sup_set_v @ A @ A )
      = A ) ).

% sup.idem
thf(fact_591_sup_Oidem,axiom,
    ! [A: product_unit] :
      ( ( sup_sup_Product_unit @ A @ A )
      = A ) ).

% sup.idem
thf(fact_592_Un__iff,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
      = ( ( member7453568604450474000od_v_v @ C @ A3 )
        | ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% Un_iff
thf(fact_593_Un__iff,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( sup_sup_set_v @ A3 @ B5 ) )
      = ( ( member_v @ C @ A3 )
        | ( member_v @ C @ B5 ) ) ) ).

% Un_iff
thf(fact_594_UnCI,axiom,
    ! [C: product_prod_v_v,B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ~ ( member7453568604450474000od_v_v @ C @ B5 )
       => ( member7453568604450474000od_v_v @ C @ A3 ) )
     => ( member7453568604450474000od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ) ).

% UnCI
thf(fact_595_UnCI,axiom,
    ! [C: v,B5: set_v,A3: set_v] :
      ( ( ~ ( member_v @ C @ B5 )
       => ( member_v @ C @ A3 ) )
     => ( member_v @ C @ ( sup_sup_set_v @ A3 @ B5 ) ) ) ).

% UnCI
thf(fact_596_le__sup__iff,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ Z )
      = ( ( ord_le3221252021190050221t_unit @ X2 @ Z )
        & ( ord_le3221252021190050221t_unit @ Y @ Z ) ) ) ).

% le_sup_iff
thf(fact_597_le__sup__iff,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( ord_less_eq_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ Z )
      = ( ( ord_less_eq_set_v @ X2 @ Z )
        & ( ord_less_eq_set_v @ Y @ Z ) ) ) ).

% le_sup_iff
thf(fact_598_le__sup__iff,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ Z )
      = ( ( ord_le7336532860387713383od_v_v @ X2 @ Z )
        & ( ord_le7336532860387713383od_v_v @ Y @ Z ) ) ) ).

% le_sup_iff
thf(fact_599_sup_Obounded__iff,axiom,
    ! [B: product_unit,C: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ B @ C ) @ A )
      = ( ( ord_le3221252021190050221t_unit @ B @ A )
        & ( ord_le3221252021190050221t_unit @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_600_sup_Obounded__iff,axiom,
    ! [B: set_v,C: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ ( sup_sup_set_v @ B @ C ) @ A )
      = ( ( ord_less_eq_set_v @ B @ A )
        & ( ord_less_eq_set_v @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_601_sup_Obounded__iff,axiom,
    ! [B: set_Product_prod_v_v,C: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ B @ C ) @ A )
      = ( ( ord_le7336532860387713383od_v_v @ B @ A )
        & ( ord_le7336532860387713383od_v_v @ C @ A ) ) ) ).

% sup.bounded_iff
thf(fact_602_sup__bot__left,axiom,
    ! [X2: set_v] :
      ( ( sup_sup_set_v @ bot_bot_set_v @ X2 )
      = X2 ) ).

% sup_bot_left
thf(fact_603_sup__bot__left,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ bot_bo723834152578015283od_v_v @ X2 )
      = X2 ) ).

% sup_bot_left
thf(fact_604_sup__bot__left,axiom,
    ! [X2: product_unit] :
      ( ( sup_sup_Product_unit @ bot_bot_Product_unit @ X2 )
      = X2 ) ).

% sup_bot_left
thf(fact_605_sup__bot__right,axiom,
    ! [X2: set_v] :
      ( ( sup_sup_set_v @ X2 @ bot_bot_set_v )
      = X2 ) ).

% sup_bot_right
thf(fact_606_sup__bot__right,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ bot_bo723834152578015283od_v_v )
      = X2 ) ).

% sup_bot_right
thf(fact_607_sup__bot__right,axiom,
    ! [X2: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ bot_bot_Product_unit )
      = X2 ) ).

% sup_bot_right
thf(fact_608_bot__eq__sup__iff,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( bot_bot_set_v
        = ( sup_sup_set_v @ X2 @ Y ) )
      = ( ( X2 = bot_bot_set_v )
        & ( Y = bot_bot_set_v ) ) ) ).

% bot_eq_sup_iff
thf(fact_609_bot__eq__sup__iff,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( sup_su414716646722978715od_v_v @ X2 @ Y ) )
      = ( ( X2 = bot_bo723834152578015283od_v_v )
        & ( Y = bot_bo723834152578015283od_v_v ) ) ) ).

% bot_eq_sup_iff
thf(fact_610_bot__eq__sup__iff,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( bot_bot_Product_unit
        = ( sup_sup_Product_unit @ X2 @ Y ) )
      = ( ( X2 = bot_bot_Product_unit )
        & ( Y = bot_bot_Product_unit ) ) ) ).

% bot_eq_sup_iff
thf(fact_611_sup__eq__bot__iff,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( ( sup_sup_set_v @ X2 @ Y )
        = bot_bot_set_v )
      = ( ( X2 = bot_bot_set_v )
        & ( Y = bot_bot_set_v ) ) ) ).

% sup_eq_bot_iff
thf(fact_612_sup__eq__bot__iff,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( ( sup_su414716646722978715od_v_v @ X2 @ Y )
        = bot_bo723834152578015283od_v_v )
      = ( ( X2 = bot_bo723834152578015283od_v_v )
        & ( Y = bot_bo723834152578015283od_v_v ) ) ) ).

% sup_eq_bot_iff
thf(fact_613_sup__eq__bot__iff,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( ( sup_sup_Product_unit @ X2 @ Y )
        = bot_bot_Product_unit )
      = ( ( X2 = bot_bot_Product_unit )
        & ( Y = bot_bot_Product_unit ) ) ) ).

% sup_eq_bot_iff
thf(fact_614_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_v,B: set_v] :
      ( ( ( sup_sup_set_v @ A @ B )
        = bot_bot_set_v )
      = ( ( A = bot_bot_set_v )
        & ( B = bot_bot_set_v ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_615_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ( sup_su414716646722978715od_v_v @ A @ B )
        = bot_bo723834152578015283od_v_v )
      = ( ( A = bot_bo723834152578015283od_v_v )
        & ( B = bot_bo723834152578015283od_v_v ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_616_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( ( sup_sup_Product_unit @ A @ B )
        = bot_bot_Product_unit )
      = ( ( A = bot_bot_Product_unit )
        & ( B = bot_bot_Product_unit ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_617_sup__bot_Oleft__neutral,axiom,
    ! [A: set_v] :
      ( ( sup_sup_set_v @ bot_bot_set_v @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_618_sup__bot_Oleft__neutral,axiom,
    ! [A: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ bot_bo723834152578015283od_v_v @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_619_sup__bot_Oleft__neutral,axiom,
    ! [A: product_unit] :
      ( ( sup_sup_Product_unit @ bot_bot_Product_unit @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_620_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_v,B: set_v] :
      ( ( bot_bot_set_v
        = ( sup_sup_set_v @ A @ B ) )
      = ( ( A = bot_bot_set_v )
        & ( B = bot_bot_set_v ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_621_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( sup_su414716646722978715od_v_v @ A @ B ) )
      = ( ( A = bot_bo723834152578015283od_v_v )
        & ( B = bot_bo723834152578015283od_v_v ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_622_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( bot_bot_Product_unit
        = ( sup_sup_Product_unit @ A @ B ) )
      = ( ( A = bot_bot_Product_unit )
        & ( B = bot_bot_Product_unit ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_623_sup__bot_Oright__neutral,axiom,
    ! [A: set_v] :
      ( ( sup_sup_set_v @ A @ bot_bot_set_v )
      = A ) ).

% sup_bot.right_neutral
thf(fact_624_sup__bot_Oright__neutral,axiom,
    ! [A: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A @ bot_bo723834152578015283od_v_v )
      = A ) ).

% sup_bot.right_neutral
thf(fact_625_sup__bot_Oright__neutral,axiom,
    ! [A: product_unit] :
      ( ( sup_sup_Product_unit @ A @ bot_bot_Product_unit )
      = A ) ).

% sup_bot.right_neutral
thf(fact_626_inf__sup__absorb,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) )
      = X2 ) ).

% inf_sup_absorb
thf(fact_627_inf__sup__absorb,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( sup_sup_set_v @ X2 @ Y ) )
      = X2 ) ).

% inf_sup_absorb
thf(fact_628_inf__sup__absorb,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( sup_sup_Product_unit @ X2 @ Y ) )
      = X2 ) ).

% inf_sup_absorb
thf(fact_629_sup__inf__absorb,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) )
      = X2 ) ).

% sup_inf_absorb
thf(fact_630_sup__inf__absorb,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( inf_inf_set_v @ X2 @ Y ) )
      = X2 ) ).

% sup_inf_absorb
thf(fact_631_sup__inf__absorb,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( inf_inf_Product_unit @ X2 @ Y ) )
      = X2 ) ).

% sup_inf_absorb
thf(fact_632_Un__empty,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ( sup_sup_set_v @ A3 @ B5 )
        = bot_bot_set_v )
      = ( ( A3 = bot_bot_set_v )
        & ( B5 = bot_bot_set_v ) ) ) ).

% Un_empty
thf(fact_633_Un__empty,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( sup_su414716646722978715od_v_v @ A3 @ B5 )
        = bot_bo723834152578015283od_v_v )
      = ( ( A3 = bot_bo723834152578015283od_v_v )
        & ( B5 = bot_bo723834152578015283od_v_v ) ) ) ).

% Un_empty
thf(fact_634_Un__subset__iff,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( ord_less_eq_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ C2 )
      = ( ( ord_less_eq_set_v @ A3 @ C2 )
        & ( ord_less_eq_set_v @ B5 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_635_Un__subset__iff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ C2 )
      = ( ( ord_le7336532860387713383od_v_v @ A3 @ C2 )
        & ( ord_le7336532860387713383od_v_v @ B5 @ C2 ) ) ) ).

% Un_subset_iff
thf(fact_636_Un__insert__left,axiom,
    ! [A: product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( insert1338601472111419319od_v_v @ A @ B5 ) @ C2 )
      = ( insert1338601472111419319od_v_v @ A @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) ) ) ).

% Un_insert_left
thf(fact_637_Un__insert__left,axiom,
    ! [A: v,B5: set_v,C2: set_v] :
      ( ( sup_sup_set_v @ ( insert_v @ A @ B5 ) @ C2 )
      = ( insert_v @ A @ ( sup_sup_set_v @ B5 @ C2 ) ) ) ).

% Un_insert_left
thf(fact_638_Un__insert__right,axiom,
    ! [A3: set_Product_prod_v_v,A: product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ ( insert1338601472111419319od_v_v @ A @ B5 ) )
      = ( insert1338601472111419319od_v_v @ A @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ) ).

% Un_insert_right
thf(fact_639_Un__insert__right,axiom,
    ! [A3: set_v,A: v,B5: set_v] :
      ( ( sup_sup_set_v @ A3 @ ( insert_v @ A @ B5 ) )
      = ( insert_v @ A @ ( sup_sup_set_v @ A3 @ B5 ) ) ) ).

% Un_insert_right
thf(fact_640_Int__Un__eq_I4_J,axiom,
    ! [T2: set_Product_prod_v_v,S: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ T2 @ ( inf_in6271465464967711157od_v_v @ S @ T2 ) )
      = T2 ) ).

% Int_Un_eq(4)
thf(fact_641_Int__Un__eq_I4_J,axiom,
    ! [T2: set_v,S: set_v] :
      ( ( sup_sup_set_v @ T2 @ ( inf_inf_set_v @ S @ T2 ) )
      = T2 ) ).

% Int_Un_eq(4)
thf(fact_642_Int__Un__eq_I3_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ S @ ( inf_in6271465464967711157od_v_v @ S @ T2 ) )
      = S ) ).

% Int_Un_eq(3)
thf(fact_643_Int__Un__eq_I3_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( sup_sup_set_v @ S @ ( inf_inf_set_v @ S @ T2 ) )
      = S ) ).

% Int_Un_eq(3)
thf(fact_644_Int__Un__eq_I2_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ S @ T2 ) @ T2 )
      = T2 ) ).

% Int_Un_eq(2)
thf(fact_645_Int__Un__eq_I2_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ S @ T2 ) @ T2 )
      = T2 ) ).

% Int_Un_eq(2)
thf(fact_646_Int__Un__eq_I1_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ S @ T2 ) @ S )
      = S ) ).

% Int_Un_eq(1)
thf(fact_647_Int__Un__eq_I1_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ S @ T2 ) @ S )
      = S ) ).

% Int_Un_eq(1)
thf(fact_648_Un__Int__eq_I4_J,axiom,
    ! [T2: set_Product_prod_v_v,S: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ T2 @ ( sup_su414716646722978715od_v_v @ S @ T2 ) )
      = T2 ) ).

% Un_Int_eq(4)
thf(fact_649_Un__Int__eq_I4_J,axiom,
    ! [T2: set_v,S: set_v] :
      ( ( inf_inf_set_v @ T2 @ ( sup_sup_set_v @ S @ T2 ) )
      = T2 ) ).

% Un_Int_eq(4)
thf(fact_650_Un__Int__eq_I3_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ S @ ( sup_su414716646722978715od_v_v @ S @ T2 ) )
      = S ) ).

% Un_Int_eq(3)
thf(fact_651_Un__Int__eq_I3_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( inf_inf_set_v @ S @ ( sup_sup_set_v @ S @ T2 ) )
      = S ) ).

% Un_Int_eq(3)
thf(fact_652_Un__Int__eq_I2_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ S @ T2 ) @ T2 )
      = T2 ) ).

% Un_Int_eq(2)
thf(fact_653_Un__Int__eq_I2_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( inf_inf_set_v @ ( sup_sup_set_v @ S @ T2 ) @ T2 )
      = T2 ) ).

% Un_Int_eq(2)
thf(fact_654_Un__Int__eq_I1_J,axiom,
    ! [S: set_Product_prod_v_v,T2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ S @ T2 ) @ S )
      = S ) ).

% Un_Int_eq(1)
thf(fact_655_Un__Int__eq_I1_J,axiom,
    ! [S: set_v,T2: set_v] :
      ( ( inf_inf_set_v @ ( sup_sup_set_v @ S @ T2 ) @ S )
      = S ) ).

% Un_Int_eq(1)
thf(fact_656_Un__Diff__cancel2,axiom,
    ! [B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( minus_4183494784930505774od_v_v @ B5 @ A3 ) @ A3 )
      = ( sup_su414716646722978715od_v_v @ B5 @ A3 ) ) ).

% Un_Diff_cancel2
thf(fact_657_Un__Diff__cancel2,axiom,
    ! [B5: set_v,A3: set_v] :
      ( ( sup_sup_set_v @ ( minus_minus_set_v @ B5 @ A3 ) @ A3 )
      = ( sup_sup_set_v @ B5 @ A3 ) ) ).

% Un_Diff_cancel2
thf(fact_658_Un__Diff__cancel,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ ( minus_4183494784930505774od_v_v @ B5 @ A3 ) )
      = ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ).

% Un_Diff_cancel
thf(fact_659_Un__Diff__cancel,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( sup_sup_set_v @ A3 @ ( minus_minus_set_v @ B5 @ A3 ) )
      = ( sup_sup_set_v @ A3 @ B5 ) ) ).

% Un_Diff_cancel
thf(fact_660_set__append,axiom,
    ! [Xs: list_P7986770385144383213od_v_v,Ys: list_P7986770385144383213od_v_v] :
      ( ( set_Product_prod_v_v2 @ ( append2138873909117096322od_v_v @ Xs @ Ys ) )
      = ( sup_su414716646722978715od_v_v @ ( set_Product_prod_v_v2 @ Xs ) @ ( set_Product_prod_v_v2 @ Ys ) ) ) ).

% set_append
thf(fact_661_set__append,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( set_v2 @ ( append_v @ Xs @ Ys ) )
      = ( sup_sup_set_v @ ( set_v2 @ Xs ) @ ( set_v2 @ Ys ) ) ) ).

% set_append
thf(fact_662_sup__left__commute,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) )
      = ( sup_su414716646722978715od_v_v @ Y @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ).

% sup_left_commute
thf(fact_663_sup__left__commute,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) )
      = ( sup_sup_set_v @ Y @ ( sup_sup_set_v @ X2 @ Z ) ) ) ).

% sup_left_commute
thf(fact_664_sup__left__commute,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) )
      = ( sup_sup_Product_unit @ Y @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ).

% sup_left_commute
thf(fact_665_sup_Oleft__commute,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ B @ ( sup_su414716646722978715od_v_v @ A @ C ) )
      = ( sup_su414716646722978715od_v_v @ A @ ( sup_su414716646722978715od_v_v @ B @ C ) ) ) ).

% sup.left_commute
thf(fact_666_sup_Oleft__commute,axiom,
    ! [B: set_v,A: set_v,C: set_v] :
      ( ( sup_sup_set_v @ B @ ( sup_sup_set_v @ A @ C ) )
      = ( sup_sup_set_v @ A @ ( sup_sup_set_v @ B @ C ) ) ) ).

% sup.left_commute
thf(fact_667_sup_Oleft__commute,axiom,
    ! [B: product_unit,A: product_unit,C: product_unit] :
      ( ( sup_sup_Product_unit @ B @ ( sup_sup_Product_unit @ A @ C ) )
      = ( sup_sup_Product_unit @ A @ ( sup_sup_Product_unit @ B @ C ) ) ) ).

% sup.left_commute
thf(fact_668_boolean__algebra__cancel_Osup2,axiom,
    ! [B5: set_Product_prod_v_v,K: set_Product_prod_v_v,B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( B5
        = ( sup_su414716646722978715od_v_v @ K @ B ) )
     => ( ( sup_su414716646722978715od_v_v @ A @ B5 )
        = ( sup_su414716646722978715od_v_v @ K @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_669_boolean__algebra__cancel_Osup2,axiom,
    ! [B5: set_v,K: set_v,B: set_v,A: set_v] :
      ( ( B5
        = ( sup_sup_set_v @ K @ B ) )
     => ( ( sup_sup_set_v @ A @ B5 )
        = ( sup_sup_set_v @ K @ ( sup_sup_set_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_670_boolean__algebra__cancel_Osup2,axiom,
    ! [B5: product_unit,K: product_unit,B: product_unit,A: product_unit] :
      ( ( B5
        = ( sup_sup_Product_unit @ K @ B ) )
     => ( ( sup_sup_Product_unit @ A @ B5 )
        = ( sup_sup_Product_unit @ K @ ( sup_sup_Product_unit @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_671_boolean__algebra__cancel_Osup1,axiom,
    ! [A3: set_Product_prod_v_v,K: set_Product_prod_v_v,A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( A3
        = ( sup_su414716646722978715od_v_v @ K @ A ) )
     => ( ( sup_su414716646722978715od_v_v @ A3 @ B )
        = ( sup_su414716646722978715od_v_v @ K @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_672_boolean__algebra__cancel_Osup1,axiom,
    ! [A3: set_v,K: set_v,A: set_v,B: set_v] :
      ( ( A3
        = ( sup_sup_set_v @ K @ A ) )
     => ( ( sup_sup_set_v @ A3 @ B )
        = ( sup_sup_set_v @ K @ ( sup_sup_set_v @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_673_boolean__algebra__cancel_Osup1,axiom,
    ! [A3: product_unit,K: product_unit,A: product_unit,B: product_unit] :
      ( ( A3
        = ( sup_sup_Product_unit @ K @ A ) )
     => ( ( sup_sup_Product_unit @ A3 @ B )
        = ( sup_sup_Product_unit @ K @ ( sup_sup_Product_unit @ A @ B ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_674_sup__commute,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [X3: set_Product_prod_v_v,Y4: set_Product_prod_v_v] : ( sup_su414716646722978715od_v_v @ Y4 @ X3 ) ) ) ).

% sup_commute
thf(fact_675_sup__commute,axiom,
    ( sup_sup_set_v
    = ( ^ [X3: set_v,Y4: set_v] : ( sup_sup_set_v @ Y4 @ X3 ) ) ) ).

% sup_commute
thf(fact_676_sup__commute,axiom,
    ( sup_sup_Product_unit
    = ( ^ [X3: product_unit,Y4: product_unit] : ( sup_sup_Product_unit @ Y4 @ X3 ) ) ) ).

% sup_commute
thf(fact_677_sup_Ocommute,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] : ( sup_su414716646722978715od_v_v @ B4 @ A5 ) ) ) ).

% sup.commute
thf(fact_678_sup_Ocommute,axiom,
    ( sup_sup_set_v
    = ( ^ [A5: set_v,B4: set_v] : ( sup_sup_set_v @ B4 @ A5 ) ) ) ).

% sup.commute
thf(fact_679_sup_Ocommute,axiom,
    ( sup_sup_Product_unit
    = ( ^ [A5: product_unit,B4: product_unit] : ( sup_sup_Product_unit @ B4 @ A5 ) ) ) ).

% sup.commute
thf(fact_680_sup__assoc,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ Z )
      = ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_681_sup__assoc,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ Z )
      = ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_682_sup__assoc,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ Z )
      = ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_683_sup_Oassoc,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ A @ B ) @ C )
      = ( sup_su414716646722978715od_v_v @ A @ ( sup_su414716646722978715od_v_v @ B @ C ) ) ) ).

% sup.assoc
thf(fact_684_sup_Oassoc,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ A @ B ) @ C )
      = ( sup_sup_set_v @ A @ ( sup_sup_set_v @ B @ C ) ) ) ).

% sup.assoc
thf(fact_685_sup_Oassoc,axiom,
    ! [A: product_unit,B: product_unit,C: product_unit] :
      ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ A @ B ) @ C )
      = ( sup_sup_Product_unit @ A @ ( sup_sup_Product_unit @ B @ C ) ) ) ).

% sup.assoc
thf(fact_686_inf__sup__aci_I5_J,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [X3: set_Product_prod_v_v,Y4: set_Product_prod_v_v] : ( sup_su414716646722978715od_v_v @ Y4 @ X3 ) ) ) ).

% inf_sup_aci(5)
thf(fact_687_inf__sup__aci_I5_J,axiom,
    ( sup_sup_set_v
    = ( ^ [X3: set_v,Y4: set_v] : ( sup_sup_set_v @ Y4 @ X3 ) ) ) ).

% inf_sup_aci(5)
thf(fact_688_inf__sup__aci_I5_J,axiom,
    ( sup_sup_Product_unit
    = ( ^ [X3: product_unit,Y4: product_unit] : ( sup_sup_Product_unit @ Y4 @ X3 ) ) ) ).

% inf_sup_aci(5)
thf(fact_689_inf__sup__aci_I6_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ Z )
      = ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_690_inf__sup__aci_I6_J,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ Z )
      = ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_691_inf__sup__aci_I6_J,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ Z )
      = ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_692_inf__sup__aci_I7_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) )
      = ( sup_su414716646722978715od_v_v @ Y @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_693_inf__sup__aci_I7_J,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) )
      = ( sup_sup_set_v @ Y @ ( sup_sup_set_v @ X2 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_694_inf__sup__aci_I7_J,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) )
      = ( sup_sup_Product_unit @ Y @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_695_inf__sup__aci_I8_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) )
      = ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_696_inf__sup__aci_I8_J,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( sup_sup_set_v @ X2 @ Y ) )
      = ( sup_sup_set_v @ X2 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_697_inf__sup__aci_I8_J,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( sup_sup_Product_unit @ X2 @ Y ) )
      = ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_698_graph_Oreachable__end_Ocong,axiom,
    sCC_Bl770211535891879572_end_v = sCC_Bl770211535891879572_end_v ).

% graph.reachable_end.cong
thf(fact_699_Un__left__commute,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) )
      = ( sup_su414716646722978715od_v_v @ B5 @ ( sup_su414716646722978715od_v_v @ A3 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_700_Un__left__commute,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( sup_sup_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) )
      = ( sup_sup_set_v @ B5 @ ( sup_sup_set_v @ A3 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_701_Un__left__absorb,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
      = ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ).

% Un_left_absorb
thf(fact_702_Un__left__absorb,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( sup_sup_set_v @ A3 @ ( sup_sup_set_v @ A3 @ B5 ) )
      = ( sup_sup_set_v @ A3 @ B5 ) ) ).

% Un_left_absorb
thf(fact_703_Un__commute,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] : ( sup_su414716646722978715od_v_v @ B6 @ A6 ) ) ) ).

% Un_commute
thf(fact_704_Un__commute,axiom,
    ( sup_sup_set_v
    = ( ^ [A6: set_v,B6: set_v] : ( sup_sup_set_v @ B6 @ A6 ) ) ) ).

% Un_commute
thf(fact_705_Un__absorb,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ A3 )
      = A3 ) ).

% Un_absorb
thf(fact_706_Un__absorb,axiom,
    ! [A3: set_v] :
      ( ( sup_sup_set_v @ A3 @ A3 )
      = A3 ) ).

% Un_absorb
thf(fact_707_Un__assoc,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ C2 )
      = ( sup_su414716646722978715od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) ) ) ).

% Un_assoc
thf(fact_708_Un__assoc,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ C2 )
      = ( sup_sup_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) ) ) ).

% Un_assoc
thf(fact_709_ball__Un,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,P: product_prod_v_v > $o] :
      ( ( ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
           => ( P @ X3 ) ) )
      = ( ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ A3 )
           => ( P @ X3 ) )
        & ! [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ B5 )
           => ( P @ X3 ) ) ) ) ).

% ball_Un
thf(fact_710_ball__Un,axiom,
    ! [A3: set_v,B5: set_v,P: v > $o] :
      ( ( ! [X3: v] :
            ( ( member_v @ X3 @ ( sup_sup_set_v @ A3 @ B5 ) )
           => ( P @ X3 ) ) )
      = ( ! [X3: v] :
            ( ( member_v @ X3 @ A3 )
           => ( P @ X3 ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ B5 )
           => ( P @ X3 ) ) ) ) ).

% ball_Un
thf(fact_711_bex__Un,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,P: product_prod_v_v > $o] :
      ( ( ? [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
            & ( P @ X3 ) ) )
      = ( ? [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ A3 )
            & ( P @ X3 ) )
        | ? [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ B5 )
            & ( P @ X3 ) ) ) ) ).

% bex_Un
thf(fact_712_bex__Un,axiom,
    ! [A3: set_v,B5: set_v,P: v > $o] :
      ( ( ? [X3: v] :
            ( ( member_v @ X3 @ ( sup_sup_set_v @ A3 @ B5 ) )
            & ( P @ X3 ) ) )
      = ( ? [X3: v] :
            ( ( member_v @ X3 @ A3 )
            & ( P @ X3 ) )
        | ? [X3: v] :
            ( ( member_v @ X3 @ B5 )
            & ( P @ X3 ) ) ) ) ).

% bex_Un
thf(fact_713_UnI2,axiom,
    ! [C: product_prod_v_v,B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ B5 )
     => ( member7453568604450474000od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ) ).

% UnI2
thf(fact_714_UnI2,axiom,
    ! [C: v,B5: set_v,A3: set_v] :
      ( ( member_v @ C @ B5 )
     => ( member_v @ C @ ( sup_sup_set_v @ A3 @ B5 ) ) ) ).

% UnI2
thf(fact_715_UnI1,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ A3 )
     => ( member7453568604450474000od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ) ).

% UnI1
thf(fact_716_UnI1,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ A3 )
     => ( member_v @ C @ ( sup_sup_set_v @ A3 @ B5 ) ) ) ).

% UnI1
thf(fact_717_UnE,axiom,
    ! [C: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
     => ( ~ ( member7453568604450474000od_v_v @ C @ A3 )
       => ( member7453568604450474000od_v_v @ C @ B5 ) ) ) ).

% UnE
thf(fact_718_UnE,axiom,
    ! [C: v,A3: set_v,B5: set_v] :
      ( ( member_v @ C @ ( sup_sup_set_v @ A3 @ B5 ) )
     => ( ~ ( member_v @ C @ A3 )
       => ( member_v @ C @ B5 ) ) ) ).

% UnE
thf(fact_719_inf__sup__ord_I4_J,axiom,
    ! [Y: product_unit,X2: product_unit] : ( ord_le3221252021190050221t_unit @ Y @ ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_720_inf__sup__ord_I4_J,axiom,
    ! [Y: set_v,X2: set_v] : ( ord_less_eq_set_v @ Y @ ( sup_sup_set_v @ X2 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_721_inf__sup__ord_I4_J,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ Y @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% inf_sup_ord(4)
thf(fact_722_inf__sup__ord_I3_J,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ X2 @ ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_723_inf__sup__ord_I3_J,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ X2 @ ( sup_sup_set_v @ X2 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_724_inf__sup__ord_I3_J,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% inf_sup_ord(3)
thf(fact_725_le__supE,axiom,
    ! [A: product_unit,B: product_unit,X2: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ A @ B ) @ X2 )
     => ~ ( ( ord_le3221252021190050221t_unit @ A @ X2 )
         => ~ ( ord_le3221252021190050221t_unit @ B @ X2 ) ) ) ).

% le_supE
thf(fact_726_le__supE,axiom,
    ! [A: set_v,B: set_v,X2: set_v] :
      ( ( ord_less_eq_set_v @ ( sup_sup_set_v @ A @ B ) @ X2 )
     => ~ ( ( ord_less_eq_set_v @ A @ X2 )
         => ~ ( ord_less_eq_set_v @ B @ X2 ) ) ) ).

% le_supE
thf(fact_727_le__supE,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A @ B ) @ X2 )
     => ~ ( ( ord_le7336532860387713383od_v_v @ A @ X2 )
         => ~ ( ord_le7336532860387713383od_v_v @ B @ X2 ) ) ) ).

% le_supE
thf(fact_728_le__supI,axiom,
    ! [A: product_unit,X2: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ X2 )
     => ( ( ord_le3221252021190050221t_unit @ B @ X2 )
       => ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ A @ B ) @ X2 ) ) ) ).

% le_supI
thf(fact_729_le__supI,axiom,
    ! [A: set_v,X2: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ X2 )
     => ( ( ord_less_eq_set_v @ B @ X2 )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ A @ B ) @ X2 ) ) ) ).

% le_supI
thf(fact_730_le__supI,axiom,
    ! [A: set_Product_prod_v_v,X2: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ X2 )
     => ( ( ord_le7336532860387713383od_v_v @ B @ X2 )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A @ B ) @ X2 ) ) ) ).

% le_supI
thf(fact_731_sup__ge1,axiom,
    ! [X2: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ X2 @ ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% sup_ge1
thf(fact_732_sup__ge1,axiom,
    ! [X2: set_v,Y: set_v] : ( ord_less_eq_set_v @ X2 @ ( sup_sup_set_v @ X2 @ Y ) ) ).

% sup_ge1
thf(fact_733_sup__ge1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% sup_ge1
thf(fact_734_sup__ge2,axiom,
    ! [Y: product_unit,X2: product_unit] : ( ord_le3221252021190050221t_unit @ Y @ ( sup_sup_Product_unit @ X2 @ Y ) ) ).

% sup_ge2
thf(fact_735_sup__ge2,axiom,
    ! [Y: set_v,X2: set_v] : ( ord_less_eq_set_v @ Y @ ( sup_sup_set_v @ X2 @ Y ) ) ).

% sup_ge2
thf(fact_736_sup__ge2,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ Y @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) ) ).

% sup_ge2
thf(fact_737_le__supI1,axiom,
    ! [X2: product_unit,A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ A )
     => ( ord_le3221252021190050221t_unit @ X2 @ ( sup_sup_Product_unit @ A @ B ) ) ) ).

% le_supI1
thf(fact_738_le__supI1,axiom,
    ! [X2: set_v,A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ A )
     => ( ord_less_eq_set_v @ X2 @ ( sup_sup_set_v @ A @ B ) ) ) ).

% le_supI1
thf(fact_739_le__supI1,axiom,
    ! [X2: set_Product_prod_v_v,A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ A )
     => ( ord_le7336532860387713383od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ).

% le_supI1
thf(fact_740_le__supI2,axiom,
    ! [X2: product_unit,B: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ B )
     => ( ord_le3221252021190050221t_unit @ X2 @ ( sup_sup_Product_unit @ A @ B ) ) ) ).

% le_supI2
thf(fact_741_le__supI2,axiom,
    ! [X2: set_v,B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ B )
     => ( ord_less_eq_set_v @ X2 @ ( sup_sup_set_v @ A @ B ) ) ) ).

% le_supI2
thf(fact_742_le__supI2,axiom,
    ! [X2: set_Product_prod_v_v,B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ B )
     => ( ord_le7336532860387713383od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ).

% le_supI2
thf(fact_743_sup_Omono,axiom,
    ! [C: product_unit,A: product_unit,D: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ C @ A )
     => ( ( ord_le3221252021190050221t_unit @ D @ B )
       => ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ C @ D ) @ ( sup_sup_Product_unit @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_744_sup_Omono,axiom,
    ! [C: set_v,A: set_v,D: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ C @ A )
     => ( ( ord_less_eq_set_v @ D @ B )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ C @ D ) @ ( sup_sup_set_v @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_745_sup_Omono,axiom,
    ! [C: set_Product_prod_v_v,A: set_Product_prod_v_v,D: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C @ A )
     => ( ( ord_le7336532860387713383od_v_v @ D @ B )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ C @ D ) @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_746_sup__mono,axiom,
    ! [A: product_unit,C: product_unit,B: product_unit,D: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ C )
     => ( ( ord_le3221252021190050221t_unit @ B @ D )
       => ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ A @ B ) @ ( sup_sup_Product_unit @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_747_sup__mono,axiom,
    ! [A: set_v,C: set_v,B: set_v,D: set_v] :
      ( ( ord_less_eq_set_v @ A @ C )
     => ( ( ord_less_eq_set_v @ B @ D )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ A @ B ) @ ( sup_sup_set_v @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_748_sup__mono,axiom,
    ! [A: set_Product_prod_v_v,C: set_Product_prod_v_v,B: set_Product_prod_v_v,D: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ C )
     => ( ( ord_le7336532860387713383od_v_v @ B @ D )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A @ B ) @ ( sup_su414716646722978715od_v_v @ C @ D ) ) ) ) ).

% sup_mono
thf(fact_749_sup__least,axiom,
    ! [Y: product_unit,X2: product_unit,Z: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ Y @ X2 )
     => ( ( ord_le3221252021190050221t_unit @ Z @ X2 )
       => ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ Y @ Z ) @ X2 ) ) ) ).

% sup_least
thf(fact_750_sup__least,axiom,
    ! [Y: set_v,X2: set_v,Z: set_v] :
      ( ( ord_less_eq_set_v @ Y @ X2 )
     => ( ( ord_less_eq_set_v @ Z @ X2 )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ Y @ Z ) @ X2 ) ) ) ).

% sup_least
thf(fact_751_sup__least,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ Y @ X2 )
     => ( ( ord_le7336532860387713383od_v_v @ Z @ X2 )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ Y @ Z ) @ X2 ) ) ) ).

% sup_least
thf(fact_752_le__iff__sup,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [X3: product_unit,Y4: product_unit] :
          ( ( sup_sup_Product_unit @ X3 @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_753_le__iff__sup,axiom,
    ( ord_less_eq_set_v
    = ( ^ [X3: set_v,Y4: set_v] :
          ( ( sup_sup_set_v @ X3 @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_754_le__iff__sup,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [X3: set_Product_prod_v_v,Y4: set_Product_prod_v_v] :
          ( ( sup_su414716646722978715od_v_v @ X3 @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_755_sup_OorderE,axiom,
    ! [B: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ A )
     => ( A
        = ( sup_sup_Product_unit @ A @ B ) ) ) ).

% sup.orderE
thf(fact_756_sup_OorderE,axiom,
    ! [B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( A
        = ( sup_sup_set_v @ A @ B ) ) ) ).

% sup.orderE
thf(fact_757_sup_OorderE,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( A
        = ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ).

% sup.orderE
thf(fact_758_sup_OorderI,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( A
        = ( sup_sup_Product_unit @ A @ B ) )
     => ( ord_le3221252021190050221t_unit @ B @ A ) ) ).

% sup.orderI
thf(fact_759_sup_OorderI,axiom,
    ! [A: set_v,B: set_v] :
      ( ( A
        = ( sup_sup_set_v @ A @ B ) )
     => ( ord_less_eq_set_v @ B @ A ) ) ).

% sup.orderI
thf(fact_760_sup_OorderI,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( A
        = ( sup_su414716646722978715od_v_v @ A @ B ) )
     => ( ord_le7336532860387713383od_v_v @ B @ A ) ) ).

% sup.orderI
thf(fact_761_sup__unique,axiom,
    ! [F: product_unit > product_unit > product_unit,X2: product_unit,Y: product_unit] :
      ( ! [X4: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ X4 @ ( F @ X4 @ Y3 ) )
     => ( ! [X4: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ Y3 @ ( F @ X4 @ Y3 ) )
       => ( ! [X4: product_unit,Y3: product_unit,Z2: product_unit] :
              ( ( ord_le3221252021190050221t_unit @ Y3 @ X4 )
             => ( ( ord_le3221252021190050221t_unit @ Z2 @ X4 )
               => ( ord_le3221252021190050221t_unit @ ( F @ Y3 @ Z2 ) @ X4 ) ) )
         => ( ( sup_sup_Product_unit @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_762_sup__unique,axiom,
    ! [F: set_v > set_v > set_v,X2: set_v,Y: set_v] :
      ( ! [X4: set_v,Y3: set_v] : ( ord_less_eq_set_v @ X4 @ ( F @ X4 @ Y3 ) )
     => ( ! [X4: set_v,Y3: set_v] : ( ord_less_eq_set_v @ Y3 @ ( F @ X4 @ Y3 ) )
       => ( ! [X4: set_v,Y3: set_v,Z2: set_v] :
              ( ( ord_less_eq_set_v @ Y3 @ X4 )
             => ( ( ord_less_eq_set_v @ Z2 @ X4 )
               => ( ord_less_eq_set_v @ ( F @ Y3 @ Z2 ) @ X4 ) ) )
         => ( ( sup_sup_set_v @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_763_sup__unique,axiom,
    ! [F: set_Product_prod_v_v > set_Product_prod_v_v > set_Product_prod_v_v,X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ X4 @ ( F @ X4 @ Y3 ) )
     => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ Y3 @ ( F @ X4 @ Y3 ) )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v,Z2: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ Y3 @ X4 )
             => ( ( ord_le7336532860387713383od_v_v @ Z2 @ X4 )
               => ( ord_le7336532860387713383od_v_v @ ( F @ Y3 @ Z2 ) @ X4 ) ) )
         => ( ( sup_su414716646722978715od_v_v @ X2 @ Y )
            = ( F @ X2 @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_764_sup_Oabsorb1,axiom,
    ! [B: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ A )
     => ( ( sup_sup_Product_unit @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_765_sup_Oabsorb1,axiom,
    ! [B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( ( sup_sup_set_v @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_766_sup_Oabsorb1,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( ( sup_su414716646722978715od_v_v @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_767_sup_Oabsorb2,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ B )
     => ( ( sup_sup_Product_unit @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_768_sup_Oabsorb2,axiom,
    ! [A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( sup_sup_set_v @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_769_sup_Oabsorb2,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( sup_su414716646722978715od_v_v @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_770_sup__absorb1,axiom,
    ! [Y: product_unit,X2: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ Y @ X2 )
     => ( ( sup_sup_Product_unit @ X2 @ Y )
        = X2 ) ) ).

% sup_absorb1
thf(fact_771_sup__absorb1,axiom,
    ! [Y: set_v,X2: set_v] :
      ( ( ord_less_eq_set_v @ Y @ X2 )
     => ( ( sup_sup_set_v @ X2 @ Y )
        = X2 ) ) ).

% sup_absorb1
thf(fact_772_sup__absorb1,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ Y @ X2 )
     => ( ( sup_su414716646722978715od_v_v @ X2 @ Y )
        = X2 ) ) ).

% sup_absorb1
thf(fact_773_sup__absorb2,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ X2 @ Y )
     => ( ( sup_sup_Product_unit @ X2 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_774_sup__absorb2,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ Y )
     => ( ( sup_sup_set_v @ X2 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_775_sup__absorb2,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
     => ( ( sup_su414716646722978715od_v_v @ X2 @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_776_sup_OboundedE,axiom,
    ! [B: product_unit,C: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ B @ C ) @ A )
     => ~ ( ( ord_le3221252021190050221t_unit @ B @ A )
         => ~ ( ord_le3221252021190050221t_unit @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_777_sup_OboundedE,axiom,
    ! [B: set_v,C: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ ( sup_sup_set_v @ B @ C ) @ A )
     => ~ ( ( ord_less_eq_set_v @ B @ A )
         => ~ ( ord_less_eq_set_v @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_778_sup_OboundedE,axiom,
    ! [B: set_Product_prod_v_v,C: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ B @ C ) @ A )
     => ~ ( ( ord_le7336532860387713383od_v_v @ B @ A )
         => ~ ( ord_le7336532860387713383od_v_v @ C @ A ) ) ) ).

% sup.boundedE
thf(fact_779_sup_OboundedI,axiom,
    ! [B: product_unit,A: product_unit,C: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ B @ A )
     => ( ( ord_le3221252021190050221t_unit @ C @ A )
       => ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_780_sup_OboundedI,axiom,
    ! [B: set_v,A: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( ( ord_less_eq_set_v @ C @ A )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_781_sup_OboundedI,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( ( ord_le7336532860387713383od_v_v @ C @ A )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ B @ C ) @ A ) ) ) ).

% sup.boundedI
thf(fact_782_sup_Oorder__iff,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [B4: product_unit,A5: product_unit] :
          ( A5
          = ( sup_sup_Product_unit @ A5 @ B4 ) ) ) ) ).

% sup.order_iff
thf(fact_783_sup_Oorder__iff,axiom,
    ( ord_less_eq_set_v
    = ( ^ [B4: set_v,A5: set_v] :
          ( A5
          = ( sup_sup_set_v @ A5 @ B4 ) ) ) ) ).

% sup.order_iff
thf(fact_784_sup_Oorder__iff,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [B4: set_Product_prod_v_v,A5: set_Product_prod_v_v] :
          ( A5
          = ( sup_su414716646722978715od_v_v @ A5 @ B4 ) ) ) ) ).

% sup.order_iff
thf(fact_785_sup_Ocobounded1,axiom,
    ! [A: product_unit,B: product_unit] : ( ord_le3221252021190050221t_unit @ A @ ( sup_sup_Product_unit @ A @ B ) ) ).

% sup.cobounded1
thf(fact_786_sup_Ocobounded1,axiom,
    ! [A: set_v,B: set_v] : ( ord_less_eq_set_v @ A @ ( sup_sup_set_v @ A @ B ) ) ).

% sup.cobounded1
thf(fact_787_sup_Ocobounded1,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ A @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ).

% sup.cobounded1
thf(fact_788_sup_Ocobounded2,axiom,
    ! [B: product_unit,A: product_unit] : ( ord_le3221252021190050221t_unit @ B @ ( sup_sup_Product_unit @ A @ B ) ) ).

% sup.cobounded2
thf(fact_789_sup_Ocobounded2,axiom,
    ! [B: set_v,A: set_v] : ( ord_less_eq_set_v @ B @ ( sup_sup_set_v @ A @ B ) ) ).

% sup.cobounded2
thf(fact_790_sup_Ocobounded2,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ B @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ).

% sup.cobounded2
thf(fact_791_sup_Oabsorb__iff1,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [B4: product_unit,A5: product_unit] :
          ( ( sup_sup_Product_unit @ A5 @ B4 )
          = A5 ) ) ) ).

% sup.absorb_iff1
thf(fact_792_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_v
    = ( ^ [B4: set_v,A5: set_v] :
          ( ( sup_sup_set_v @ A5 @ B4 )
          = A5 ) ) ) ).

% sup.absorb_iff1
thf(fact_793_sup_Oabsorb__iff1,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [B4: set_Product_prod_v_v,A5: set_Product_prod_v_v] :
          ( ( sup_su414716646722978715od_v_v @ A5 @ B4 )
          = A5 ) ) ) ).

% sup.absorb_iff1
thf(fact_794_sup_Oabsorb__iff2,axiom,
    ( ord_le3221252021190050221t_unit
    = ( ^ [A5: product_unit,B4: product_unit] :
          ( ( sup_sup_Product_unit @ A5 @ B4 )
          = B4 ) ) ) ).

% sup.absorb_iff2
thf(fact_795_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A5: set_v,B4: set_v] :
          ( ( sup_sup_set_v @ A5 @ B4 )
          = B4 ) ) ) ).

% sup.absorb_iff2
thf(fact_796_sup_Oabsorb__iff2,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] :
          ( ( sup_su414716646722978715od_v_v @ A5 @ B4 )
          = B4 ) ) ) ).

% sup.absorb_iff2
thf(fact_797_sup_OcoboundedI1,axiom,
    ! [C: product_unit,A: product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ C @ A )
     => ( ord_le3221252021190050221t_unit @ C @ ( sup_sup_Product_unit @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_798_sup_OcoboundedI1,axiom,
    ! [C: set_v,A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ C @ A )
     => ( ord_less_eq_set_v @ C @ ( sup_sup_set_v @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_799_sup_OcoboundedI1,axiom,
    ! [C: set_Product_prod_v_v,A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C @ A )
     => ( ord_le7336532860387713383od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_800_sup_OcoboundedI2,axiom,
    ! [C: product_unit,B: product_unit,A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ C @ B )
     => ( ord_le3221252021190050221t_unit @ C @ ( sup_sup_Product_unit @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_801_sup_OcoboundedI2,axiom,
    ! [C: set_v,B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ C @ B )
     => ( ord_less_eq_set_v @ C @ ( sup_sup_set_v @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_802_sup_OcoboundedI2,axiom,
    ! [C: set_Product_prod_v_v,B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C @ B )
     => ( ord_le7336532860387713383od_v_v @ C @ ( sup_su414716646722978715od_v_v @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_803_boolean__algebra_Odisj__zero__right,axiom,
    ! [X2: set_v] :
      ( ( sup_sup_set_v @ X2 @ bot_bot_set_v )
      = X2 ) ).

% boolean_algebra.disj_zero_right
thf(fact_804_boolean__algebra_Odisj__zero__right,axiom,
    ! [X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ bot_bo723834152578015283od_v_v )
      = X2 ) ).

% boolean_algebra.disj_zero_right
thf(fact_805_boolean__algebra_Odisj__zero__right,axiom,
    ! [X2: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ bot_bot_Product_unit )
      = X2 ) ).

% boolean_algebra.disj_zero_right
thf(fact_806_distrib__imp1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v,Z2: set_Product_prod_v_v] :
          ( ( inf_in6271465464967711157od_v_v @ X4 @ ( sup_su414716646722978715od_v_v @ Y3 @ Z2 ) )
          = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ X4 @ Y3 ) @ ( inf_in6271465464967711157od_v_v @ X4 @ Z2 ) ) )
     => ( ( sup_su414716646722978715od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) )
        = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ) ).

% distrib_imp1
thf(fact_807_distrib__imp1,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ! [X4: set_v,Y3: set_v,Z2: set_v] :
          ( ( inf_inf_set_v @ X4 @ ( sup_sup_set_v @ Y3 @ Z2 ) )
          = ( sup_sup_set_v @ ( inf_inf_set_v @ X4 @ Y3 ) @ ( inf_inf_set_v @ X4 @ Z2 ) ) )
     => ( ( sup_sup_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
        = ( inf_inf_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ ( sup_sup_set_v @ X2 @ Z ) ) ) ) ).

% distrib_imp1
thf(fact_808_distrib__imp1,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ! [X4: product_unit,Y3: product_unit,Z2: product_unit] :
          ( ( inf_inf_Product_unit @ X4 @ ( sup_sup_Product_unit @ Y3 @ Z2 ) )
          = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X4 @ Y3 ) @ ( inf_inf_Product_unit @ X4 @ Z2 ) ) )
     => ( ( sup_sup_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
        = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ) ).

% distrib_imp1
thf(fact_809_distrib__imp2,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v,Z2: set_Product_prod_v_v] :
          ( ( sup_su414716646722978715od_v_v @ X4 @ ( inf_in6271465464967711157od_v_v @ Y3 @ Z2 ) )
          = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ X4 @ Y3 ) @ ( sup_su414716646722978715od_v_v @ X4 @ Z2 ) ) )
     => ( ( inf_in6271465464967711157od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) )
        = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ ( inf_in6271465464967711157od_v_v @ X2 @ Z ) ) ) ) ).

% distrib_imp2
thf(fact_810_distrib__imp2,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ! [X4: set_v,Y3: set_v,Z2: set_v] :
          ( ( sup_sup_set_v @ X4 @ ( inf_inf_set_v @ Y3 @ Z2 ) )
          = ( inf_inf_set_v @ ( sup_sup_set_v @ X4 @ Y3 ) @ ( sup_sup_set_v @ X4 @ Z2 ) ) )
     => ( ( inf_inf_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) )
        = ( sup_sup_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ ( inf_inf_set_v @ X2 @ Z ) ) ) ) ).

% distrib_imp2
thf(fact_811_distrib__imp2,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ! [X4: product_unit,Y3: product_unit,Z2: product_unit] :
          ( ( sup_sup_Product_unit @ X4 @ ( inf_inf_Product_unit @ Y3 @ Z2 ) )
          = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X4 @ Y3 ) @ ( sup_sup_Product_unit @ X4 @ Z2 ) ) )
     => ( ( inf_inf_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) )
        = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ ( inf_inf_Product_unit @ X2 @ Z ) ) ) ) ).

% distrib_imp2
thf(fact_812_inf__sup__distrib1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ ( inf_in6271465464967711157od_v_v @ X2 @ Z ) ) ) ).

% inf_sup_distrib1
thf(fact_813_inf__sup__distrib1,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ ( inf_inf_set_v @ X2 @ Z ) ) ) ).

% inf_sup_distrib1
thf(fact_814_inf__sup__distrib1,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) )
      = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ ( inf_inf_Product_unit @ X2 @ Z ) ) ) ).

% inf_sup_distrib1
thf(fact_815_inf__sup__distrib2,axiom,
    ! [Y: set_Product_prod_v_v,Z: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ Y @ Z ) @ X2 )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ Y @ X2 ) @ ( inf_in6271465464967711157od_v_v @ Z @ X2 ) ) ) ).

% inf_sup_distrib2
thf(fact_816_inf__sup__distrib2,axiom,
    ! [Y: set_v,Z: set_v,X2: set_v] :
      ( ( inf_inf_set_v @ ( sup_sup_set_v @ Y @ Z ) @ X2 )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ Y @ X2 ) @ ( inf_inf_set_v @ Z @ X2 ) ) ) ).

% inf_sup_distrib2
thf(fact_817_inf__sup__distrib2,axiom,
    ! [Y: product_unit,Z: product_unit,X2: product_unit] :
      ( ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ Z ) @ X2 )
      = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ X2 ) @ ( inf_inf_Product_unit @ Z @ X2 ) ) ) ).

% inf_sup_distrib2
thf(fact_818_sup__inf__distrib1,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ).

% sup_inf_distrib1
thf(fact_819_sup__inf__distrib1,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ ( sup_sup_set_v @ X2 @ Z ) ) ) ).

% sup_inf_distrib1
thf(fact_820_sup__inf__distrib1,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
      = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ).

% sup_inf_distrib1
thf(fact_821_sup__inf__distrib2,axiom,
    ! [Y: set_Product_prod_v_v,Z: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) @ X2 )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ Y @ X2 ) @ ( sup_su414716646722978715od_v_v @ Z @ X2 ) ) ) ).

% sup_inf_distrib2
thf(fact_822_sup__inf__distrib2,axiom,
    ! [Y: set_v,Z: set_v,X2: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ Y @ Z ) @ X2 )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ Y @ X2 ) @ ( sup_sup_set_v @ Z @ X2 ) ) ) ).

% sup_inf_distrib2
thf(fact_823_sup__inf__distrib2,axiom,
    ! [Y: product_unit,Z: product_unit,X2: product_unit] :
      ( ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ Z ) @ X2 )
      = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ X2 ) @ ( sup_sup_Product_unit @ Z @ X2 ) ) ) ).

% sup_inf_distrib2
thf(fact_824_boolean__algebra_Oconj__disj__distrib,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ ( inf_in6271465464967711157od_v_v @ X2 @ Z ) ) ) ).

% boolean_algebra.conj_disj_distrib
thf(fact_825_boolean__algebra_Oconj__disj__distrib,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( inf_inf_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ ( inf_inf_set_v @ X2 @ Z ) ) ) ).

% boolean_algebra.conj_disj_distrib
thf(fact_826_boolean__algebra_Oconj__disj__distrib,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( inf_inf_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) )
      = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ ( inf_inf_Product_unit @ X2 @ Z ) ) ) ).

% boolean_algebra.conj_disj_distrib
thf(fact_827_boolean__algebra_Odisj__conj__distrib,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ).

% boolean_algebra.disj_conj_distrib
thf(fact_828_boolean__algebra_Odisj__conj__distrib,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( sup_sup_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ ( sup_sup_set_v @ X2 @ Z ) ) ) ).

% boolean_algebra.disj_conj_distrib
thf(fact_829_boolean__algebra_Odisj__conj__distrib,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] :
      ( ( sup_sup_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) )
      = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ).

% boolean_algebra.disj_conj_distrib
thf(fact_830_boolean__algebra_Oconj__disj__distrib2,axiom,
    ! [Y: set_Product_prod_v_v,Z: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ Y @ Z ) @ X2 )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ Y @ X2 ) @ ( inf_in6271465464967711157od_v_v @ Z @ X2 ) ) ) ).

% boolean_algebra.conj_disj_distrib2
thf(fact_831_boolean__algebra_Oconj__disj__distrib2,axiom,
    ! [Y: set_v,Z: set_v,X2: set_v] :
      ( ( inf_inf_set_v @ ( sup_sup_set_v @ Y @ Z ) @ X2 )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ Y @ X2 ) @ ( inf_inf_set_v @ Z @ X2 ) ) ) ).

% boolean_algebra.conj_disj_distrib2
thf(fact_832_boolean__algebra_Oconj__disj__distrib2,axiom,
    ! [Y: product_unit,Z: product_unit,X2: product_unit] :
      ( ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ Z ) @ X2 )
      = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ X2 ) @ ( inf_inf_Product_unit @ Z @ X2 ) ) ) ).

% boolean_algebra.conj_disj_distrib2
thf(fact_833_boolean__algebra_Odisj__conj__distrib2,axiom,
    ! [Y: set_Product_prod_v_v,Z: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) @ X2 )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ Y @ X2 ) @ ( sup_su414716646722978715od_v_v @ Z @ X2 ) ) ) ).

% boolean_algebra.disj_conj_distrib2
thf(fact_834_boolean__algebra_Odisj__conj__distrib2,axiom,
    ! [Y: set_v,Z: set_v,X2: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ Y @ Z ) @ X2 )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ Y @ X2 ) @ ( sup_sup_set_v @ Z @ X2 ) ) ) ).

% boolean_algebra.disj_conj_distrib2
thf(fact_835_boolean__algebra_Odisj__conj__distrib2,axiom,
    ! [Y: product_unit,Z: product_unit,X2: product_unit] :
      ( ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ Z ) @ X2 )
      = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ X2 ) @ ( sup_sup_Product_unit @ Z @ X2 ) ) ) ).

% boolean_algebra.disj_conj_distrib2
thf(fact_836_Un__empty__left,axiom,
    ! [B5: set_v] :
      ( ( sup_sup_set_v @ bot_bot_set_v @ B5 )
      = B5 ) ).

% Un_empty_left
thf(fact_837_Un__empty__left,axiom,
    ! [B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ bot_bo723834152578015283od_v_v @ B5 )
      = B5 ) ).

% Un_empty_left
thf(fact_838_Un__empty__right,axiom,
    ! [A3: set_v] :
      ( ( sup_sup_set_v @ A3 @ bot_bot_set_v )
      = A3 ) ).

% Un_empty_right
thf(fact_839_Un__empty__right,axiom,
    ! [A3: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ bot_bo723834152578015283od_v_v )
      = A3 ) ).

% Un_empty_right
thf(fact_840_Un__mono,axiom,
    ! [A3: set_v,C2: set_v,B5: set_v,D2: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ C2 )
     => ( ( ord_less_eq_set_v @ B5 @ D2 )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ ( sup_sup_set_v @ C2 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_841_Un__mono,axiom,
    ! [A3: set_Product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v,D2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ C2 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ D2 )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ ( sup_su414716646722978715od_v_v @ C2 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_842_Un__least,axiom,
    ! [A3: set_v,C2: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ C2 )
     => ( ( ord_less_eq_set_v @ B5 @ C2 )
       => ( ord_less_eq_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ C2 ) ) ) ).

% Un_least
thf(fact_843_Un__least,axiom,
    ! [A3: set_Product_prod_v_v,C2: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ C2 )
     => ( ( ord_le7336532860387713383od_v_v @ B5 @ C2 )
       => ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ C2 ) ) ) ).

% Un_least
thf(fact_844_Un__upper1,axiom,
    ! [A3: set_v,B5: set_v] : ( ord_less_eq_set_v @ A3 @ ( sup_sup_set_v @ A3 @ B5 ) ) ).

% Un_upper1
thf(fact_845_Un__upper1,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ).

% Un_upper1
thf(fact_846_Un__upper2,axiom,
    ! [B5: set_v,A3: set_v] : ( ord_less_eq_set_v @ B5 @ ( sup_sup_set_v @ A3 @ B5 ) ) ).

% Un_upper2
thf(fact_847_Un__upper2,axiom,
    ! [B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ B5 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) ) ).

% Un_upper2
thf(fact_848_Un__absorb1,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( sup_sup_set_v @ A3 @ B5 )
        = B5 ) ) ).

% Un_absorb1
thf(fact_849_Un__absorb1,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( sup_su414716646722978715od_v_v @ A3 @ B5 )
        = B5 ) ) ).

% Un_absorb1
thf(fact_850_Un__absorb2,axiom,
    ! [B5: set_v,A3: set_v] :
      ( ( ord_less_eq_set_v @ B5 @ A3 )
     => ( ( sup_sup_set_v @ A3 @ B5 )
        = A3 ) ) ).

% Un_absorb2
thf(fact_851_Un__absorb2,axiom,
    ! [B5: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B5 @ A3 )
     => ( ( sup_su414716646722978715od_v_v @ A3 @ B5 )
        = A3 ) ) ).

% Un_absorb2
thf(fact_852_subset__UnE,axiom,
    ! [C2: set_v,A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ C2 @ ( sup_sup_set_v @ A3 @ B5 ) )
     => ~ ! [A7: set_v] :
            ( ( ord_less_eq_set_v @ A7 @ A3 )
           => ! [B8: set_v] :
                ( ( ord_less_eq_set_v @ B8 @ B5 )
               => ( C2
                 != ( sup_sup_set_v @ A7 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_853_subset__UnE,axiom,
    ! [C2: set_Product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ C2 @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
     => ~ ! [A7: set_Product_prod_v_v] :
            ( ( ord_le7336532860387713383od_v_v @ A7 @ A3 )
           => ! [B8: set_Product_prod_v_v] :
                ( ( ord_le7336532860387713383od_v_v @ B8 @ B5 )
               => ( C2
                 != ( sup_su414716646722978715od_v_v @ A7 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_854_subset__Un__eq,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( ( sup_sup_set_v @ A6 @ B6 )
          = B6 ) ) ) ).

% subset_Un_eq
thf(fact_855_subset__Un__eq,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( ( sup_su414716646722978715od_v_v @ A6 @ B6 )
          = B6 ) ) ) ).

% subset_Un_eq
thf(fact_856_Un__Int__crazy,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) ) @ ( inf_in6271465464967711157od_v_v @ C2 @ A3 ) )
      = ( inf_in6271465464967711157od_v_v @ ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) ) @ ( sup_su414716646722978715od_v_v @ C2 @ A3 ) ) ) ).

% Un_Int_crazy
thf(fact_857_Un__Int__crazy,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( sup_sup_set_v @ ( sup_sup_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ ( inf_inf_set_v @ B5 @ C2 ) ) @ ( inf_inf_set_v @ C2 @ A3 ) )
      = ( inf_inf_set_v @ ( inf_inf_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ ( sup_sup_set_v @ B5 @ C2 ) ) @ ( sup_sup_set_v @ C2 @ A3 ) ) ) ).

% Un_Int_crazy
thf(fact_858_Int__Un__distrib,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ ( inf_in6271465464967711157od_v_v @ A3 @ C2 ) ) ) ).

% Int_Un_distrib
thf(fact_859_Int__Un__distrib,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( inf_inf_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ ( inf_inf_set_v @ A3 @ C2 ) ) ) ).

% Int_Un_distrib
thf(fact_860_Un__Int__distrib,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ A3 @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ ( sup_su414716646722978715od_v_v @ A3 @ C2 ) ) ) ).

% Un_Int_distrib
thf(fact_861_Un__Int__distrib,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( sup_sup_set_v @ A3 @ ( inf_inf_set_v @ B5 @ C2 ) )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ ( sup_sup_set_v @ A3 @ C2 ) ) ) ).

% Un_Int_distrib
thf(fact_862_Int__Un__distrib2,axiom,
    ! [B5: set_Product_prod_v_v,C2: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) @ A3 )
      = ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ B5 @ A3 ) @ ( inf_in6271465464967711157od_v_v @ C2 @ A3 ) ) ) ).

% Int_Un_distrib2
thf(fact_863_Int__Un__distrib2,axiom,
    ! [B5: set_v,C2: set_v,A3: set_v] :
      ( ( inf_inf_set_v @ ( sup_sup_set_v @ B5 @ C2 ) @ A3 )
      = ( sup_sup_set_v @ ( inf_inf_set_v @ B5 @ A3 ) @ ( inf_inf_set_v @ C2 @ A3 ) ) ) ).

% Int_Un_distrib2
thf(fact_864_Un__Int__distrib2,axiom,
    ! [B5: set_Product_prod_v_v,C2: set_Product_prod_v_v,A3: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) @ A3 )
      = ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ B5 @ A3 ) @ ( sup_su414716646722978715od_v_v @ C2 @ A3 ) ) ) ).

% Un_Int_distrib2
thf(fact_865_Un__Int__distrib2,axiom,
    ! [B5: set_v,C2: set_v,A3: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ B5 @ C2 ) @ A3 )
      = ( inf_inf_set_v @ ( sup_sup_set_v @ B5 @ A3 ) @ ( sup_sup_set_v @ C2 @ A3 ) ) ) ).

% Un_Int_distrib2
thf(fact_866_Un__Diff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ ( sup_su414716646722978715od_v_v @ A3 @ B5 ) @ C2 )
      = ( sup_su414716646722978715od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ C2 ) @ ( minus_4183494784930505774od_v_v @ B5 @ C2 ) ) ) ).

% Un_Diff
thf(fact_867_Un__Diff,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( minus_minus_set_v @ ( sup_sup_set_v @ A3 @ B5 ) @ C2 )
      = ( sup_sup_set_v @ ( minus_minus_set_v @ A3 @ C2 ) @ ( minus_minus_set_v @ B5 @ C2 ) ) ) ).

% Un_Diff
thf(fact_868_graph_Osucc__re,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,Y: product_prod_v_v,X2: product_prod_v_v,Z: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( member7453568604450474000od_v_v @ Y @ ( Successors @ X2 ) )
       => ( ( sCC_Bl4714988717384592488od_v_v @ Successors @ Y @ Z )
         => ( sCC_Bl4714988717384592488od_v_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.succ_re
thf(fact_869_graph_Osucc__re,axiom,
    ! [Vertices: set_v,Successors: v > set_v,Y: v,X2: v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( member_v @ Y @ ( Successors @ X2 ) )
       => ( ( sCC_Bl770211535891879572_end_v @ Successors @ Y @ Z )
         => ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.succ_re
thf(fact_870_graph_Oreachable__end_Ocases,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4714988717384592488od_v_v @ Successors @ A1 @ A22 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: product_prod_v_v] :
                ( ( sCC_Bl4714988717384592488od_v_v @ Successors @ A1 @ Y3 )
               => ~ ( member7453568604450474000od_v_v @ A22 @ ( Successors @ Y3 ) ) ) ) ) ) ).

% graph.reachable_end.cases
thf(fact_871_graph_Oreachable__end_Ocases,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl770211535891879572_end_v @ Successors @ A1 @ A22 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: v] :
                ( ( sCC_Bl770211535891879572_end_v @ Successors @ A1 @ Y3 )
               => ~ ( member_v @ A22 @ ( Successors @ Y3 ) ) ) ) ) ) ).

% graph.reachable_end.cases
thf(fact_872_graph_Oreachable__end_Osimps,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4714988717384592488od_v_v @ Successors @ A1 @ A22 )
        = ( ? [X3: product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = X3 ) )
          | ? [X3: product_prod_v_v,Y4: product_prod_v_v,Z4: product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( sCC_Bl4714988717384592488od_v_v @ Successors @ X3 @ Y4 )
              & ( member7453568604450474000od_v_v @ Z4 @ ( Successors @ Y4 ) ) ) ) ) ) ).

% graph.reachable_end.simps
thf(fact_873_graph_Oreachable__end_Osimps,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl770211535891879572_end_v @ Successors @ A1 @ A22 )
        = ( ? [X3: v] :
              ( ( A1 = X3 )
              & ( A22 = X3 ) )
          | ? [X3: v,Y4: v,Z4: v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( sCC_Bl770211535891879572_end_v @ Successors @ X3 @ Y4 )
              & ( member_v @ Z4 @ ( Successors @ Y4 ) ) ) ) ) ) ).

% graph.reachable_end.simps
thf(fact_874_graph_Ore__refl,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ X2 ) ) ).

% graph.re_refl
thf(fact_875_graph_Ore__succ,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v,Z: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl4714988717384592488od_v_v @ Successors @ X2 @ Y )
       => ( ( member7453568604450474000od_v_v @ Z @ ( Successors @ Y ) )
         => ( sCC_Bl4714988717384592488od_v_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.re_succ
thf(fact_876_graph_Ore__succ,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ Y )
       => ( ( member_v @ Z @ ( Successors @ Y ) )
         => ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ Z ) ) ) ) ).

% graph.re_succ
thf(fact_877_distrib__inf__le,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] : ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X2 @ Y ) @ ( inf_inf_Product_unit @ X2 @ Z ) ) @ ( inf_inf_Product_unit @ X2 @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).

% distrib_inf_le
thf(fact_878_distrib__inf__le,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] : ( ord_less_eq_set_v @ ( sup_sup_set_v @ ( inf_inf_set_v @ X2 @ Y ) @ ( inf_inf_set_v @ X2 @ Z ) ) @ ( inf_inf_set_v @ X2 @ ( sup_sup_set_v @ Y @ Z ) ) ) ).

% distrib_inf_le
thf(fact_879_distrib__inf__le,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ X2 @ Y ) @ ( inf_in6271465464967711157od_v_v @ X2 @ Z ) ) @ ( inf_in6271465464967711157od_v_v @ X2 @ ( sup_su414716646722978715od_v_v @ Y @ Z ) ) ) ).

% distrib_inf_le
thf(fact_880_distrib__sup__le,axiom,
    ! [X2: product_unit,Y: product_unit,Z: product_unit] : ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ X2 @ ( inf_inf_Product_unit @ Y @ Z ) ) @ ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X2 @ Y ) @ ( sup_sup_Product_unit @ X2 @ Z ) ) ) ).

% distrib_sup_le
thf(fact_881_distrib__sup__le,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] : ( ord_less_eq_set_v @ ( sup_sup_set_v @ X2 @ ( inf_inf_set_v @ Y @ Z ) ) @ ( inf_inf_set_v @ ( sup_sup_set_v @ X2 @ Y ) @ ( sup_sup_set_v @ X2 @ Z ) ) ) ).

% distrib_sup_le
thf(fact_882_distrib__sup__le,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ Y @ Z ) ) @ ( inf_in6271465464967711157od_v_v @ ( sup_su414716646722978715od_v_v @ X2 @ Y ) @ ( sup_su414716646722978715od_v_v @ X2 @ Z ) ) ) ).

% distrib_sup_le
thf(fact_883_insert__is__Un,axiom,
    ( insert_v
    = ( ^ [A5: v] : ( sup_sup_set_v @ ( insert_v @ A5 @ bot_bot_set_v ) ) ) ) ).

% insert_is_Un
thf(fact_884_insert__is__Un,axiom,
    ( insert1338601472111419319od_v_v
    = ( ^ [A5: product_prod_v_v] : ( sup_su414716646722978715od_v_v @ ( insert1338601472111419319od_v_v @ A5 @ bot_bo723834152578015283od_v_v ) ) ) ) ).

% insert_is_Un
thf(fact_885_Un__singleton__iff,axiom,
    ! [A3: set_v,B5: set_v,X2: v] :
      ( ( ( sup_sup_set_v @ A3 @ B5 )
        = ( insert_v @ X2 @ bot_bot_set_v ) )
      = ( ( ( A3 = bot_bot_set_v )
          & ( B5
            = ( insert_v @ X2 @ bot_bot_set_v ) ) )
        | ( ( A3
            = ( insert_v @ X2 @ bot_bot_set_v ) )
          & ( B5 = bot_bot_set_v ) )
        | ( ( A3
            = ( insert_v @ X2 @ bot_bot_set_v ) )
          & ( B5
            = ( insert_v @ X2 @ bot_bot_set_v ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_886_Un__singleton__iff,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,X2: product_prod_v_v] :
      ( ( ( sup_su414716646722978715od_v_v @ A3 @ B5 )
        = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
      = ( ( ( A3 = bot_bo723834152578015283od_v_v )
          & ( B5
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) )
        | ( ( A3
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
          & ( B5 = bot_bo723834152578015283od_v_v ) )
        | ( ( A3
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
          & ( B5
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_887_singleton__Un__iff,axiom,
    ! [X2: v,A3: set_v,B5: set_v] :
      ( ( ( insert_v @ X2 @ bot_bot_set_v )
        = ( sup_sup_set_v @ A3 @ B5 ) )
      = ( ( ( A3 = bot_bot_set_v )
          & ( B5
            = ( insert_v @ X2 @ bot_bot_set_v ) ) )
        | ( ( A3
            = ( insert_v @ X2 @ bot_bot_set_v ) )
          & ( B5 = bot_bot_set_v ) )
        | ( ( A3
            = ( insert_v @ X2 @ bot_bot_set_v ) )
          & ( B5
            = ( insert_v @ X2 @ bot_bot_set_v ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_888_singleton__Un__iff,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v )
        = ( sup_su414716646722978715od_v_v @ A3 @ B5 ) )
      = ( ( ( A3 = bot_bo723834152578015283od_v_v )
          & ( B5
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) )
        | ( ( A3
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
          & ( B5 = bot_bo723834152578015283od_v_v ) )
        | ( ( A3
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) )
          & ( B5
            = ( insert1338601472111419319od_v_v @ X2 @ bot_bo723834152578015283od_v_v ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_889_Un__Int__assoc__eq,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( ( sup_sup_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ C2 )
        = ( inf_inf_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) ) )
      = ( ord_less_eq_set_v @ C2 @ A3 ) ) ).

% Un_Int_assoc_eq
thf(fact_890_Un__Int__assoc__eq,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ C2 )
        = ( inf_in6271465464967711157od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) ) )
      = ( ord_le7336532860387713383od_v_v @ C2 @ A3 ) ) ).

% Un_Int_assoc_eq
thf(fact_891_Diff__partition,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( ord_less_eq_set_v @ A3 @ B5 )
     => ( ( sup_sup_set_v @ A3 @ ( minus_minus_set_v @ B5 @ A3 ) )
        = B5 ) ) ).

% Diff_partition
thf(fact_892_Diff__partition,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A3 @ B5 )
     => ( ( sup_su414716646722978715od_v_v @ A3 @ ( minus_4183494784930505774od_v_v @ B5 @ A3 ) )
        = B5 ) ) ).

% Diff_partition
thf(fact_893_Diff__subset__conv,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( ord_less_eq_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ C2 )
      = ( ord_less_eq_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) ) ) ).

% Diff_subset_conv
thf(fact_894_Diff__subset__conv,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ C2 )
      = ( ord_le7336532860387713383od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) ) ) ).

% Diff_subset_conv
thf(fact_895_Diff__Un,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ ( sup_su414716646722978715od_v_v @ B5 @ C2 ) )
      = ( inf_in6271465464967711157od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ ( minus_4183494784930505774od_v_v @ A3 @ C2 ) ) ) ).

% Diff_Un
thf(fact_896_Diff__Un,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( minus_minus_set_v @ A3 @ ( sup_sup_set_v @ B5 @ C2 ) )
      = ( inf_inf_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ ( minus_minus_set_v @ A3 @ C2 ) ) ) ).

% Diff_Un
thf(fact_897_Diff__Int,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v,C2: set_Product_prod_v_v] :
      ( ( minus_4183494784930505774od_v_v @ A3 @ ( inf_in6271465464967711157od_v_v @ B5 @ C2 ) )
      = ( sup_su414716646722978715od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ ( minus_4183494784930505774od_v_v @ A3 @ C2 ) ) ) ).

% Diff_Int
thf(fact_898_Diff__Int,axiom,
    ! [A3: set_v,B5: set_v,C2: set_v] :
      ( ( minus_minus_set_v @ A3 @ ( inf_inf_set_v @ B5 @ C2 ) )
      = ( sup_sup_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ ( minus_minus_set_v @ A3 @ C2 ) ) ) ).

% Diff_Int
thf(fact_899_Int__Diff__Un,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) )
      = A3 ) ).

% Int_Diff_Un
thf(fact_900_Int__Diff__Un,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( sup_sup_set_v @ ( inf_inf_set_v @ A3 @ B5 ) @ ( minus_minus_set_v @ A3 @ B5 ) )
      = A3 ) ).

% Int_Diff_Un
thf(fact_901_Un__Diff__Int,axiom,
    ! [A3: set_Product_prod_v_v,B5: set_Product_prod_v_v] :
      ( ( sup_su414716646722978715od_v_v @ ( minus_4183494784930505774od_v_v @ A3 @ B5 ) @ ( inf_in6271465464967711157od_v_v @ A3 @ B5 ) )
      = A3 ) ).

% Un_Diff_Int
thf(fact_902_Un__Diff__Int,axiom,
    ! [A3: set_v,B5: set_v] :
      ( ( sup_sup_set_v @ ( minus_minus_set_v @ A3 @ B5 ) @ ( inf_inf_set_v @ A3 @ B5 ) )
      = A3 ) ).

% Un_Diff_Int
thf(fact_903_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_v,Z3: set_v] : ( Y5 = Z3 ) )
    = ( ^ [X3: set_v,Y4: set_v] :
          ( ( ord_less_eq_set_v @ X3 @ Y4 )
          & ( ord_less_eq_set_v @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_904_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_Product_prod_v_v,Z3: set_Product_prod_v_v] : ( Y5 = Z3 ) )
    = ( ^ [X3: set_Product_prod_v_v,Y4: set_Product_prod_v_v] :
          ( ( ord_le7336532860387713383od_v_v @ X3 @ Y4 )
          & ( ord_le7336532860387713383od_v_v @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_905_ord__eq__le__trans,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( A = B )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ord_less_eq_set_v @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_906_ord__eq__le__trans,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( A = B )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ord_le7336532860387713383od_v_v @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_907_ord__le__eq__trans,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_set_v @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_908_ord__le__eq__trans,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( B = C )
       => ( ord_le7336532860387713383od_v_v @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_909_order__antisym,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ Y )
     => ( ( ord_less_eq_set_v @ Y @ X2 )
       => ( X2 = Y ) ) ) ).

% order_antisym
thf(fact_910_order__antisym,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
     => ( ( ord_le7336532860387713383od_v_v @ Y @ X2 )
       => ( X2 = Y ) ) ) ).

% order_antisym
thf(fact_911_order_Otrans,axiom,
    ! [A: set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ord_less_eq_set_v @ A @ C ) ) ) ).

% order.trans
thf(fact_912_order_Otrans,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ord_le7336532860387713383od_v_v @ A @ C ) ) ) ).

% order.trans
thf(fact_913_order__trans,axiom,
    ! [X2: set_v,Y: set_v,Z: set_v] :
      ( ( ord_less_eq_set_v @ X2 @ Y )
     => ( ( ord_less_eq_set_v @ Y @ Z )
       => ( ord_less_eq_set_v @ X2 @ Z ) ) ) ).

% order_trans
thf(fact_914_order__trans,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v,Z: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
     => ( ( ord_le7336532860387713383od_v_v @ Y @ Z )
       => ( ord_le7336532860387713383od_v_v @ X2 @ Z ) ) ) ).

% order_trans
thf(fact_915_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y5: set_v,Z3: set_v] : ( Y5 = Z3 ) )
    = ( ^ [A5: set_v,B4: set_v] :
          ( ( ord_less_eq_set_v @ B4 @ A5 )
          & ( ord_less_eq_set_v @ A5 @ B4 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_916_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y5: set_Product_prod_v_v,Z3: set_Product_prod_v_v] : ( Y5 = Z3 ) )
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] :
          ( ( ord_le7336532860387713383od_v_v @ B4 @ A5 )
          & ( ord_le7336532860387713383od_v_v @ A5 @ B4 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_917_dual__order_Oantisym,axiom,
    ! [B: set_v,A: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( ( ord_less_eq_set_v @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_918_dual__order_Oantisym,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( ( ord_le7336532860387713383od_v_v @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_919_dual__order_Otrans,axiom,
    ! [B: set_v,A: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ B @ A )
     => ( ( ord_less_eq_set_v @ C @ B )
       => ( ord_less_eq_set_v @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_920_dual__order_Otrans,axiom,
    ! [B: set_Product_prod_v_v,A: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ B @ A )
     => ( ( ord_le7336532860387713383od_v_v @ C @ B )
       => ( ord_le7336532860387713383od_v_v @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_921_antisym,axiom,
    ! [A: set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ord_less_eq_set_v @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_922_antisym,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ord_le7336532860387713383od_v_v @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_923_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_v,Z3: set_v] : ( Y5 = Z3 ) )
    = ( ^ [A5: set_v,B4: set_v] :
          ( ( ord_less_eq_set_v @ A5 @ B4 )
          & ( ord_less_eq_set_v @ B4 @ A5 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_924_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: set_Product_prod_v_v,Z3: set_Product_prod_v_v] : ( Y5 = Z3 ) )
    = ( ^ [A5: set_Product_prod_v_v,B4: set_Product_prod_v_v] :
          ( ( ord_le7336532860387713383od_v_v @ A5 @ B4 )
          & ( ord_le7336532860387713383od_v_v @ B4 @ A5 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_925_order__subst1,axiom,
    ! [A: set_v,F: set_v > set_v,B: set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ ( F @ B ) )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_926_order__subst1,axiom,
    ! [A: set_v,F: set_Product_prod_v_v > set_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_less_eq_set_v @ A @ ( F @ B ) )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_927_order__subst1,axiom,
    ! [A: set_Product_prod_v_v,F: set_v > set_Product_prod_v_v,B: set_v,C: set_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ ( F @ B ) )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_928_order__subst1,axiom,
    ! [A: set_Product_prod_v_v,F: set_Product_prod_v_v > set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ ( F @ B ) )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ A @ ( F @ C ) ) ) ) ) ).

% order_subst1
thf(fact_929_order__subst2,axiom,
    ! [A: set_v,B: set_v,F: set_v > set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ord_less_eq_set_v @ ( F @ B ) @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_930_order__subst2,axiom,
    ! [A: set_v,B: set_v,F: set_v > set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ord_le7336532860387713383od_v_v @ ( F @ B ) @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_931_order__subst2,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,F: set_Product_prod_v_v > set_v,C: set_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ord_less_eq_set_v @ ( F @ B ) @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_932_order__subst2,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,F: set_Product_prod_v_v > set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ord_le7336532860387713383od_v_v @ ( F @ B ) @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ ( F @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_933_order__eq__refl,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( X2 = Y )
     => ( ord_less_eq_set_v @ X2 @ Y ) ) ).

% order_eq_refl
thf(fact_934_order__eq__refl,axiom,
    ! [X2: set_Product_prod_v_v,Y: set_Product_prod_v_v] :
      ( ( X2 = Y )
     => ( ord_le7336532860387713383od_v_v @ X2 @ Y ) ) ).

% order_eq_refl
thf(fact_935_ord__eq__le__subst,axiom,
    ! [A: set_v,F: set_v > set_v,B: set_v,C: set_v] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_936_ord__eq__le__subst,axiom,
    ! [A: set_Product_prod_v_v,F: set_v > set_Product_prod_v_v,B: set_v,C: set_v] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_set_v @ B @ C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_937_ord__eq__le__subst,axiom,
    ! [A: set_v,F: set_Product_prod_v_v > set_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_938_ord__eq__le__subst,axiom,
    ! [A: set_Product_prod_v_v,F: set_Product_prod_v_v > set_Product_prod_v_v,B: set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_le7336532860387713383od_v_v @ B @ C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ A @ ( F @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_939_ord__le__eq__subst,axiom,
    ! [A: set_v,B: set_v,F: set_v > set_v,C: set_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_940_ord__le__eq__subst,axiom,
    ! [A: set_v,B: set_v,F: set_v > set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_less_eq_set_v @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: set_v,Y3: set_v] :
              ( ( ord_less_eq_set_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_941_ord__le__eq__subst,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,F: set_Product_prod_v_v > set_v,C: set_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_less_eq_set_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_less_eq_set_v @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_942_ord__le__eq__subst,axiom,
    ! [A: set_Product_prod_v_v,B: set_Product_prod_v_v,F: set_Product_prod_v_v > set_Product_prod_v_v,C: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ B )
     => ( ( ( F @ B )
          = C )
       => ( ! [X4: set_Product_prod_v_v,Y3: set_Product_prod_v_v] :
              ( ( ord_le7336532860387713383od_v_v @ X4 @ Y3 )
             => ( ord_le7336532860387713383od_v_v @ ( F @ X4 ) @ ( F @ Y3 ) ) )
         => ( ord_le7336532860387713383od_v_v @ ( F @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_943_order__antisym__conv,axiom,
    ! [Y: set_v,X2: set_v] :
      ( ( ord_less_eq_set_v @ Y @ X2 )
     => ( ( ord_less_eq_set_v @ X2 @ Y )
        = ( X2 = Y ) ) ) ).

% order_antisym_conv
thf(fact_944_order__antisym__conv,axiom,
    ! [Y: set_Product_prod_v_v,X2: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ Y @ X2 )
     => ( ( ord_le7336532860387713383od_v_v @ X2 @ Y )
        = ( X2 = Y ) ) ) ).

% order_antisym_conv
thf(fact_945_graph_Ore__reachable,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ Y )
       => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y ) ) ) ).

% graph.re_reachable
thf(fact_946_graph_Oreachable__re,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y )
       => ( sCC_Bl770211535891879572_end_v @ Successors @ X2 @ Y ) ) ) ).

% graph.reachable_re
thf(fact_947_bot_Oextremum,axiom,
    ! [A: product_unit] : ( ord_le3221252021190050221t_unit @ bot_bot_Product_unit @ A ) ).

% bot.extremum
thf(fact_948_bot_Oextremum,axiom,
    ! [A: set_v] : ( ord_less_eq_set_v @ bot_bot_set_v @ A ) ).

% bot.extremum
thf(fact_949_bot_Oextremum,axiom,
    ! [A: set_Product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ bot_bo723834152578015283od_v_v @ A ) ).

% bot.extremum
thf(fact_950_bot_Oextremum__unique,axiom,
    ! [A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ bot_bot_Product_unit )
      = ( A = bot_bot_Product_unit ) ) ).

% bot.extremum_unique
thf(fact_951_bot_Oextremum__unique,axiom,
    ! [A: set_v] :
      ( ( ord_less_eq_set_v @ A @ bot_bot_set_v )
      = ( A = bot_bot_set_v ) ) ).

% bot.extremum_unique
thf(fact_952_bot_Oextremum__unique,axiom,
    ! [A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ bot_bo723834152578015283od_v_v )
      = ( A = bot_bo723834152578015283od_v_v ) ) ).

% bot.extremum_unique
thf(fact_953_bot_Oextremum__uniqueI,axiom,
    ! [A: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ A @ bot_bot_Product_unit )
     => ( A = bot_bot_Product_unit ) ) ).

% bot.extremum_uniqueI
thf(fact_954_bot_Oextremum__uniqueI,axiom,
    ! [A: set_v] :
      ( ( ord_less_eq_set_v @ A @ bot_bot_set_v )
     => ( A = bot_bot_set_v ) ) ).

% bot.extremum_uniqueI
thf(fact_955_bot_Oextremum__uniqueI,axiom,
    ! [A: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ A @ bot_bo723834152578015283od_v_v )
     => ( A = bot_bo723834152578015283od_v_v ) ) ).

% bot.extremum_uniqueI
thf(fact_956_pre__dfss__def,axiom,
    ! [V2: v,E: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bl1748261141445803503t_unit @ successors @ V2 @ E )
      = ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
        & ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
        & ( ( sCC_Bl8828226123343373779t_unit @ E )
         != nil_v )
        & ( member_v @ V2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
           => ( member_v @ X3 @ ( sup_sup_set_v @ ( sCC_Bl157864678168468314t_unit @ E ) @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) ) ) )
        & ! [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
           => ( sCC_Bl649662514949026229able_v @ successors @ X3 @ V2 ) )
        & ? [Ns: list_v] :
            ( ( sCC_Bl9201514103433284750t_unit @ E )
            = ( cons_v @ V2 @ Ns ) ) ) ) ).

% pre_dfss_def
thf(fact_957_Sup__insert,axiom,
    ! [A: set_Product_prod_v_v,A3: set_se8455005133513928103od_v_v] :
      ( ( comple5788137035815166516od_v_v @ ( insert7504383016908236695od_v_v @ A @ A3 ) )
      = ( sup_su414716646722978715od_v_v @ A @ ( comple5788137035815166516od_v_v @ A3 ) ) ) ).

% Sup_insert
thf(fact_958_Sup__insert,axiom,
    ! [A: set_v,A3: set_set_v] :
      ( ( comple2307003700295860064_set_v @ ( insert_set_v @ A @ A3 ) )
      = ( sup_sup_set_v @ A @ ( comple2307003700295860064_set_v @ A3 ) ) ) ).

% Sup_insert
thf(fact_959_Sup__insert,axiom,
    ! [A: product_unit,A3: set_Product_unit] :
      ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ A @ A3 ) )
      = ( sup_sup_Product_unit @ A @ ( comple4687483117567863418t_unit @ A3 ) ) ) ).

% Sup_insert
thf(fact_960_ccpo__Sup__singleton,axiom,
    ! [X2: set_v] :
      ( ( comple2307003700295860064_set_v @ ( insert_set_v @ X2 @ bot_bot_set_set_v ) )
      = X2 ) ).

% ccpo_Sup_singleton
thf(fact_961_ccpo__Sup__singleton,axiom,
    ! [X2: product_unit] :
      ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) )
      = X2 ) ).

% ccpo_Sup_singleton
thf(fact_962_cSup__singleton,axiom,
    ! [X2: set_v] :
      ( ( comple2307003700295860064_set_v @ ( insert_set_v @ X2 @ bot_bot_set_set_v ) )
      = X2 ) ).

% cSup_singleton
thf(fact_963_cSup__singleton,axiom,
    ! [X2: product_unit] :
      ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) )
      = X2 ) ).

% cSup_singleton
thf(fact_964_Sup__empty,axiom,
    ( ( comple5788137035815166516od_v_v @ bot_bo3497076220358800403od_v_v )
    = bot_bo723834152578015283od_v_v ) ).

% Sup_empty
thf(fact_965_Sup__empty,axiom,
    ( ( comple2307003700295860064_set_v @ bot_bot_set_set_v )
    = bot_bot_set_v ) ).

% Sup_empty
thf(fact_966_Sup__empty,axiom,
    ( ( comple4687483117567863418t_unit @ bot_bo3957492148770167129t_unit )
    = bot_bot_Product_unit ) ).

% Sup_empty
thf(fact_967_Sup__bot__conv_I1_J,axiom,
    ! [A3: set_se8455005133513928103od_v_v] :
      ( ( ( comple5788137035815166516od_v_v @ A3 )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ A3 )
           => ( X3 = bot_bo723834152578015283od_v_v ) ) ) ) ).

% Sup_bot_conv(1)
thf(fact_968_Sup__bot__conv_I1_J,axiom,
    ! [A3: set_set_v] :
      ( ( ( comple2307003700295860064_set_v @ A3 )
        = bot_bot_set_v )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
           => ( X3 = bot_bot_set_v ) ) ) ) ).

% Sup_bot_conv(1)
thf(fact_969_Sup__bot__conv_I1_J,axiom,
    ! [A3: set_Product_unit] :
      ( ( ( comple4687483117567863418t_unit @ A3 )
        = bot_bot_Product_unit )
      = ( ! [X3: product_unit] :
            ( ( member_Product_unit @ X3 @ A3 )
           => ( X3 = bot_bot_Product_unit ) ) ) ) ).

% Sup_bot_conv(1)
thf(fact_970_Sup__bot__conv_I2_J,axiom,
    ! [A3: set_se8455005133513928103od_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( comple5788137035815166516od_v_v @ A3 ) )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ A3 )
           => ( X3 = bot_bo723834152578015283od_v_v ) ) ) ) ).

% Sup_bot_conv(2)
thf(fact_971_Sup__bot__conv_I2_J,axiom,
    ! [A3: set_set_v] :
      ( ( bot_bot_set_v
        = ( comple2307003700295860064_set_v @ A3 ) )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
           => ( X3 = bot_bot_set_v ) ) ) ) ).

% Sup_bot_conv(2)
thf(fact_972_Sup__bot__conv_I2_J,axiom,
    ! [A3: set_Product_unit] :
      ( ( bot_bot_Product_unit
        = ( comple4687483117567863418t_unit @ A3 ) )
      = ( ! [X3: product_unit] :
            ( ( member_Product_unit @ X3 @ A3 )
           => ( X3 = bot_bot_Product_unit ) ) ) ) ).

% Sup_bot_conv(2)
thf(fact_973_list_Osimps_I15_J,axiom,
    ! [X21: product_prod_v_v,X222: list_P7986770385144383213od_v_v] :
      ( ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X21 @ X222 ) )
      = ( insert1338601472111419319od_v_v @ X21 @ ( set_Product_prod_v_v2 @ X222 ) ) ) ).

% list.simps(15)
thf(fact_974_list_Osimps_I15_J,axiom,
    ! [X21: v,X222: list_v] :
      ( ( set_v2 @ ( cons_v @ X21 @ X222 ) )
      = ( insert_v @ X21 @ ( set_v2 @ X222 ) ) ) ).

% list.simps(15)
thf(fact_975_append1__eq__conv,axiom,
    ! [Xs: list_v,X2: v,Ys: list_v,Y: v] :
      ( ( ( append_v @ Xs @ ( cons_v @ X2 @ nil_v ) )
        = ( append_v @ Ys @ ( cons_v @ Y @ nil_v ) ) )
      = ( ( Xs = Ys )
        & ( X2 = Y ) ) ) ).

% append1_eq_conv
thf(fact_976_list_Ocollapse,axiom,
    ! [List: list_v] :
      ( ( List != nil_v )
     => ( ( cons_v @ ( hd_v @ List ) @ ( tl_v @ List ) )
        = List ) ) ).

% list.collapse
thf(fact_977_hd__Cons__tl,axiom,
    ! [Xs: list_v] :
      ( ( Xs != nil_v )
     => ( ( cons_v @ ( hd_v @ Xs ) @ ( tl_v @ Xs ) )
        = Xs ) ) ).

% hd_Cons_tl
thf(fact_978_transpose_Ocases,axiom,
    ! [X2: list_list_v] :
      ( ( X2 != nil_list_v )
     => ( ! [Xss: list_list_v] :
            ( X2
           != ( cons_list_v @ nil_v @ Xss ) )
       => ~ ! [X4: v,Xs3: list_v,Xss: list_list_v] :
              ( X2
             != ( cons_list_v @ ( cons_v @ X4 @ Xs3 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_979_splice_Ocases,axiom,
    ! [X2: produc1391462591744249447list_v] :
      ( ! [Ys3: list_v] :
          ( X2
         != ( produc6795410681906604247list_v @ nil_v @ Ys3 ) )
     => ~ ! [X4: v,Xs3: list_v,Ys3: list_v] :
            ( X2
           != ( produc6795410681906604247list_v @ ( cons_v @ X4 @ Xs3 ) @ Ys3 ) ) ) ).

% splice.cases
thf(fact_980_shuffles_Ocases,axiom,
    ! [X2: produc1391462591744249447list_v] :
      ( ! [Ys3: list_v] :
          ( X2
         != ( produc6795410681906604247list_v @ nil_v @ Ys3 ) )
     => ( ! [Xs3: list_v] :
            ( X2
           != ( produc6795410681906604247list_v @ Xs3 @ nil_v ) )
       => ~ ! [X4: v,Xs3: list_v,Y3: v,Ys3: list_v] :
              ( X2
             != ( produc6795410681906604247list_v @ ( cons_v @ X4 @ Xs3 ) @ ( cons_v @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_981_sorted__wrt_Ocases,axiom,
    ! [X2: produc8237170675765753490list_v] :
      ( ! [P3: v > v > $o] :
          ( X2
         != ( produc601102195597853570list_v @ P3 @ nil_v ) )
     => ~ ! [P3: v > v > $o,X4: v,Ys3: list_v] :
            ( X2
           != ( produc601102195597853570list_v @ P3 @ ( cons_v @ X4 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_982_successively_Ocases,axiom,
    ! [X2: produc8237170675765753490list_v] :
      ( ! [P3: v > v > $o] :
          ( X2
         != ( produc601102195597853570list_v @ P3 @ nil_v ) )
     => ( ! [P3: v > v > $o,X4: v] :
            ( X2
           != ( produc601102195597853570list_v @ P3 @ ( cons_v @ X4 @ nil_v ) ) )
       => ~ ! [P3: v > v > $o,X4: v,Y3: v,Xs3: list_v] :
              ( X2
             != ( produc601102195597853570list_v @ P3 @ ( cons_v @ X4 @ ( cons_v @ Y3 @ Xs3 ) ) ) ) ) ) ).

% successively.cases
thf(fact_983_list__nonempty__induct,axiom,
    ! [Xs: list_v,P: list_v > $o] :
      ( ( Xs != nil_v )
     => ( ! [X4: v] : ( P @ ( cons_v @ X4 @ nil_v ) )
       => ( ! [X4: v,Xs3: list_v] :
              ( ( Xs3 != nil_v )
             => ( ( P @ Xs3 )
               => ( P @ ( cons_v @ X4 @ Xs3 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_984_list__induct2_H,axiom,
    ! [P: list_v > list_v > $o,Xs: list_v,Ys: list_v] :
      ( ( P @ nil_v @ nil_v )
     => ( ! [X4: v,Xs3: list_v] : ( P @ ( cons_v @ X4 @ Xs3 ) @ nil_v )
       => ( ! [Y3: v,Ys3: list_v] : ( P @ nil_v @ ( cons_v @ Y3 @ Ys3 ) )
         => ( ! [X4: v,Xs3: list_v,Y3: v,Ys3: list_v] :
                ( ( P @ Xs3 @ Ys3 )
               => ( P @ ( cons_v @ X4 @ Xs3 ) @ ( cons_v @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_985_neq__Nil__conv,axiom,
    ! [Xs: list_v] :
      ( ( Xs != nil_v )
      = ( ? [Y4: v,Ys4: list_v] :
            ( Xs
            = ( cons_v @ Y4 @ Ys4 ) ) ) ) ).

% neq_Nil_conv
thf(fact_986_remdups__adj_Ocases,axiom,
    ! [X2: list_v] :
      ( ( X2 != nil_v )
     => ( ! [X4: v] :
            ( X2
           != ( cons_v @ X4 @ nil_v ) )
       => ~ ! [X4: v,Y3: v,Xs3: list_v] :
              ( X2
             != ( cons_v @ X4 @ ( cons_v @ Y3 @ Xs3 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_987_list_Oexhaust,axiom,
    ! [Y: list_v] :
      ( ( Y != nil_v )
     => ~ ! [X212: v,X223: list_v] :
            ( Y
           != ( cons_v @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_988_list_OdiscI,axiom,
    ! [List: list_v,X21: v,X222: list_v] :
      ( ( List
        = ( cons_v @ X21 @ X222 ) )
     => ( List != nil_v ) ) ).

% list.discI
thf(fact_989_list_Odistinct_I1_J,axiom,
    ! [X21: v,X222: list_v] :
      ( nil_v
     != ( cons_v @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_990_set__ConsD,axiom,
    ! [Y: product_prod_v_v,X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) ) )
     => ( ( Y = X2 )
        | ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_991_set__ConsD,axiom,
    ! [Y: v,X2: v,Xs: list_v] :
      ( ( member_v @ Y @ ( set_v2 @ ( cons_v @ X2 @ Xs ) ) )
     => ( ( Y = X2 )
        | ( member_v @ Y @ ( set_v2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_992_list_Oset__cases,axiom,
    ! [E: product_prod_v_v,A: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ E @ ( set_Product_prod_v_v2 @ A ) )
     => ( ! [Z22: list_P7986770385144383213od_v_v] :
            ( A
           != ( cons_P4120604216776828829od_v_v @ E @ Z22 ) )
       => ~ ! [Z1: product_prod_v_v,Z22: list_P7986770385144383213od_v_v] :
              ( ( A
                = ( cons_P4120604216776828829od_v_v @ Z1 @ Z22 ) )
             => ~ ( member7453568604450474000od_v_v @ E @ ( set_Product_prod_v_v2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_993_list_Oset__cases,axiom,
    ! [E: v,A: list_v] :
      ( ( member_v @ E @ ( set_v2 @ A ) )
     => ( ! [Z22: list_v] :
            ( A
           != ( cons_v @ E @ Z22 ) )
       => ~ ! [Z1: v,Z22: list_v] :
              ( ( A
                = ( cons_v @ Z1 @ Z22 ) )
             => ~ ( member_v @ E @ ( set_v2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_994_list_Oset__intros_I1_J,axiom,
    ! [X21: product_prod_v_v,X222: list_P7986770385144383213od_v_v] : ( member7453568604450474000od_v_v @ X21 @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X21 @ X222 ) ) ) ).

% list.set_intros(1)
thf(fact_995_list_Oset__intros_I1_J,axiom,
    ! [X21: v,X222: list_v] : ( member_v @ X21 @ ( set_v2 @ ( cons_v @ X21 @ X222 ) ) ) ).

% list.set_intros(1)
thf(fact_996_list_Oset__intros_I2_J,axiom,
    ! [Y: product_prod_v_v,X222: list_P7986770385144383213od_v_v,X21: product_prod_v_v] :
      ( ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ X222 ) )
     => ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X21 @ X222 ) ) ) ) ).

% list.set_intros(2)
thf(fact_997_list_Oset__intros_I2_J,axiom,
    ! [Y: v,X222: list_v,X21: v] :
      ( ( member_v @ Y @ ( set_v2 @ X222 ) )
     => ( member_v @ Y @ ( set_v2 @ ( cons_v @ X21 @ X222 ) ) ) ) ).

% list.set_intros(2)
thf(fact_998_Cons__eq__appendI,axiom,
    ! [X2: v,Xs1: list_v,Ys: list_v,Xs: list_v,Zs: list_v] :
      ( ( ( cons_v @ X2 @ Xs1 )
        = Ys )
     => ( ( Xs
          = ( append_v @ Xs1 @ Zs ) )
       => ( ( cons_v @ X2 @ Xs )
          = ( append_v @ Ys @ Zs ) ) ) ) ).

% Cons_eq_appendI
thf(fact_999_append__Cons,axiom,
    ! [X2: v,Xs: list_v,Ys: list_v] :
      ( ( append_v @ ( cons_v @ X2 @ Xs ) @ Ys )
      = ( cons_v @ X2 @ ( append_v @ Xs @ Ys ) ) ) ).

% append_Cons
thf(fact_1000_distinct__length__2__or__more,axiom,
    ! [A: v,B: v,Xs: list_v] :
      ( ( distinct_v @ ( cons_v @ A @ ( cons_v @ B @ Xs ) ) )
      = ( ( A != B )
        & ( distinct_v @ ( cons_v @ A @ Xs ) )
        & ( distinct_v @ ( cons_v @ B @ Xs ) ) ) ) ).

% distinct_length_2_or_more
thf(fact_1001_list_Osel_I1_J,axiom,
    ! [X21: v,X222: list_v] :
      ( ( hd_v @ ( cons_v @ X21 @ X222 ) )
      = X21 ) ).

% list.sel(1)
thf(fact_1002_list_Osel_I3_J,axiom,
    ! [X21: v,X222: list_v] :
      ( ( tl_v @ ( cons_v @ X21 @ X222 ) )
      = X222 ) ).

% list.sel(3)
thf(fact_1003_precedes__in__tail,axiom,
    ! [X2: v,Z: v,Y: v,Zs: list_v] :
      ( ( X2 != Z )
     => ( ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( cons_v @ Z @ Zs ) )
        = ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ Zs ) ) ) ).

% precedes_in_tail
thf(fact_1004_set__subset__Cons,axiom,
    ! [Xs: list_v,X2: v] : ( ord_less_eq_set_v @ ( set_v2 @ Xs ) @ ( set_v2 @ ( cons_v @ X2 @ Xs ) ) ) ).

% set_subset_Cons
thf(fact_1005_set__subset__Cons,axiom,
    ! [Xs: list_P7986770385144383213od_v_v,X2: product_prod_v_v] : ( ord_le7336532860387713383od_v_v @ ( set_Product_prod_v_v2 @ Xs ) @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) ) ) ).

% set_subset_Cons
thf(fact_1006_rev__nonempty__induct,axiom,
    ! [Xs: list_v,P: list_v > $o] :
      ( ( Xs != nil_v )
     => ( ! [X4: v] : ( P @ ( cons_v @ X4 @ nil_v ) )
       => ( ! [X4: v,Xs3: list_v] :
              ( ( Xs3 != nil_v )
             => ( ( P @ Xs3 )
               => ( P @ ( append_v @ Xs3 @ ( cons_v @ X4 @ nil_v ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_1007_append__eq__Cons__conv,axiom,
    ! [Ys: list_v,Zs: list_v,X2: v,Xs: list_v] :
      ( ( ( append_v @ Ys @ Zs )
        = ( cons_v @ X2 @ Xs ) )
      = ( ( ( Ys = nil_v )
          & ( Zs
            = ( cons_v @ X2 @ Xs ) ) )
        | ? [Ys5: list_v] :
            ( ( Ys
              = ( cons_v @ X2 @ Ys5 ) )
            & ( ( append_v @ Ys5 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_1008_Cons__eq__append__conv,axiom,
    ! [X2: v,Xs: list_v,Ys: list_v,Zs: list_v] :
      ( ( ( cons_v @ X2 @ Xs )
        = ( append_v @ Ys @ Zs ) )
      = ( ( ( Ys = nil_v )
          & ( ( cons_v @ X2 @ Xs )
            = Zs ) )
        | ? [Ys5: list_v] :
            ( ( ( cons_v @ X2 @ Ys5 )
              = Ys )
            & ( Xs
              = ( append_v @ Ys5 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_1009_rev__exhaust,axiom,
    ! [Xs: list_v] :
      ( ( Xs != nil_v )
     => ~ ! [Ys3: list_v,Y3: v] :
            ( Xs
           != ( append_v @ Ys3 @ ( cons_v @ Y3 @ nil_v ) ) ) ) ).

% rev_exhaust
thf(fact_1010_rev__induct,axiom,
    ! [P: list_v > $o,Xs: list_v] :
      ( ( P @ nil_v )
     => ( ! [X4: v,Xs3: list_v] :
            ( ( P @ Xs3 )
           => ( P @ ( append_v @ Xs3 @ ( cons_v @ X4 @ nil_v ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_1011_split__list,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
     => ? [Ys3: list_P7986770385144383213od_v_v,Zs2: list_P7986770385144383213od_v_v] :
          ( Xs
          = ( append2138873909117096322od_v_v @ Ys3 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_1012_split__list,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
     => ? [Ys3: list_v,Zs2: list_v] :
          ( Xs
          = ( append_v @ Ys3 @ ( cons_v @ X2 @ Zs2 ) ) ) ) ).

% split_list
thf(fact_1013_split__list__last,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
     => ? [Ys3: list_P7986770385144383213od_v_v,Zs2: list_P7986770385144383213od_v_v] :
          ( ( Xs
            = ( append2138873909117096322od_v_v @ Ys3 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs2 ) ) )
          & ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_1014_split__list__last,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
     => ? [Ys3: list_v,Zs2: list_v] :
          ( ( Xs
            = ( append_v @ Ys3 @ ( cons_v @ X2 @ Zs2 ) ) )
          & ~ ( member_v @ X2 @ ( set_v2 @ Zs2 ) ) ) ) ).

% split_list_last
thf(fact_1015_split__list__prop,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ? [Ys3: list_v,X4: v] :
          ( ? [Zs2: list_v] :
              ( Xs
              = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
          & ( P @ X4 ) ) ) ).

% split_list_prop
thf(fact_1016_split__list__first,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
     => ? [Ys3: list_P7986770385144383213od_v_v,Zs2: list_P7986770385144383213od_v_v] :
          ( ( Xs
            = ( append2138873909117096322od_v_v @ Ys3 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs2 ) ) )
          & ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_1017_split__list__first,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
     => ? [Ys3: list_v,Zs2: list_v] :
          ( ( Xs
            = ( append_v @ Ys3 @ ( cons_v @ X2 @ Zs2 ) ) )
          & ~ ( member_v @ X2 @ ( set_v2 @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_1018_split__list__propE,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ~ ! [Ys3: list_v,X4: v] :
            ( ? [Zs2: list_v] :
                ( Xs
                = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
           => ~ ( P @ X4 ) ) ) ).

% split_list_propE
thf(fact_1019_append__Cons__eq__iff,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v,Ys: list_P7986770385144383213od_v_v,Xs4: list_P7986770385144383213od_v_v,Ys6: list_P7986770385144383213od_v_v] :
      ( ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
     => ( ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Ys ) )
       => ( ( ( append2138873909117096322od_v_v @ Xs @ ( cons_P4120604216776828829od_v_v @ X2 @ Ys ) )
            = ( append2138873909117096322od_v_v @ Xs4 @ ( cons_P4120604216776828829od_v_v @ X2 @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_1020_append__Cons__eq__iff,axiom,
    ! [X2: v,Xs: list_v,Ys: list_v,Xs4: list_v,Ys6: list_v] :
      ( ~ ( member_v @ X2 @ ( set_v2 @ Xs ) )
     => ( ~ ( member_v @ X2 @ ( set_v2 @ Ys ) )
       => ( ( ( append_v @ Xs @ ( cons_v @ X2 @ Ys ) )
            = ( append_v @ Xs4 @ ( cons_v @ X2 @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_1021_in__set__conv__decomp,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
      = ( ? [Ys4: list_P7986770385144383213od_v_v,Zs3: list_P7986770385144383213od_v_v] :
            ( Xs
            = ( append2138873909117096322od_v_v @ Ys4 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_1022_in__set__conv__decomp,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
      = ( ? [Ys4: list_v,Zs3: list_v] :
            ( Xs
            = ( append_v @ Ys4 @ ( cons_v @ X2 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_1023_split__list__last__prop,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ? [Ys3: list_v,X4: v,Zs2: list_v] :
          ( ( Xs
            = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
          & ( P @ X4 )
          & ! [Xa: v] :
              ( ( member_v @ Xa @ ( set_v2 @ Zs2 ) )
             => ~ ( P @ Xa ) ) ) ) ).

% split_list_last_prop
thf(fact_1024_split__list__first__prop,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ? [Ys3: list_v,X4: v] :
          ( ? [Zs2: list_v] :
              ( Xs
              = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
          & ( P @ X4 )
          & ! [Xa: v] :
              ( ( member_v @ Xa @ ( set_v2 @ Ys3 ) )
             => ~ ( P @ Xa ) ) ) ) ).

% split_list_first_prop
thf(fact_1025_split__list__last__propE,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ~ ! [Ys3: list_v,X4: v,Zs2: list_v] :
            ( ( Xs
              = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa: v] :
                    ( ( member_v @ Xa @ ( set_v2 @ Zs2 ) )
                   => ~ ( P @ Xa ) ) ) ) ) ).

% split_list_last_propE
thf(fact_1026_split__list__first__propE,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ? [X: v] :
          ( ( member_v @ X @ ( set_v2 @ Xs ) )
          & ( P @ X ) )
     => ~ ! [Ys3: list_v,X4: v] :
            ( ? [Zs2: list_v] :
                ( Xs
                = ( append_v @ Ys3 @ ( cons_v @ X4 @ Zs2 ) ) )
           => ( ( P @ X4 )
             => ~ ! [Xa: v] :
                    ( ( member_v @ Xa @ ( set_v2 @ Ys3 ) )
                   => ~ ( P @ Xa ) ) ) ) ) ).

% split_list_first_propE
thf(fact_1027_in__set__conv__decomp__last,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
      = ( ? [Ys4: list_P7986770385144383213od_v_v,Zs3: list_P7986770385144383213od_v_v] :
            ( ( Xs
              = ( append2138873909117096322od_v_v @ Ys4 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs3 ) ) )
            & ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_1028_in__set__conv__decomp__last,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
      = ( ? [Ys4: list_v,Zs3: list_v] :
            ( ( Xs
              = ( append_v @ Ys4 @ ( cons_v @ X2 @ Zs3 ) ) )
            & ~ ( member_v @ X2 @ ( set_v2 @ Zs3 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_1029_in__set__conv__decomp__first,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
      = ( ? [Ys4: list_P7986770385144383213od_v_v,Zs3: list_P7986770385144383213od_v_v] :
            ( ( Xs
              = ( append2138873909117096322od_v_v @ Ys4 @ ( cons_P4120604216776828829od_v_v @ X2 @ Zs3 ) ) )
            & ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Ys4 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_1030_in__set__conv__decomp__first,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( member_v @ X2 @ ( set_v2 @ Xs ) )
      = ( ? [Ys4: list_v,Zs3: list_v] :
            ( ( Xs
              = ( append_v @ Ys4 @ ( cons_v @ X2 @ Zs3 ) ) )
            & ~ ( member_v @ X2 @ ( set_v2 @ Ys4 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_1031_split__list__last__prop__iff,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ( ? [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ Xs ) )
            & ( P @ X3 ) ) )
      = ( ? [Ys4: list_v,X3: v,Zs3: list_v] :
            ( ( Xs
              = ( append_v @ Ys4 @ ( cons_v @ X3 @ Zs3 ) ) )
            & ( P @ X3 )
            & ! [Y4: v] :
                ( ( member_v @ Y4 @ ( set_v2 @ Zs3 ) )
               => ~ ( P @ Y4 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_1032_split__list__first__prop__iff,axiom,
    ! [Xs: list_v,P: v > $o] :
      ( ( ? [X3: v] :
            ( ( member_v @ X3 @ ( set_v2 @ Xs ) )
            & ( P @ X3 ) ) )
      = ( ? [Ys4: list_v,X3: v] :
            ( ? [Zs3: list_v] :
                ( Xs
                = ( append_v @ Ys4 @ ( cons_v @ X3 @ Zs3 ) ) )
            & ( P @ X3 )
            & ! [Y4: v] :
                ( ( member_v @ Y4 @ ( set_v2 @ Ys4 ) )
               => ~ ( P @ Y4 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_1033_distinct__singleton,axiom,
    ! [X2: v] : ( distinct_v @ ( cons_v @ X2 @ nil_v ) ) ).

% distinct_singleton
thf(fact_1034_distinct_Osimps_I2_J,axiom,
    ! [X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( distin6159370996967099744od_v_v @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) )
      = ( ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
        & ( distin6159370996967099744od_v_v @ Xs ) ) ) ).

% distinct.simps(2)
thf(fact_1035_distinct_Osimps_I2_J,axiom,
    ! [X2: v,Xs: list_v] :
      ( ( distinct_v @ ( cons_v @ X2 @ Xs ) )
      = ( ~ ( member_v @ X2 @ ( set_v2 @ Xs ) )
        & ( distinct_v @ Xs ) ) ) ).

% distinct.simps(2)
thf(fact_1036_tl__Nil,axiom,
    ! [Xs: list_v] :
      ( ( ( tl_v @ Xs )
        = nil_v )
      = ( ( Xs = nil_v )
        | ? [X3: v] :
            ( Xs
            = ( cons_v @ X3 @ nil_v ) ) ) ) ).

% tl_Nil
thf(fact_1037_Nil__tl,axiom,
    ! [Xs: list_v] :
      ( ( nil_v
        = ( tl_v @ Xs ) )
      = ( ( Xs = nil_v )
        | ? [X3: v] :
            ( Xs
            = ( cons_v @ X3 @ nil_v ) ) ) ) ).

% Nil_tl
thf(fact_1038_tail__not__precedes,axiom,
    ! [Y: product_prod_v_v,X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( sCC_Bl2026170059108282219od_v_v @ Y @ X2 @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) )
     => ( ~ ( member7453568604450474000od_v_v @ X2 @ ( set_Product_prod_v_v2 @ Xs ) )
       => ( X2 = Y ) ) ) ).

% tail_not_precedes
thf(fact_1039_tail__not__precedes,axiom,
    ! [Y: v,X2: v,Xs: list_v] :
      ( ( sCC_Bl4022239298816431255edes_v @ Y @ X2 @ ( cons_v @ X2 @ Xs ) )
     => ( ~ ( member_v @ X2 @ ( set_v2 @ Xs ) )
       => ( X2 = Y ) ) ) ).

% tail_not_precedes
thf(fact_1040_head__precedes,axiom,
    ! [Y: product_prod_v_v,X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) ) )
     => ( sCC_Bl2026170059108282219od_v_v @ X2 @ Y @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) ) ) ).

% head_precedes
thf(fact_1041_head__precedes,axiom,
    ! [Y: v,X2: v,Xs: list_v] :
      ( ( member_v @ Y @ ( set_v2 @ ( cons_v @ X2 @ Xs ) ) )
     => ( sCC_Bl4022239298816431255edes_v @ X2 @ Y @ ( cons_v @ X2 @ Xs ) ) ) ).

% head_precedes
thf(fact_1042_not__distinct__decomp,axiom,
    ! [Ws: list_v] :
      ( ~ ( distinct_v @ Ws )
     => ? [Xs3: list_v,Ys3: list_v,Zs2: list_v,Y3: v] :
          ( Ws
          = ( append_v @ Xs3 @ ( append_v @ ( cons_v @ Y3 @ nil_v ) @ ( append_v @ Ys3 @ ( append_v @ ( cons_v @ Y3 @ nil_v ) @ Zs2 ) ) ) ) ) ) ).

% not_distinct_decomp
thf(fact_1043_not__distinct__conv__prefix,axiom,
    ! [As: list_P7986770385144383213od_v_v] :
      ( ( ~ ( distin6159370996967099744od_v_v @ As ) )
      = ( ? [Xs5: list_P7986770385144383213od_v_v,Y4: product_prod_v_v,Ys4: list_P7986770385144383213od_v_v] :
            ( ( member7453568604450474000od_v_v @ Y4 @ ( set_Product_prod_v_v2 @ Xs5 ) )
            & ( distin6159370996967099744od_v_v @ Xs5 )
            & ( As
              = ( append2138873909117096322od_v_v @ Xs5 @ ( cons_P4120604216776828829od_v_v @ Y4 @ Ys4 ) ) ) ) ) ) ).

% not_distinct_conv_prefix
thf(fact_1044_not__distinct__conv__prefix,axiom,
    ! [As: list_v] :
      ( ( ~ ( distinct_v @ As ) )
      = ( ? [Xs5: list_v,Y4: v,Ys4: list_v] :
            ( ( member_v @ Y4 @ ( set_v2 @ Xs5 ) )
            & ( distinct_v @ Xs5 )
            & ( As
              = ( append_v @ Xs5 @ ( cons_v @ Y4 @ Ys4 ) ) ) ) ) ) ).

% not_distinct_conv_prefix
thf(fact_1045_list_Oexhaust__sel,axiom,
    ! [List: list_v] :
      ( ( List != nil_v )
     => ( List
        = ( cons_v @ ( hd_v @ List ) @ ( tl_v @ List ) ) ) ) ).

% list.exhaust_sel
thf(fact_1046_precedes__def,axiom,
    ( sCC_Bl2026170059108282219od_v_v
    = ( ^ [X3: product_prod_v_v,Y4: product_prod_v_v,Xs5: list_P7986770385144383213od_v_v] :
        ? [L: list_P7986770385144383213od_v_v,R3: list_P7986770385144383213od_v_v] :
          ( ( Xs5
            = ( append2138873909117096322od_v_v @ L @ ( cons_P4120604216776828829od_v_v @ X3 @ R3 ) ) )
          & ( member7453568604450474000od_v_v @ Y4 @ ( set_Product_prod_v_v2 @ ( cons_P4120604216776828829od_v_v @ X3 @ R3 ) ) ) ) ) ) ).

% precedes_def
thf(fact_1047_precedes__def,axiom,
    ( sCC_Bl4022239298816431255edes_v
    = ( ^ [X3: v,Y4: v,Xs5: list_v] :
        ? [L: list_v,R3: list_v] :
          ( ( Xs5
            = ( append_v @ L @ ( cons_v @ X3 @ R3 ) ) )
          & ( member_v @ Y4 @ ( set_v2 @ ( cons_v @ X3 @ R3 ) ) ) ) ) ) ).

% precedes_def
thf(fact_1048_split__list__precedes,axiom,
    ! [Y: product_prod_v_v,Ys: list_P7986770385144383213od_v_v,X2: product_prod_v_v,Xs: list_P7986770385144383213od_v_v] :
      ( ( member7453568604450474000od_v_v @ Y @ ( set_Product_prod_v_v2 @ ( append2138873909117096322od_v_v @ Ys @ ( cons_P4120604216776828829od_v_v @ X2 @ nil_Product_prod_v_v ) ) ) )
     => ( sCC_Bl2026170059108282219od_v_v @ Y @ X2 @ ( append2138873909117096322od_v_v @ Ys @ ( cons_P4120604216776828829od_v_v @ X2 @ Xs ) ) ) ) ).

% split_list_precedes
thf(fact_1049_split__list__precedes,axiom,
    ! [Y: v,Ys: list_v,X2: v,Xs: list_v] :
      ( ( member_v @ Y @ ( set_v2 @ ( append_v @ Ys @ ( cons_v @ X2 @ nil_v ) ) ) )
     => ( sCC_Bl4022239298816431255edes_v @ Y @ X2 @ ( append_v @ Ys @ ( cons_v @ X2 @ Xs ) ) ) ) ).

% split_list_precedes
thf(fact_1050_cSup__eq__maximum,axiom,
    ! [Z: set_Product_prod_v_v,X5: set_se8455005133513928103od_v_v] :
      ( ( member8406446414694345712od_v_v @ Z @ X5 )
     => ( ! [X4: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X4 @ X5 )
           => ( ord_le7336532860387713383od_v_v @ X4 @ Z ) )
       => ( ( comple5788137035815166516od_v_v @ X5 )
          = Z ) ) ) ).

% cSup_eq_maximum
thf(fact_1051_cSup__eq__maximum,axiom,
    ! [Z: set_v,X5: set_set_v] :
      ( ( member_set_v @ Z @ X5 )
     => ( ! [X4: set_v] :
            ( ( member_set_v @ X4 @ X5 )
           => ( ord_less_eq_set_v @ X4 @ Z ) )
       => ( ( comple2307003700295860064_set_v @ X5 )
          = Z ) ) ) ).

% cSup_eq_maximum
thf(fact_1052_cSup__eq__maximum,axiom,
    ! [Z: product_unit,X5: set_Product_unit] :
      ( ( member_Product_unit @ Z @ X5 )
     => ( ! [X4: product_unit] :
            ( ( member_Product_unit @ X4 @ X5 )
           => ( ord_le3221252021190050221t_unit @ X4 @ Z ) )
       => ( ( comple4687483117567863418t_unit @ X5 )
          = Z ) ) ) ).

% cSup_eq_maximum
thf(fact_1053_Sup__upper2,axiom,
    ! [U: set_Product_prod_v_v,A3: set_se8455005133513928103od_v_v,V2: set_Product_prod_v_v] :
      ( ( member8406446414694345712od_v_v @ U @ A3 )
     => ( ( ord_le7336532860387713383od_v_v @ V2 @ U )
       => ( ord_le7336532860387713383od_v_v @ V2 @ ( comple5788137035815166516od_v_v @ A3 ) ) ) ) ).

% Sup_upper2
thf(fact_1054_Sup__upper2,axiom,
    ! [U: set_v,A3: set_set_v,V2: set_v] :
      ( ( member_set_v @ U @ A3 )
     => ( ( ord_less_eq_set_v @ V2 @ U )
       => ( ord_less_eq_set_v @ V2 @ ( comple2307003700295860064_set_v @ A3 ) ) ) ) ).

% Sup_upper2
thf(fact_1055_Sup__upper2,axiom,
    ! [U: product_unit,A3: set_Product_unit,V2: product_unit] :
      ( ( member_Product_unit @ U @ A3 )
     => ( ( ord_le3221252021190050221t_unit @ V2 @ U )
       => ( ord_le3221252021190050221t_unit @ V2 @ ( comple4687483117567863418t_unit @ A3 ) ) ) ) ).

% Sup_upper2
thf(fact_1056_Sup__le__iff,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B: set_Product_prod_v_v] :
      ( ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ B )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ A3 )
           => ( ord_le7336532860387713383od_v_v @ X3 @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1057_Sup__le__iff,axiom,
    ! [A3: set_set_v,B: set_v] :
      ( ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ B )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
           => ( ord_less_eq_set_v @ X3 @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1058_Sup__le__iff,axiom,
    ! [A3: set_Product_unit,B: product_unit] :
      ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ A3 ) @ B )
      = ( ! [X3: product_unit] :
            ( ( member_Product_unit @ X3 @ A3 )
           => ( ord_le3221252021190050221t_unit @ X3 @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1059_Sup__upper,axiom,
    ! [X2: set_Product_prod_v_v,A3: set_se8455005133513928103od_v_v] :
      ( ( member8406446414694345712od_v_v @ X2 @ A3 )
     => ( ord_le7336532860387713383od_v_v @ X2 @ ( comple5788137035815166516od_v_v @ A3 ) ) ) ).

% Sup_upper
thf(fact_1060_Sup__upper,axiom,
    ! [X2: set_v,A3: set_set_v] :
      ( ( member_set_v @ X2 @ A3 )
     => ( ord_less_eq_set_v @ X2 @ ( comple2307003700295860064_set_v @ A3 ) ) ) ).

% Sup_upper
thf(fact_1061_Sup__upper,axiom,
    ! [X2: product_unit,A3: set_Product_unit] :
      ( ( member_Product_unit @ X2 @ A3 )
     => ( ord_le3221252021190050221t_unit @ X2 @ ( comple4687483117567863418t_unit @ A3 ) ) ) ).

% Sup_upper
thf(fact_1062_Sup__least,axiom,
    ! [A3: set_se8455005133513928103od_v_v,Z: set_Product_prod_v_v] :
      ( ! [X4: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ X4 @ A3 )
         => ( ord_le7336532860387713383od_v_v @ X4 @ Z ) )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ Z ) ) ).

% Sup_least
thf(fact_1063_Sup__least,axiom,
    ! [A3: set_set_v,Z: set_v] :
      ( ! [X4: set_v] :
          ( ( member_set_v @ X4 @ A3 )
         => ( ord_less_eq_set_v @ X4 @ Z ) )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ Z ) ) ).

% Sup_least
thf(fact_1064_Sup__least,axiom,
    ! [A3: set_Product_unit,Z: product_unit] :
      ( ! [X4: product_unit] :
          ( ( member_Product_unit @ X4 @ A3 )
         => ( ord_le3221252021190050221t_unit @ X4 @ Z ) )
     => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ A3 ) @ Z ) ) ).

% Sup_least
thf(fact_1065_Sup__mono,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] :
      ( ! [A4: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ A4 @ A3 )
         => ? [X: set_Product_prod_v_v] :
              ( ( member8406446414694345712od_v_v @ X @ B5 )
              & ( ord_le7336532860387713383od_v_v @ A4 @ X ) ) )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Sup_mono
thf(fact_1066_Sup__mono,axiom,
    ! [A3: set_set_v,B5: set_set_v] :
      ( ! [A4: set_v] :
          ( ( member_set_v @ A4 @ A3 )
         => ? [X: set_v] :
              ( ( member_set_v @ X @ B5 )
              & ( ord_less_eq_set_v @ A4 @ X ) ) )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Sup_mono
thf(fact_1067_Sup__mono,axiom,
    ! [A3: set_Product_unit,B5: set_Product_unit] :
      ( ! [A4: product_unit] :
          ( ( member_Product_unit @ A4 @ A3 )
         => ? [X: product_unit] :
              ( ( member_Product_unit @ X @ B5 )
              & ( ord_le3221252021190050221t_unit @ A4 @ X ) ) )
     => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ A3 ) @ ( comple4687483117567863418t_unit @ B5 ) ) ) ).

% Sup_mono
thf(fact_1068_Sup__eqI,axiom,
    ! [A3: set_se8455005133513928103od_v_v,X2: set_Product_prod_v_v] :
      ( ! [Y3: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ Y3 @ A3 )
         => ( ord_le7336532860387713383od_v_v @ Y3 @ X2 ) )
     => ( ! [Y3: set_Product_prod_v_v] :
            ( ! [Z5: set_Product_prod_v_v] :
                ( ( member8406446414694345712od_v_v @ Z5 @ A3 )
               => ( ord_le7336532860387713383od_v_v @ Z5 @ Y3 ) )
           => ( ord_le7336532860387713383od_v_v @ X2 @ Y3 ) )
       => ( ( comple5788137035815166516od_v_v @ A3 )
          = X2 ) ) ) ).

% Sup_eqI
thf(fact_1069_Sup__eqI,axiom,
    ! [A3: set_set_v,X2: set_v] :
      ( ! [Y3: set_v] :
          ( ( member_set_v @ Y3 @ A3 )
         => ( ord_less_eq_set_v @ Y3 @ X2 ) )
     => ( ! [Y3: set_v] :
            ( ! [Z5: set_v] :
                ( ( member_set_v @ Z5 @ A3 )
               => ( ord_less_eq_set_v @ Z5 @ Y3 ) )
           => ( ord_less_eq_set_v @ X2 @ Y3 ) )
       => ( ( comple2307003700295860064_set_v @ A3 )
          = X2 ) ) ) ).

% Sup_eqI
thf(fact_1070_Sup__eqI,axiom,
    ! [A3: set_Product_unit,X2: product_unit] :
      ( ! [Y3: product_unit] :
          ( ( member_Product_unit @ Y3 @ A3 )
         => ( ord_le3221252021190050221t_unit @ Y3 @ X2 ) )
     => ( ! [Y3: product_unit] :
            ( ! [Z5: product_unit] :
                ( ( member_Product_unit @ Z5 @ A3 )
               => ( ord_le3221252021190050221t_unit @ Z5 @ Y3 ) )
           => ( ord_le3221252021190050221t_unit @ X2 @ Y3 ) )
       => ( ( comple4687483117567863418t_unit @ A3 )
          = X2 ) ) ) ).

% Sup_eqI
thf(fact_1071_empty__Union__conv,axiom,
    ! [A3: set_se8455005133513928103od_v_v] :
      ( ( bot_bo723834152578015283od_v_v
        = ( comple5788137035815166516od_v_v @ A3 ) )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ A3 )
           => ( X3 = bot_bo723834152578015283od_v_v ) ) ) ) ).

% empty_Union_conv
thf(fact_1072_empty__Union__conv,axiom,
    ! [A3: set_set_v] :
      ( ( bot_bot_set_v
        = ( comple2307003700295860064_set_v @ A3 ) )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
           => ( X3 = bot_bot_set_v ) ) ) ) ).

% empty_Union_conv
thf(fact_1073_Union__empty__conv,axiom,
    ! [A3: set_se8455005133513928103od_v_v] :
      ( ( ( comple5788137035815166516od_v_v @ A3 )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ A3 )
           => ( X3 = bot_bo723834152578015283od_v_v ) ) ) ) ).

% Union_empty_conv
thf(fact_1074_Union__empty__conv,axiom,
    ! [A3: set_set_v] :
      ( ( ( comple2307003700295860064_set_v @ A3 )
        = bot_bot_set_v )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
           => ( X3 = bot_bot_set_v ) ) ) ) ).

% Union_empty_conv
thf(fact_1075_Union__empty,axiom,
    ( ( comple5788137035815166516od_v_v @ bot_bo3497076220358800403od_v_v )
    = bot_bo723834152578015283od_v_v ) ).

% Union_empty
thf(fact_1076_Union__empty,axiom,
    ( ( comple2307003700295860064_set_v @ bot_bot_set_set_v )
    = bot_bot_set_v ) ).

% Union_empty
thf(fact_1077_Union__mono,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] :
      ( ( ord_le4714265922333009223od_v_v @ A3 @ B5 )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Union_mono
thf(fact_1078_Union__mono,axiom,
    ! [A3: set_set_v,B5: set_set_v] :
      ( ( ord_le5216385588623774835_set_v @ A3 @ B5 )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Union_mono
thf(fact_1079_Union__least,axiom,
    ! [A3: set_se8455005133513928103od_v_v,C2: set_Product_prod_v_v] :
      ( ! [X6: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ X6 @ A3 )
         => ( ord_le7336532860387713383od_v_v @ X6 @ C2 ) )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ C2 ) ) ).

% Union_least
thf(fact_1080_Union__least,axiom,
    ! [A3: set_set_v,C2: set_v] :
      ( ! [X6: set_v] :
          ( ( member_set_v @ X6 @ A3 )
         => ( ord_less_eq_set_v @ X6 @ C2 ) )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ C2 ) ) ).

% Union_least
thf(fact_1081_Union__upper,axiom,
    ! [B5: set_Product_prod_v_v,A3: set_se8455005133513928103od_v_v] :
      ( ( member8406446414694345712od_v_v @ B5 @ A3 )
     => ( ord_le7336532860387713383od_v_v @ B5 @ ( comple5788137035815166516od_v_v @ A3 ) ) ) ).

% Union_upper
thf(fact_1082_Union__upper,axiom,
    ! [B5: set_v,A3: set_set_v] :
      ( ( member_set_v @ B5 @ A3 )
     => ( ord_less_eq_set_v @ B5 @ ( comple2307003700295860064_set_v @ A3 ) ) ) ).

% Union_upper
thf(fact_1083_Union__subsetI,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] :
      ( ! [X4: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ X4 @ A3 )
         => ? [Y6: set_Product_prod_v_v] :
              ( ( member8406446414694345712od_v_v @ Y6 @ B5 )
              & ( ord_le7336532860387713383od_v_v @ X4 @ Y6 ) ) )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Union_subsetI
thf(fact_1084_Union__subsetI,axiom,
    ! [A3: set_set_v,B5: set_set_v] :
      ( ! [X4: set_v] :
          ( ( member_set_v @ X4 @ A3 )
         => ? [Y6: set_v] :
              ( ( member_set_v @ Y6 @ B5 )
              & ( ord_less_eq_set_v @ X4 @ Y6 ) ) )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Union_subsetI
thf(fact_1085_Union__insert,axiom,
    ! [A: set_Product_prod_v_v,B5: set_se8455005133513928103od_v_v] :
      ( ( comple5788137035815166516od_v_v @ ( insert7504383016908236695od_v_v @ A @ B5 ) )
      = ( sup_su414716646722978715od_v_v @ A @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Union_insert
thf(fact_1086_Union__insert,axiom,
    ! [A: set_v,B5: set_set_v] :
      ( ( comple2307003700295860064_set_v @ ( insert_set_v @ A @ B5 ) )
      = ( sup_sup_set_v @ A @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Union_insert
thf(fact_1087_cSup__eq__non__empty,axiom,
    ! [X5: set_se8455005133513928103od_v_v,A: set_Product_prod_v_v] :
      ( ( X5 != bot_bo3497076220358800403od_v_v )
     => ( ! [X4: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X4 @ X5 )
           => ( ord_le7336532860387713383od_v_v @ X4 @ A ) )
       => ( ! [Y3: set_Product_prod_v_v] :
              ( ! [X: set_Product_prod_v_v] :
                  ( ( member8406446414694345712od_v_v @ X @ X5 )
                 => ( ord_le7336532860387713383od_v_v @ X @ Y3 ) )
             => ( ord_le7336532860387713383od_v_v @ A @ Y3 ) )
         => ( ( comple5788137035815166516od_v_v @ X5 )
            = A ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1088_cSup__eq__non__empty,axiom,
    ! [X5: set_set_v,A: set_v] :
      ( ( X5 != bot_bot_set_set_v )
     => ( ! [X4: set_v] :
            ( ( member_set_v @ X4 @ X5 )
           => ( ord_less_eq_set_v @ X4 @ A ) )
       => ( ! [Y3: set_v] :
              ( ! [X: set_v] :
                  ( ( member_set_v @ X @ X5 )
                 => ( ord_less_eq_set_v @ X @ Y3 ) )
             => ( ord_less_eq_set_v @ A @ Y3 ) )
         => ( ( comple2307003700295860064_set_v @ X5 )
            = A ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1089_cSup__eq__non__empty,axiom,
    ! [X5: set_Product_unit,A: product_unit] :
      ( ( X5 != bot_bo3957492148770167129t_unit )
     => ( ! [X4: product_unit] :
            ( ( member_Product_unit @ X4 @ X5 )
           => ( ord_le3221252021190050221t_unit @ X4 @ A ) )
       => ( ! [Y3: product_unit] :
              ( ! [X: product_unit] :
                  ( ( member_Product_unit @ X @ X5 )
                 => ( ord_le3221252021190050221t_unit @ X @ Y3 ) )
             => ( ord_le3221252021190050221t_unit @ A @ Y3 ) )
         => ( ( comple4687483117567863418t_unit @ X5 )
            = A ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1090_cSup__least,axiom,
    ! [X5: set_se8455005133513928103od_v_v,Z: set_Product_prod_v_v] :
      ( ( X5 != bot_bo3497076220358800403od_v_v )
     => ( ! [X4: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X4 @ X5 )
           => ( ord_le7336532860387713383od_v_v @ X4 @ Z ) )
       => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ X5 ) @ Z ) ) ) ).

% cSup_least
thf(fact_1091_cSup__least,axiom,
    ! [X5: set_set_v,Z: set_v] :
      ( ( X5 != bot_bot_set_set_v )
     => ( ! [X4: set_v] :
            ( ( member_set_v @ X4 @ X5 )
           => ( ord_less_eq_set_v @ X4 @ Z ) )
       => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ X5 ) @ Z ) ) ) ).

% cSup_least
thf(fact_1092_cSup__least,axiom,
    ! [X5: set_Product_unit,Z: product_unit] :
      ( ( X5 != bot_bo3957492148770167129t_unit )
     => ( ! [X4: product_unit] :
            ( ( member_Product_unit @ X4 @ X5 )
           => ( ord_le3221252021190050221t_unit @ X4 @ Z ) )
       => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ X5 ) @ Z ) ) ) ).

% cSup_least
thf(fact_1093_less__eq__Sup,axiom,
    ! [A3: set_se8455005133513928103od_v_v,U: set_Product_prod_v_v] :
      ( ! [V: set_Product_prod_v_v] :
          ( ( member8406446414694345712od_v_v @ V @ A3 )
         => ( ord_le7336532860387713383od_v_v @ U @ V ) )
     => ( ( A3 != bot_bo3497076220358800403od_v_v )
       => ( ord_le7336532860387713383od_v_v @ U @ ( comple5788137035815166516od_v_v @ A3 ) ) ) ) ).

% less_eq_Sup
thf(fact_1094_less__eq__Sup,axiom,
    ! [A3: set_set_v,U: set_v] :
      ( ! [V: set_v] :
          ( ( member_set_v @ V @ A3 )
         => ( ord_less_eq_set_v @ U @ V ) )
     => ( ( A3 != bot_bot_set_set_v )
       => ( ord_less_eq_set_v @ U @ ( comple2307003700295860064_set_v @ A3 ) ) ) ) ).

% less_eq_Sup
thf(fact_1095_less__eq__Sup,axiom,
    ! [A3: set_Product_unit,U: product_unit] :
      ( ! [V: product_unit] :
          ( ( member_Product_unit @ V @ A3 )
         => ( ord_le3221252021190050221t_unit @ U @ V ) )
     => ( ( A3 != bot_bo3957492148770167129t_unit )
       => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ A3 ) ) ) ) ).

% less_eq_Sup
thf(fact_1096_Sup__subset__mono,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] :
      ( ( ord_le4714265922333009223od_v_v @ A3 @ B5 )
     => ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Sup_subset_mono
thf(fact_1097_Sup__subset__mono,axiom,
    ! [A3: set_set_v,B5: set_set_v] :
      ( ( ord_le5216385588623774835_set_v @ A3 @ B5 )
     => ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Sup_subset_mono
thf(fact_1098_Sup__subset__mono,axiom,
    ! [A3: set_Product_unit,B5: set_Product_unit] :
      ( ( ord_le3507040750410214029t_unit @ A3 @ B5 )
     => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ A3 ) @ ( comple4687483117567863418t_unit @ B5 ) ) ) ).

% Sup_subset_mono
thf(fact_1099_Union__disjoint,axiom,
    ! [C2: set_se8455005133513928103od_v_v,A3: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ ( comple5788137035815166516od_v_v @ C2 ) @ A3 )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ C2 )
           => ( ( inf_in6271465464967711157od_v_v @ X3 @ A3 )
              = bot_bo723834152578015283od_v_v ) ) ) ) ).

% Union_disjoint
thf(fact_1100_Union__disjoint,axiom,
    ! [C2: set_set_v,A3: set_v] :
      ( ( ( inf_inf_set_v @ ( comple2307003700295860064_set_v @ C2 ) @ A3 )
        = bot_bot_set_v )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ C2 )
           => ( ( inf_inf_set_v @ X3 @ A3 )
              = bot_bot_set_v ) ) ) ) ).

% Union_disjoint
thf(fact_1101_Union__Int__subset,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] : ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ ( inf_in6058586722421118357od_v_v @ A3 @ B5 ) ) @ ( inf_in6271465464967711157od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Union_Int_subset
thf(fact_1102_Union__Int__subset,axiom,
    ! [A3: set_set_v,B5: set_set_v] : ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ ( inf_inf_set_set_v @ A3 @ B5 ) ) @ ( inf_inf_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Union_Int_subset
thf(fact_1103_Sup__inter__less__eq,axiom,
    ! [A3: set_se8455005133513928103od_v_v,B5: set_se8455005133513928103od_v_v] : ( ord_le7336532860387713383od_v_v @ ( comple5788137035815166516od_v_v @ ( inf_in6058586722421118357od_v_v @ A3 @ B5 ) ) @ ( inf_in6271465464967711157od_v_v @ ( comple5788137035815166516od_v_v @ A3 ) @ ( comple5788137035815166516od_v_v @ B5 ) ) ) ).

% Sup_inter_less_eq
thf(fact_1104_Sup__inter__less__eq,axiom,
    ! [A3: set_set_v,B5: set_set_v] : ( ord_less_eq_set_v @ ( comple2307003700295860064_set_v @ ( inf_inf_set_set_v @ A3 @ B5 ) ) @ ( inf_inf_set_v @ ( comple2307003700295860064_set_v @ A3 ) @ ( comple2307003700295860064_set_v @ B5 ) ) ) ).

% Sup_inter_less_eq
thf(fact_1105_Sup__inter__less__eq,axiom,
    ! [A3: set_Product_unit,B5: set_Product_unit] : ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( inf_in4660618365625256667t_unit @ A3 @ B5 ) ) @ ( inf_inf_Product_unit @ ( comple4687483117567863418t_unit @ A3 ) @ ( comple4687483117567863418t_unit @ B5 ) ) ) ).

% Sup_inter_less_eq
thf(fact_1106_graph_Opre__dfss__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,V2: v,E: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl1748261141445803503t_unit @ Successors @ V2 @ E )
        = ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
          & ( member_v @ V2 @ ( sCC_Bl4645233313691564917t_unit @ E ) )
          & ( ( sCC_Bl8828226123343373779t_unit @ E )
           != nil_v )
          & ( member_v @ V2 @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) )
          & ! [X3: v] :
              ( ( member_v @ X3 @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
             => ( member_v @ X3 @ ( sup_sup_set_v @ ( sCC_Bl157864678168468314t_unit @ E ) @ ( sCC_Bl1280885523602775798t_unit @ E @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) ) ) )
          & ! [X3: v] :
              ( ( member_v @ X3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) )
             => ( sCC_Bl649662514949026229able_v @ Successors @ X3 @ V2 ) )
          & ? [Ns: list_v] :
              ( ( sCC_Bl9201514103433284750t_unit @ E )
              = ( cons_v @ V2 @ Ns ) ) ) ) ) ).

% graph.pre_dfss_def
thf(fact_1107_set__union,axiom,
    ! [Xs: list_P7986770385144383213od_v_v,Ys: list_P7986770385144383213od_v_v] :
      ( ( set_Product_prod_v_v2 @ ( union_4602324378607836129od_v_v @ Xs @ Ys ) )
      = ( sup_su414716646722978715od_v_v @ ( set_Product_prod_v_v2 @ Xs ) @ ( set_Product_prod_v_v2 @ Ys ) ) ) ).

% set_union
thf(fact_1108_set__union,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( set_v2 @ ( union_v @ Xs @ Ys ) )
      = ( sup_sup_set_v @ ( set_v2 @ Xs ) @ ( set_v2 @ Ys ) ) ) ).

% set_union
thf(fact_1109_surjective,axiom,
    ! [R: sCC_Bl1394983891496994913t_unit] :
      ( R
      = ( sCC_Bl8064756265740546429t_unit @ ( sCC_Bl1090238580953940555t_unit @ R ) @ ( sCC_Bl1280885523602775798t_unit @ R ) @ ( sCC_Bl157864678168468314t_unit @ R ) @ ( sCC_Bl4645233313691564917t_unit @ R ) @ ( sCC_Bl3795065053823578884t_unit @ R ) @ ( sCC_Bl2536197123907397897t_unit @ R ) @ ( sCC_Bl8828226123343373779t_unit @ R ) @ ( sCC_Bl9201514103433284750t_unit @ R ) @ ( sCC_Bl3567736435408124606t_unit @ R ) ) ) ).

% surjective
thf(fact_1110_avoiding__explored,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,X2: v,Y: v,E5: set_Product_prod_v_v,W: v,V2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
       => ( ~ ( member_v @ Y @ ( sCC_Bl157864678168468314t_unit @ E ) )
         => ( ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
           => ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) ) ) ) ) ) ).

% avoiding_explored
thf(fact_1111_insert__partition,axiom,
    ! [X2: set_Product_prod_v_v,F2: set_se8455005133513928103od_v_v] :
      ( ~ ( member8406446414694345712od_v_v @ X2 @ F2 )
     => ( ! [X4: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X4 @ ( insert7504383016908236695od_v_v @ X2 @ F2 ) )
           => ! [Xa2: set_Product_prod_v_v] :
                ( ( member8406446414694345712od_v_v @ Xa2 @ ( insert7504383016908236695od_v_v @ X2 @ F2 ) )
               => ( ( X4 != Xa2 )
                 => ( ( inf_in6271465464967711157od_v_v @ X4 @ Xa2 )
                    = bot_bo723834152578015283od_v_v ) ) ) )
       => ( ( inf_in6271465464967711157od_v_v @ X2 @ ( comple5788137035815166516od_v_v @ F2 ) )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% insert_partition
thf(fact_1112_insert__partition,axiom,
    ! [X2: set_v,F2: set_set_v] :
      ( ~ ( member_set_v @ X2 @ F2 )
     => ( ! [X4: set_v] :
            ( ( member_set_v @ X4 @ ( insert_set_v @ X2 @ F2 ) )
           => ! [Xa2: set_v] :
                ( ( member_set_v @ Xa2 @ ( insert_set_v @ X2 @ F2 ) )
               => ( ( X4 != Xa2 )
                 => ( ( inf_inf_set_v @ X4 @ Xa2 )
                    = bot_bot_set_v ) ) ) )
       => ( ( inf_inf_set_v @ X2 @ ( comple2307003700295860064_set_v @ F2 ) )
          = bot_bot_set_v ) ) ) ).

% insert_partition
thf(fact_1113_ra__mono,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v,E6: set_Product_prod_v_v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( ( ord_le7336532860387713383od_v_v @ E6 @ E5 )
       => ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E6 ) ) ) ).

% ra_mono
thf(fact_1114_ra__refl,axiom,
    ! [X2: v,E5: set_Product_prod_v_v] : ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ X2 @ E5 ) ).

% ra_refl
thf(fact_1115_ra__trans,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v,Z: v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( ( sCC_Bl4291963740693775144ding_v @ successors @ Y @ Z @ E5 )
       => ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Z @ E5 ) ) ) ).

% ra_trans
thf(fact_1116_ra__reachable,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y ) ) ).

% ra_reachable
thf(fact_1117_ra__cases,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( ( X2 = Y )
        | ? [Z2: v] :
            ( ( member_v @ Z2 @ ( successors @ X2 ) )
            & ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ X2 @ Z2 ) @ E5 )
            & ( sCC_Bl4291963740693775144ding_v @ successors @ Z2 @ Y @ E5 ) ) ) ) ).

% ra_cases
thf(fact_1118_edge__ra,axiom,
    ! [Y: v,X2: v,E5: set_Product_prod_v_v] :
      ( ( member_v @ Y @ ( successors @ X2 ) )
     => ( ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ X2 @ Y ) @ E5 )
       => ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 ) ) ) ).

% edge_ra
thf(fact_1119_reachable__avoiding_Osimps,axiom,
    ! [A1: v,A22: v,A32: set_Product_prod_v_v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ A1 @ A22 @ A32 )
      = ( ? [X3: v,E7: set_Product_prod_v_v] :
            ( ( A1 = X3 )
            & ( A22 = X3 )
            & ( A32 = E7 ) )
        | ? [X3: v,Y4: v,E7: set_Product_prod_v_v,Z4: v] :
            ( ( A1 = X3 )
            & ( A22 = Z4 )
            & ( A32 = E7 )
            & ( sCC_Bl4291963740693775144ding_v @ successors @ X3 @ Y4 @ E7 )
            & ( member_v @ Z4 @ ( successors @ Y4 ) )
            & ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y4 @ Z4 ) @ E7 ) ) ) ) ).

% reachable_avoiding.simps
thf(fact_1120_ra__succ,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v,Z: v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( ( member_v @ Z @ ( successors @ Y ) )
       => ( ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y @ Z ) @ E5 )
         => ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Z @ E5 ) ) ) ) ).

% ra_succ
thf(fact_1121_reachable__avoiding_Ocases,axiom,
    ! [A1: v,A22: v,A32: set_Product_prod_v_v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ A1 @ A22 @ A32 )
     => ( ( A22 != A1 )
       => ~ ! [Y3: v] :
              ( ( sCC_Bl4291963740693775144ding_v @ successors @ A1 @ Y3 @ A32 )
             => ( ( member_v @ A22 @ ( successors @ Y3 ) )
               => ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y3 @ A22 ) @ A32 ) ) ) ) ) ).

% reachable_avoiding.cases
thf(fact_1122_ra__empty,axiom,
    ! [X2: v,Y: v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ bot_bo723834152578015283od_v_v )
      = ( sCC_Bl649662514949026229able_v @ successors @ X2 @ Y ) ) ).

% ra_empty
thf(fact_1123_ra__add__edge,axiom,
    ! [X2: v,Y: v,E5: set_Product_prod_v_v,V2: v,W: v] :
      ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ E5 )
     => ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) )
        | ( ( sCC_Bl4291963740693775144ding_v @ successors @ X2 @ V2 @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) )
          & ( sCC_Bl4291963740693775144ding_v @ successors @ W @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) ) ) ) ) ).

% ra_add_edge
thf(fact_1124_distinct__union,axiom,
    ! [Xs: list_v,Ys: list_v] :
      ( ( distinct_v @ ( union_v @ Xs @ Ys ) )
      = ( distinct_v @ Ys ) ) ).

% distinct_union
thf(fact_1125_select__convs_I7_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Stack ) ).

% select_convs(7)
thf(fact_1126_select__convs_I2_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = S4 ) ).

% select_convs(2)
thf(fact_1127_select__convs_I4_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl4645233313691564917t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Visited ) ).

% select_convs(4)
thf(fact_1128_select__convs_I5_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl3795065053823578884t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Vsuccs ) ).

% select_convs(5)
thf(fact_1129_select__convs_I3_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl157864678168468314t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Explored ) ).

% select_convs(3)
thf(fact_1130_graph_Oreachable__avoiding_Ocong,axiom,
    sCC_Bl4291963740693775144ding_v = sCC_Bl4291963740693775144ding_v ).

% graph.reachable_avoiding.cong
thf(fact_1131_select__convs_I8_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl9201514103433284750t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Cstack ) ).

% select_convs(8)
thf(fact_1132_graph_Ora__trans,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ Y @ Z @ E5 )
         => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Z @ E5 ) ) ) ) ).

% graph.ra_trans
thf(fact_1133_graph_Ora__refl,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ X2 @ E5 ) ) ).

% graph.ra_refl
thf(fact_1134_graph_Ora__mono,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v,E6: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( ( ord_le7336532860387713383od_v_v @ E6 @ E5 )
         => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E6 ) ) ) ) ).

% graph.ra_mono
thf(fact_1135_select__convs_I1_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl1090238580953940555t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Root ) ).

% select_convs(1)
thf(fact_1136_select__convs_I6_J,axiom,
    ! [Root: v,S4: v > set_v,Explored: set_v,Visited: set_v,Vsuccs: v > set_v,Sccs: set_set_v,Stack: list_v,Cstack: list_v,More: product_unit] :
      ( ( sCC_Bl2536197123907397897t_unit @ ( sCC_Bl8064756265740546429t_unit @ Root @ S4 @ Explored @ Visited @ Vsuccs @ Sccs @ Stack @ Cstack @ More ) )
      = Sccs ) ).

% select_convs(6)
thf(fact_1137_graph_Ora__add__edge,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v,V2: v,W: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) )
          | ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ V2 @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) )
            & ( sCC_Bl4291963740693775144ding_v @ Successors @ W @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) ) ) ) ) ) ).

% graph.ra_add_edge
thf(fact_1138_graph_Ora__succ,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v,E5: set_Pr2149350503807050951od_v_v,Z: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl5370300055464682748od_v_v @ Successors @ X2 @ Y @ E5 )
       => ( ( member7453568604450474000od_v_v @ Z @ ( Successors @ Y ) )
         => ( ~ ( member3038538357316246288od_v_v @ ( produc4031800376763917143od_v_v @ Y @ Z ) @ E5 )
           => ( sCC_Bl5370300055464682748od_v_v @ Successors @ X2 @ Z @ E5 ) ) ) ) ) ).

% graph.ra_succ
thf(fact_1139_graph_Ora__succ,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v,Z: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( ( member_v @ Z @ ( Successors @ Y ) )
         => ( ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y @ Z ) @ E5 )
           => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Z @ E5 ) ) ) ) ) ).

% graph.ra_succ
thf(fact_1140_graph_Oreachable__avoiding_Osimps,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v,A32: set_Pr2149350503807050951od_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl5370300055464682748od_v_v @ Successors @ A1 @ A22 @ A32 )
        = ( ? [X3: product_prod_v_v,E7: set_Pr2149350503807050951od_v_v] :
              ( ( A1 = X3 )
              & ( A22 = X3 )
              & ( A32 = E7 ) )
          | ? [X3: product_prod_v_v,Y4: product_prod_v_v,E7: set_Pr2149350503807050951od_v_v,Z4: product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( A32 = E7 )
              & ( sCC_Bl5370300055464682748od_v_v @ Successors @ X3 @ Y4 @ E7 )
              & ( member7453568604450474000od_v_v @ Z4 @ ( Successors @ Y4 ) )
              & ~ ( member3038538357316246288od_v_v @ ( produc4031800376763917143od_v_v @ Y4 @ Z4 ) @ E7 ) ) ) ) ) ).

% graph.reachable_avoiding.simps
thf(fact_1141_graph_Oreachable__avoiding_Osimps,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v,A32: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ A1 @ A22 @ A32 )
        = ( ? [X3: v,E7: set_Product_prod_v_v] :
              ( ( A1 = X3 )
              & ( A22 = X3 )
              & ( A32 = E7 ) )
          | ? [X3: v,Y4: v,E7: set_Product_prod_v_v,Z4: v] :
              ( ( A1 = X3 )
              & ( A22 = Z4 )
              & ( A32 = E7 )
              & ( sCC_Bl4291963740693775144ding_v @ Successors @ X3 @ Y4 @ E7 )
              & ( member_v @ Z4 @ ( Successors @ Y4 ) )
              & ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y4 @ Z4 ) @ E7 ) ) ) ) ) ).

% graph.reachable_avoiding.simps
thf(fact_1142_graph_Oreachable__avoiding_Ocases,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,A1: product_prod_v_v,A22: product_prod_v_v,A32: set_Pr2149350503807050951od_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl5370300055464682748od_v_v @ Successors @ A1 @ A22 @ A32 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: product_prod_v_v] :
                ( ( sCC_Bl5370300055464682748od_v_v @ Successors @ A1 @ Y3 @ A32 )
               => ( ( member7453568604450474000od_v_v @ A22 @ ( Successors @ Y3 ) )
                 => ( member3038538357316246288od_v_v @ ( produc4031800376763917143od_v_v @ Y3 @ A22 ) @ A32 ) ) ) ) ) ) ).

% graph.reachable_avoiding.cases
thf(fact_1143_graph_Oreachable__avoiding_Ocases,axiom,
    ! [Vertices: set_v,Successors: v > set_v,A1: v,A22: v,A32: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ A1 @ A22 @ A32 )
       => ( ( A22 != A1 )
         => ~ ! [Y3: v] :
                ( ( sCC_Bl4291963740693775144ding_v @ Successors @ A1 @ Y3 @ A32 )
               => ( ( member_v @ A22 @ ( Successors @ Y3 ) )
                 => ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ Y3 @ A22 ) @ A32 ) ) ) ) ) ) ).

% graph.reachable_avoiding.cases
thf(fact_1144_graph_Ora__cases,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,X2: product_prod_v_v,Y: product_prod_v_v,E5: set_Pr2149350503807050951od_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl5370300055464682748od_v_v @ Successors @ X2 @ Y @ E5 )
       => ( ( X2 = Y )
          | ? [Z2: product_prod_v_v] :
              ( ( member7453568604450474000od_v_v @ Z2 @ ( Successors @ X2 ) )
              & ~ ( member3038538357316246288od_v_v @ ( produc4031800376763917143od_v_v @ X2 @ Z2 ) @ E5 )
              & ( sCC_Bl5370300055464682748od_v_v @ Successors @ Z2 @ Y @ E5 ) ) ) ) ) ).

% graph.ra_cases
thf(fact_1145_graph_Ora__cases,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( ( X2 = Y )
          | ? [Z2: v] :
              ( ( member_v @ Z2 @ ( Successors @ X2 ) )
              & ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ X2 @ Z2 ) @ E5 )
              & ( sCC_Bl4291963740693775144ding_v @ Successors @ Z2 @ Y @ E5 ) ) ) ) ) ).

% graph.ra_cases
thf(fact_1146_graph_Oedge__ra,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,Y: product_prod_v_v,X2: product_prod_v_v,E5: set_Pr2149350503807050951od_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( member7453568604450474000od_v_v @ Y @ ( Successors @ X2 ) )
       => ( ~ ( member3038538357316246288od_v_v @ ( produc4031800376763917143od_v_v @ X2 @ Y ) @ E5 )
         => ( sCC_Bl5370300055464682748od_v_v @ Successors @ X2 @ Y @ E5 ) ) ) ) ).

% graph.edge_ra
thf(fact_1147_graph_Oedge__ra,axiom,
    ! [Vertices: set_v,Successors: v > set_v,Y: v,X2: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( member_v @ Y @ ( Successors @ X2 ) )
       => ( ~ ( member7453568604450474000od_v_v @ ( product_Pair_v_v @ X2 @ Y ) @ E5 )
         => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 ) ) ) ) ).

% graph.edge_ra
thf(fact_1148_graph_Ora__empty,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ bot_bo723834152578015283od_v_v )
        = ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y ) ) ) ).

% graph.ra_empty
thf(fact_1149_graph_Ora__reachable,axiom,
    ! [Vertices: set_v,Successors: v > set_v,X2: v,Y: v,E5: set_Product_prod_v_v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
       => ( sCC_Bl649662514949026229able_v @ Successors @ X2 @ Y ) ) ) ).

% graph.ra_reachable
thf(fact_1150_graph_Oavoiding__explored,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,X2: v,Y: v,E5: set_Product_prod_v_v,W: v,V2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ E5 )
         => ( ~ ( member_v @ Y @ ( sCC_Bl157864678168468314t_unit @ E ) )
           => ( ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
             => ( sCC_Bl4291963740693775144ding_v @ Successors @ X2 @ Y @ ( sup_su414716646722978715od_v_v @ E5 @ ( insert1338601472111419319od_v_v @ ( product_Pair_v_v @ V2 @ W ) @ bot_bo723834152578015283od_v_v ) ) ) ) ) ) ) ) ).

% graph.avoiding_explored
thf(fact_1151_Sup__inf__eq__bot__iff,axiom,
    ! [B5: set_se8455005133513928103od_v_v,A: set_Product_prod_v_v] :
      ( ( ( inf_in6271465464967711157od_v_v @ ( comple5788137035815166516od_v_v @ B5 ) @ A )
        = bot_bo723834152578015283od_v_v )
      = ( ! [X3: set_Product_prod_v_v] :
            ( ( member8406446414694345712od_v_v @ X3 @ B5 )
           => ( ( inf_in6271465464967711157od_v_v @ X3 @ A )
              = bot_bo723834152578015283od_v_v ) ) ) ) ).

% Sup_inf_eq_bot_iff
thf(fact_1152_Sup__inf__eq__bot__iff,axiom,
    ! [B5: set_set_v,A: set_v] :
      ( ( ( inf_inf_set_v @ ( comple2307003700295860064_set_v @ B5 ) @ A )
        = bot_bot_set_v )
      = ( ! [X3: set_v] :
            ( ( member_set_v @ X3 @ B5 )
           => ( ( inf_inf_set_v @ X3 @ A )
              = bot_bot_set_v ) ) ) ) ).

% Sup_inf_eq_bot_iff
thf(fact_1153_Sup__inf__eq__bot__iff,axiom,
    ! [B5: set_Product_unit,A: product_unit] :
      ( ( ( inf_inf_Product_unit @ ( comple4687483117567863418t_unit @ B5 ) @ A )
        = bot_bot_Product_unit )
      = ( ! [X3: product_unit] :
            ( ( member_Product_unit @ X3 @ B5 )
           => ( ( inf_inf_Product_unit @ X3 @ A )
              = bot_bot_Product_unit ) ) ) ) ).

% Sup_inf_eq_bot_iff
thf(fact_1154_cc__def,axiom,
    ( cc
    = ( comple2307003700295860064_set_v
      @ ( collect_set_v
        @ ^ [Uu: set_v] :
          ? [N4: v] :
            ( ( Uu
              = ( sCC_Bl1280885523602775798t_unit @ e @ N4 ) )
            & ( member_v @ N4 @ ( sup_sup_set_v @ ( set_v2 @ pfx ) @ ( insert_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ bot_bot_set_v ) ) ) ) ) ) ) ).

% cc_def
thf(fact_1155_cc__Un,axiom,
    ( cc
    = ( comple2307003700295860064_set_v
      @ ( collect_set_v
        @ ^ [Uu: set_v] :
          ? [X3: v] :
            ( ( Uu
              = ( sCC_Bl1280885523602775798t_unit @ e @ X3 ) )
            & ( member_v @ X3 @ cc ) ) ) ) ) ).

% cc_Un
thf(fact_1156_unvisited__def,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,U: v] :
      ( ( sCC_Bl3123350270117520219t_unit @ successors @ E @ U )
      = ( collec140062887454715474od_v_v
        @ ^ [Uu: product_prod_v_v] :
          ? [A5: v,B4: v] :
            ( ( Uu
              = ( product_Pair_v_v @ A5 @ B4 ) )
            & ( member_v @ A5 @ ( sCC_Bl1280885523602775798t_unit @ E @ U ) )
            & ( member_v @ B4 @ ( minus_minus_set_v @ ( successors @ A5 ) @ ( sCC_Bl3795065053823578884t_unit @ E @ A5 ) ) ) ) ) ) ).

% unvisited_def
thf(fact_1157_pfx_I3_J,axiom,
    ( ( sCC_Bl1280885523602775798t_unit @ e2 )
    = ( ^ [X3: v] :
          ( if_set_v
          @ ( member_v @ X3
            @ ( comple2307003700295860064_set_v
              @ ( collect_set_v
                @ ^ [Uu: set_v] :
                  ? [N4: v] :
                    ( ( Uu
                      = ( sCC_Bl1280885523602775798t_unit @ e @ N4 ) )
                    & ( member_v @ N4 @ ( sup_sup_set_v @ ( set_v2 @ pfx ) @ ( insert_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ bot_bot_set_v ) ) ) ) ) ) )
          @ ( comple2307003700295860064_set_v
            @ ( collect_set_v
              @ ^ [Uu: set_v] :
                ? [N4: v] :
                  ( ( Uu
                    = ( sCC_Bl1280885523602775798t_unit @ e @ N4 ) )
                  & ( member_v @ N4 @ ( sup_sup_set_v @ ( set_v2 @ pfx ) @ ( insert_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ bot_bot_set_v ) ) ) ) ) )
          @ ( sCC_Bl1280885523602775798t_unit @ e @ X3 ) ) ) ) ).

% pfx(3)
thf(fact_1158_singleton__conv2,axiom,
    ! [A: set_v] :
      ( ( collect_set_v
        @ ( ^ [Y5: set_v,Z3: set_v] : ( Y5 = Z3 )
          @ A ) )
      = ( insert_set_v @ A @ bot_bot_set_set_v ) ) ).

% singleton_conv2
thf(fact_1159_singleton__conv2,axiom,
    ! [A: v] :
      ( ( collect_v
        @ ( ^ [Y5: v,Z3: v] : ( Y5 = Z3 )
          @ A ) )
      = ( insert_v @ A @ bot_bot_set_v ) ) ).

% singleton_conv2
thf(fact_1160_singleton__conv2,axiom,
    ! [A: product_prod_v_v] :
      ( ( collec140062887454715474od_v_v
        @ ( ^ [Y5: product_prod_v_v,Z3: product_prod_v_v] : ( Y5 = Z3 )
          @ A ) )
      = ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) ).

% singleton_conv2
thf(fact_1161_singleton__conv,axiom,
    ! [A: set_v] :
      ( ( collect_set_v
        @ ^ [X3: set_v] : ( X3 = A ) )
      = ( insert_set_v @ A @ bot_bot_set_set_v ) ) ).

% singleton_conv
thf(fact_1162_singleton__conv,axiom,
    ! [A: v] :
      ( ( collect_v
        @ ^ [X3: v] : ( X3 = A ) )
      = ( insert_v @ A @ bot_bot_set_v ) ) ).

% singleton_conv
thf(fact_1163_singleton__conv,axiom,
    ! [A: product_prod_v_v] :
      ( ( collec140062887454715474od_v_v
        @ ^ [X3: product_prod_v_v] : ( X3 = A ) )
      = ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) ).

% singleton_conv
thf(fact_1164_calculation_I18_J,axiom,
    ( ( comple2307003700295860064_set_v
      @ ( collect_set_v
        @ ^ [Uu: set_v] :
          ? [N4: v] :
            ( ( Uu
              = ( sCC_Bl1280885523602775798t_unit @ e2 @ N4 ) )
            & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) ) ) )
    = ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ e2 ) @ ( sCC_Bl157864678168468314t_unit @ e2 ) ) ) ).

% calculation(18)
thf(fact_1165_sub__env__def,axiom,
    ( sCC_Bl5768913643336123637t_unit
    = ( ^ [E8: sCC_Bl1394983891496994913t_unit,E9: sCC_Bl1394983891496994913t_unit] :
          ( ( ( sCC_Bl1090238580953940555t_unit @ E9 )
            = ( sCC_Bl1090238580953940555t_unit @ E8 ) )
          & ( ord_less_eq_set_v @ ( sCC_Bl4645233313691564917t_unit @ E8 ) @ ( sCC_Bl4645233313691564917t_unit @ E9 ) )
          & ( ord_less_eq_set_v @ ( sCC_Bl157864678168468314t_unit @ E8 ) @ ( sCC_Bl157864678168468314t_unit @ E9 ) )
          & ! [V3: v] : ( ord_less_eq_set_v @ ( sCC_Bl3795065053823578884t_unit @ E8 @ V3 ) @ ( sCC_Bl3795065053823578884t_unit @ E9 @ V3 ) )
          & ! [V3: v] : ( ord_less_eq_set_v @ ( sCC_Bl1280885523602775798t_unit @ E8 @ V3 ) @ ( sCC_Bl1280885523602775798t_unit @ E9 @ V3 ) )
          & ( ord_less_eq_set_v
            @ ( comple2307003700295860064_set_v
              @ ( collect_set_v
                @ ^ [Uu: set_v] :
                  ? [V3: v] :
                    ( ( Uu
                      = ( sCC_Bl1280885523602775798t_unit @ E8 @ V3 ) )
                    & ( member_v @ V3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E8 ) ) ) ) ) )
            @ ( comple2307003700295860064_set_v
              @ ( collect_set_v
                @ ^ [Uu: set_v] :
                  ? [V3: v] :
                    ( ( Uu
                      = ( sCC_Bl1280885523602775798t_unit @ E9 @ V3 ) )
                    & ( member_v @ V3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E9 ) ) ) ) ) ) ) ) ) ) ).

% sub_env_def
thf(fact_1166__092_060open_062_092_060Union_062_A_123_092_060S_062_Ae_H_An_A_124n_O_An_A_092_060in_062_Aset_A_Istack_Ae_H_J_125_A_061_Avisited_Ae_A_N_Aexplored_Ae_092_060close_062,axiom,
    ( ( comple2307003700295860064_set_v
      @ ( collect_set_v
        @ ^ [Uu: set_v] :
          ? [N4: v] :
            ( ( Uu
              = ( sCC_Bl1280885523602775798t_unit @ e2 @ N4 ) )
            & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) ) ) ) )
    = ( minus_minus_set_v @ ( sCC_Bl4645233313691564917t_unit @ e ) @ ( sCC_Bl157864678168468314t_unit @ e ) ) ) ).

% \<open>\<Union> {\<S> e' n |n. n \<in> set (stack e')} = visited e - explored e\<close>
thf(fact_1167_unite__S__equal,axiom,
    ! [E: sCC_Bl1394983891496994913t_unit,W: v,V2: v] :
      ( ( sCC_Bl9196236973127232072t_unit @ successors @ E )
     => ( ( member_v @ W @ ( successors @ V2 ) )
       => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
         => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
           => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
             => ( ( comple2307003700295860064_set_v
                  @ ( collect_set_v
                    @ ^ [Uu: set_v] :
                      ? [N4: v] :
                        ( ( Uu
                          = ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ N4 ) )
                        & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) )
                = ( comple2307003700295860064_set_v
                  @ ( collect_set_v
                    @ ^ [Uu: set_v] :
                      ? [N4: v] :
                        ( ( Uu
                          = ( sCC_Bl1280885523602775798t_unit @ E @ N4 ) )
                        & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) ) ) ) ) ) ) ) ) ) ).

% unite_S_equal
thf(fact_1168__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pfx_O_A_092_060lbrakk_062stack_Ae_A_061_Apfx_A_064_Astack_Ae_H_059_Astack_Ae_H_A_092_060noteq_062_A_091_093_059_Alet_Acc_A_061_A_092_060Union_062_A_123_092_060S_062_Ae_An_A_124n_O_An_A_092_060in_062_Aset_Apfx_A_092_060union_062_A_123hd_A_Istack_Ae_H_J_125_125_Ain_A_092_060S_062_Ae_H_A_061_A_I_092_060lambda_062x_O_Aif_Ax_A_092_060in_062_Acc_Athen_Acc_Aelse_A_092_060S_062_Ae_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Pfx: list_v] :
        ( ( ( sCC_Bl8828226123343373779t_unit @ e )
          = ( append_v @ Pfx @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) )
       => ( ( ( sCC_Bl8828226123343373779t_unit @ e2 )
           != nil_v )
         => ( ( sCC_Bl1280885523602775798t_unit @ e2 )
           != ( ^ [X3: v] :
                  ( if_set_v
                  @ ( member_v @ X3
                    @ ( comple2307003700295860064_set_v
                      @ ( collect_set_v
                        @ ^ [Uu: set_v] :
                          ? [N4: v] :
                            ( ( Uu
                              = ( sCC_Bl1280885523602775798t_unit @ e @ N4 ) )
                            & ( member_v @ N4 @ ( sup_sup_set_v @ ( set_v2 @ Pfx ) @ ( insert_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ bot_bot_set_v ) ) ) ) ) ) )
                  @ ( comple2307003700295860064_set_v
                    @ ( collect_set_v
                      @ ^ [Uu: set_v] :
                        ? [N4: v] :
                          ( ( Uu
                            = ( sCC_Bl1280885523602775798t_unit @ e @ N4 ) )
                          & ( member_v @ N4 @ ( sup_sup_set_v @ ( set_v2 @ Pfx ) @ ( insert_v @ ( hd_v @ ( sCC_Bl8828226123343373779t_unit @ e2 ) ) @ bot_bot_set_v ) ) ) ) ) )
                  @ ( sCC_Bl1280885523602775798t_unit @ e @ X3 ) ) ) ) ) ) ).

% \<open>\<And>thesis. (\<And>pfx. \<lbrakk>stack e = pfx @ stack e'; stack e' \<noteq> []; let cc = \<Union> {\<S> e n |n. n \<in> set pfx \<union> {hd (stack e')}} in \<S> e' = (\<lambda>x. if x \<in> cc then cc else \<S> e x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_1169_Collect__disj__eq,axiom,
    ! [P: set_v > $o,Q: set_v > $o] :
      ( ( collect_set_v
        @ ^ [X3: set_v] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_set_v @ ( collect_set_v @ P ) @ ( collect_set_v @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1170_Collect__disj__eq,axiom,
    ! [P: product_prod_v_v > $o,Q: product_prod_v_v > $o] :
      ( ( collec140062887454715474od_v_v
        @ ^ [X3: product_prod_v_v] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_su414716646722978715od_v_v @ ( collec140062887454715474od_v_v @ P ) @ ( collec140062887454715474od_v_v @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1171_Collect__disj__eq,axiom,
    ! [P: v > $o,Q: v > $o] :
      ( ( collect_v
        @ ^ [X3: v] :
            ( ( P @ X3 )
            | ( Q @ X3 ) ) )
      = ( sup_sup_set_v @ ( collect_v @ P ) @ ( collect_v @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_1172_sup__set__def,axiom,
    ( sup_sup_set_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ( sup_sup_set_v_o
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ A6 )
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% sup_set_def
thf(fact_1173_sup__set__def,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ( sup_su5941406310530359554_v_v_o
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A6 )
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% sup_set_def
thf(fact_1174_sup__set__def,axiom,
    ( sup_sup_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ( sup_sup_v_o
            @ ^ [X3: v] : ( member_v @ X3 @ A6 )
            @ ^ [X3: v] : ( member_v @ X3 @ B6 ) ) ) ) ) ).

% sup_set_def
thf(fact_1175_Un__def,axiom,
    ( sup_sup_set_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ^ [X3: set_v] :
              ( ( member_set_v @ X3 @ A6 )
              | ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% Un_def
thf(fact_1176_Un__def,axiom,
    ( sup_su414716646722978715od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ^ [X3: product_prod_v_v] :
              ( ( member7453568604450474000od_v_v @ X3 @ A6 )
              | ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% Un_def
thf(fact_1177_Un__def,axiom,
    ( sup_sup_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ^ [X3: v] :
              ( ( member_v @ X3 @ A6 )
              | ( member_v @ X3 @ B6 ) ) ) ) ) ).

% Un_def
thf(fact_1178_insert__def,axiom,
    ( insert_set_v
    = ( ^ [A5: set_v] :
          ( sup_sup_set_set_v
          @ ( collect_set_v
            @ ^ [X3: set_v] : ( X3 = A5 ) ) ) ) ) ).

% insert_def
thf(fact_1179_insert__def,axiom,
    ( insert1338601472111419319od_v_v
    = ( ^ [A5: product_prod_v_v] :
          ( sup_su414716646722978715od_v_v
          @ ( collec140062887454715474od_v_v
            @ ^ [X3: product_prod_v_v] : ( X3 = A5 ) ) ) ) ) ).

% insert_def
thf(fact_1180_insert__def,axiom,
    ( insert_v
    = ( ^ [A5: v] :
          ( sup_sup_set_v
          @ ( collect_v
            @ ^ [X3: v] : ( X3 = A5 ) ) ) ) ) ).

% insert_def
thf(fact_1181_less__eq__set__def,axiom,
    ( ord_less_eq_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( ord_less_eq_v_o
          @ ^ [X3: v] : ( member_v @ X3 @ A6 )
          @ ^ [X3: v] : ( member_v @ X3 @ B6 ) ) ) ) ).

% less_eq_set_def
thf(fact_1182_less__eq__set__def,axiom,
    ( ord_le7336532860387713383od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( ord_le5892402249245633078_v_v_o
          @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A6 )
          @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ).

% less_eq_set_def
thf(fact_1183_Collect__subset,axiom,
    ! [A3: set_set_v,P: set_v > $o] :
      ( ord_le5216385588623774835_set_v
      @ ( collect_set_v
        @ ^ [X3: set_v] :
            ( ( member_set_v @ X3 @ A3 )
            & ( P @ X3 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_1184_Collect__subset,axiom,
    ! [A3: set_v,P: v > $o] :
      ( ord_less_eq_set_v
      @ ( collect_v
        @ ^ [X3: v] :
            ( ( member_v @ X3 @ A3 )
            & ( P @ X3 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_1185_Collect__subset,axiom,
    ! [A3: set_Product_prod_v_v,P: product_prod_v_v > $o] :
      ( ord_le7336532860387713383od_v_v
      @ ( collec140062887454715474od_v_v
        @ ^ [X3: product_prod_v_v] :
            ( ( member7453568604450474000od_v_v @ X3 @ A3 )
            & ( P @ X3 ) ) )
      @ A3 ) ).

% Collect_subset
thf(fact_1186_insert__compr,axiom,
    ( insert_v
    = ( ^ [A5: v,B6: set_v] :
          ( collect_v
          @ ^ [X3: v] :
              ( ( X3 = A5 )
              | ( member_v @ X3 @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_1187_insert__compr,axiom,
    ( insert1338601472111419319od_v_v
    = ( ^ [A5: product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ^ [X3: product_prod_v_v] :
              ( ( X3 = A5 )
              | ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_1188_insert__compr,axiom,
    ( insert_set_v
    = ( ^ [A5: set_v,B6: set_set_v] :
          ( collect_set_v
          @ ^ [X3: set_v] :
              ( ( X3 = A5 )
              | ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% insert_compr
thf(fact_1189_insert__Collect,axiom,
    ! [A: v,P: v > $o] :
      ( ( insert_v @ A @ ( collect_v @ P ) )
      = ( collect_v
        @ ^ [U2: v] :
            ( ( U2 != A )
           => ( P @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_1190_insert__Collect,axiom,
    ! [A: product_prod_v_v,P: product_prod_v_v > $o] :
      ( ( insert1338601472111419319od_v_v @ A @ ( collec140062887454715474od_v_v @ P ) )
      = ( collec140062887454715474od_v_v
        @ ^ [U2: product_prod_v_v] :
            ( ( U2 != A )
           => ( P @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_1191_insert__Collect,axiom,
    ! [A: set_v,P: set_v > $o] :
      ( ( insert_set_v @ A @ ( collect_set_v @ P ) )
      = ( collect_set_v
        @ ^ [U2: set_v] :
            ( ( U2 != A )
           => ( P @ U2 ) ) ) ) ).

% insert_Collect
thf(fact_1192_Int__def,axiom,
    ( inf_in6271465464967711157od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ^ [X3: product_prod_v_v] :
              ( ( member7453568604450474000od_v_v @ X3 @ A6 )
              & ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% Int_def
thf(fact_1193_Int__def,axiom,
    ( inf_inf_set_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ^ [X3: set_v] :
              ( ( member_set_v @ X3 @ A6 )
              & ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% Int_def
thf(fact_1194_Int__def,axiom,
    ( inf_inf_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ^ [X3: v] :
              ( ( member_v @ X3 @ A6 )
              & ( member_v @ X3 @ B6 ) ) ) ) ) ).

% Int_def
thf(fact_1195_Int__Collect,axiom,
    ! [X2: product_prod_v_v,A3: set_Product_prod_v_v,P: product_prod_v_v > $o] :
      ( ( member7453568604450474000od_v_v @ X2 @ ( inf_in6271465464967711157od_v_v @ A3 @ ( collec140062887454715474od_v_v @ P ) ) )
      = ( ( member7453568604450474000od_v_v @ X2 @ A3 )
        & ( P @ X2 ) ) ) ).

% Int_Collect
thf(fact_1196_Int__Collect,axiom,
    ! [X2: set_v,A3: set_set_v,P: set_v > $o] :
      ( ( member_set_v @ X2 @ ( inf_inf_set_set_v @ A3 @ ( collect_set_v @ P ) ) )
      = ( ( member_set_v @ X2 @ A3 )
        & ( P @ X2 ) ) ) ).

% Int_Collect
thf(fact_1197_Int__Collect,axiom,
    ! [X2: v,A3: set_v,P: v > $o] :
      ( ( member_v @ X2 @ ( inf_inf_set_v @ A3 @ ( collect_v @ P ) ) )
      = ( ( member_v @ X2 @ A3 )
        & ( P @ X2 ) ) ) ).

% Int_Collect
thf(fact_1198_inf__set__def,axiom,
    ( inf_in6271465464967711157od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ( inf_in6860806757119575912_v_v_o
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A6 )
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% inf_set_def
thf(fact_1199_inf__set__def,axiom,
    ( inf_inf_set_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ( inf_inf_set_v_o
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ A6 )
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% inf_set_def
thf(fact_1200_inf__set__def,axiom,
    ( inf_inf_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ( inf_inf_v_o
            @ ^ [X3: v] : ( member_v @ X3 @ A6 )
            @ ^ [X3: v] : ( member_v @ X3 @ B6 ) ) ) ) ) ).

% inf_set_def
thf(fact_1201_Collect__conj__eq,axiom,
    ! [P: set_v > $o,Q: set_v > $o] :
      ( ( collect_set_v
        @ ^ [X3: set_v] :
            ( ( P @ X3 )
            & ( Q @ X3 ) ) )
      = ( inf_inf_set_set_v @ ( collect_set_v @ P ) @ ( collect_set_v @ Q ) ) ) ).

% Collect_conj_eq
thf(fact_1202_Collect__conj__eq,axiom,
    ! [P: v > $o,Q: v > $o] :
      ( ( collect_v
        @ ^ [X3: v] :
            ( ( P @ X3 )
            & ( Q @ X3 ) ) )
      = ( inf_inf_set_v @ ( collect_v @ P ) @ ( collect_v @ Q ) ) ) ).

% Collect_conj_eq
thf(fact_1203_Collect__conv__if,axiom,
    ! [P: set_v > $o,A: set_v] :
      ( ( ( P @ A )
       => ( ( collect_set_v
            @ ^ [X3: set_v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = ( insert_set_v @ A @ bot_bot_set_set_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_set_v
            @ ^ [X3: set_v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = bot_bot_set_set_v ) ) ) ).

% Collect_conv_if
thf(fact_1204_Collect__conv__if,axiom,
    ! [P: v > $o,A: v] :
      ( ( ( P @ A )
       => ( ( collect_v
            @ ^ [X3: v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = ( insert_v @ A @ bot_bot_set_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_v
            @ ^ [X3: v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = bot_bot_set_v ) ) ) ).

% Collect_conv_if
thf(fact_1205_Collect__conv__if,axiom,
    ! [P: product_prod_v_v > $o,A: product_prod_v_v] :
      ( ( ( P @ A )
       => ( ( collec140062887454715474od_v_v
            @ ^ [X3: product_prod_v_v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collec140062887454715474od_v_v
            @ ^ [X3: product_prod_v_v] :
                ( ( X3 = A )
                & ( P @ X3 ) ) )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% Collect_conv_if
thf(fact_1206_Collect__conv__if2,axiom,
    ! [P: set_v > $o,A: set_v] :
      ( ( ( P @ A )
       => ( ( collect_set_v
            @ ^ [X3: set_v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = ( insert_set_v @ A @ bot_bot_set_set_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_set_v
            @ ^ [X3: set_v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = bot_bot_set_set_v ) ) ) ).

% Collect_conv_if2
thf(fact_1207_Collect__conv__if2,axiom,
    ! [P: v > $o,A: v] :
      ( ( ( P @ A )
       => ( ( collect_v
            @ ^ [X3: v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = ( insert_v @ A @ bot_bot_set_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_v
            @ ^ [X3: v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = bot_bot_set_v ) ) ) ).

% Collect_conv_if2
thf(fact_1208_Collect__conv__if2,axiom,
    ! [P: product_prod_v_v > $o,A: product_prod_v_v] :
      ( ( ( P @ A )
       => ( ( collec140062887454715474od_v_v
            @ ^ [X3: product_prod_v_v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = ( insert1338601472111419319od_v_v @ A @ bot_bo723834152578015283od_v_v ) ) )
      & ( ~ ( P @ A )
       => ( ( collec140062887454715474od_v_v
            @ ^ [X3: product_prod_v_v] :
                ( ( A = X3 )
                & ( P @ X3 ) ) )
          = bot_bo723834152578015283od_v_v ) ) ) ).

% Collect_conv_if2
thf(fact_1209_empty__def,axiom,
    ( bot_bot_set_set_v
    = ( collect_set_v
      @ ^ [X3: set_v] : $false ) ) ).

% empty_def
thf(fact_1210_empty__def,axiom,
    ( bot_bot_set_v
    = ( collect_v
      @ ^ [X3: v] : $false ) ) ).

% empty_def
thf(fact_1211_empty__def,axiom,
    ( bot_bo723834152578015283od_v_v
    = ( collec140062887454715474od_v_v
      @ ^ [X3: product_prod_v_v] : $false ) ) ).

% empty_def
thf(fact_1212_set__diff__eq,axiom,
    ( minus_4183494784930505774od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ^ [X3: product_prod_v_v] :
              ( ( member7453568604450474000od_v_v @ X3 @ A6 )
              & ~ ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1213_set__diff__eq,axiom,
    ( minus_7228012346218142266_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ^ [X3: set_v] :
              ( ( member_set_v @ X3 @ A6 )
              & ~ ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1214_set__diff__eq,axiom,
    ( minus_minus_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ^ [X3: v] :
              ( ( member_v @ X3 @ A6 )
              & ~ ( member_v @ X3 @ B6 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1215_minus__set__def,axiom,
    ( minus_4183494784930505774od_v_v
    = ( ^ [A6: set_Product_prod_v_v,B6: set_Product_prod_v_v] :
          ( collec140062887454715474od_v_v
          @ ( minus_9095120230875558447_v_v_o
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ A6 )
            @ ^ [X3: product_prod_v_v] : ( member7453568604450474000od_v_v @ X3 @ B6 ) ) ) ) ) ).

% minus_set_def
thf(fact_1216_minus__set__def,axiom,
    ( minus_7228012346218142266_set_v
    = ( ^ [A6: set_set_v,B6: set_set_v] :
          ( collect_set_v
          @ ( minus_minus_set_v_o
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ A6 )
            @ ^ [X3: set_v] : ( member_set_v @ X3 @ B6 ) ) ) ) ) ).

% minus_set_def
thf(fact_1217_minus__set__def,axiom,
    ( minus_minus_set_v
    = ( ^ [A6: set_v,B6: set_v] :
          ( collect_v
          @ ( minus_minus_v_o
            @ ^ [X3: v] : ( member_v @ X3 @ A6 )
            @ ^ [X3: v] : ( member_v @ X3 @ B6 ) ) ) ) ) ).

% minus_set_def
thf(fact_1218_graph_Ounvisited__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,U: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl3123350270117520219t_unit @ Successors @ E @ U )
        = ( collec140062887454715474od_v_v
          @ ^ [Uu: product_prod_v_v] :
            ? [A5: v,B4: v] :
              ( ( Uu
                = ( product_Pair_v_v @ A5 @ B4 ) )
              & ( member_v @ A5 @ ( sCC_Bl1280885523602775798t_unit @ E @ U ) )
              & ( member_v @ B4 @ ( minus_minus_set_v @ ( Successors @ A5 ) @ ( sCC_Bl3795065053823578884t_unit @ E @ A5 ) ) ) ) ) ) ) ).

% graph.unvisited_def
thf(fact_1219_graph_Ounite__S__equal,axiom,
    ! [Vertices: set_Product_prod_v_v,Successors: product_prod_v_v > set_Product_prod_v_v,E: sCC_Bl7326425374436813197t_unit,W: product_prod_v_v,V2: product_prod_v_v] :
      ( ( sCC_Bl8307124943676871238od_v_v @ Vertices @ Successors )
     => ( ( sCC_Bl7798947040364291444t_unit @ Successors @ E )
       => ( ( member7453568604450474000od_v_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl3878977043676959280t_unit @ E @ V2 ) )
           => ( ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5498988629518860705t_unit @ E ) )
             => ( ~ ( member7453568604450474000od_v_v @ W @ ( sCC_Bl5094201334446601350t_unit @ E ) )
               => ( ( comple5788137035815166516od_v_v
                    @ ( collec8263177866097347122od_v_v
                      @ ^ [Uu: set_Product_prod_v_v] :
                        ? [N4: product_prod_v_v] :
                          ( ( Uu
                            = ( sCC_Bl8440648026628373538t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) @ N4 ) )
                          & ( member7453568604450474000od_v_v @ N4 @ ( set_Product_prod_v_v2 @ ( sCC_Bl2021302119412358655t_unit @ ( sCC_Bl4702006153222411093od_v_v @ V2 @ W @ E ) ) ) ) ) ) )
                  = ( comple5788137035815166516od_v_v
                    @ ( collec8263177866097347122od_v_v
                      @ ^ [Uu: set_Product_prod_v_v] :
                        ? [N4: product_prod_v_v] :
                          ( ( Uu
                            = ( sCC_Bl8440648026628373538t_unit @ E @ N4 ) )
                          & ( member7453568604450474000od_v_v @ N4 @ ( set_Product_prod_v_v2 @ ( sCC_Bl2021302119412358655t_unit @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% graph.unite_S_equal
thf(fact_1220_graph_Ounite__S__equal,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,W: v,V2: v] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl9196236973127232072t_unit @ Successors @ E )
       => ( ( member_v @ W @ ( Successors @ V2 ) )
         => ( ~ ( member_v @ W @ ( sCC_Bl3795065053823578884t_unit @ E @ V2 ) )
           => ( ( member_v @ W @ ( sCC_Bl4645233313691564917t_unit @ E ) )
             => ( ~ ( member_v @ W @ ( sCC_Bl157864678168468314t_unit @ E ) )
               => ( ( comple2307003700295860064_set_v
                    @ ( collect_set_v
                      @ ^ [Uu: set_v] :
                        ? [N4: v] :
                          ( ( Uu
                            = ( sCC_Bl1280885523602775798t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) @ N4 ) )
                          & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ ( sCC_Bloemen_unite_v @ V2 @ W @ E ) ) ) ) ) ) )
                  = ( comple2307003700295860064_set_v
                    @ ( collect_set_v
                      @ ^ [Uu: set_v] :
                        ? [N4: v] :
                          ( ( Uu
                            = ( sCC_Bl1280885523602775798t_unit @ E @ N4 ) )
                          & ( member_v @ N4 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% graph.unite_S_equal
thf(fact_1221_graph_Osub__env__def,axiom,
    ! [Vertices: set_v,Successors: v > set_v,E: sCC_Bl1394983891496994913t_unit,E2: sCC_Bl1394983891496994913t_unit] :
      ( ( sCC_Bloemen_graph_v @ Vertices @ Successors )
     => ( ( sCC_Bl5768913643336123637t_unit @ E @ E2 )
        = ( ( ( sCC_Bl1090238580953940555t_unit @ E2 )
            = ( sCC_Bl1090238580953940555t_unit @ E ) )
          & ( ord_less_eq_set_v @ ( sCC_Bl4645233313691564917t_unit @ E ) @ ( sCC_Bl4645233313691564917t_unit @ E2 ) )
          & ( ord_less_eq_set_v @ ( sCC_Bl157864678168468314t_unit @ E ) @ ( sCC_Bl157864678168468314t_unit @ E2 ) )
          & ! [V3: v] : ( ord_less_eq_set_v @ ( sCC_Bl3795065053823578884t_unit @ E @ V3 ) @ ( sCC_Bl3795065053823578884t_unit @ E2 @ V3 ) )
          & ! [V3: v] : ( ord_less_eq_set_v @ ( sCC_Bl1280885523602775798t_unit @ E @ V3 ) @ ( sCC_Bl1280885523602775798t_unit @ E2 @ V3 ) )
          & ( ord_less_eq_set_v
            @ ( comple2307003700295860064_set_v
              @ ( collect_set_v
                @ ^ [Uu: set_v] :
                  ? [V3: v] :
                    ( ( Uu
                      = ( sCC_Bl1280885523602775798t_unit @ E @ V3 ) )
                    & ( member_v @ V3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E ) ) ) ) ) )
            @ ( comple2307003700295860064_set_v
              @ ( collect_set_v
                @ ^ [Uu: set_v] :
                  ? [V3: v] :
                    ( ( Uu
                      = ( sCC_Bl1280885523602775798t_unit @ E2 @ V3 ) )
                    & ( member_v @ V3 @ ( set_v2 @ ( sCC_Bl8828226123343373779t_unit @ E2 ) ) ) ) ) ) ) ) ) ) ).

% graph.sub_env_def
thf(fact_1222_vfin,axiom,
    finite_finite_v @ vertices ).

% vfin
thf(fact_1223_sup__unit__def,axiom,
    ( sup_sup_Product_unit
    = ( ^ [Uu2: product_unit,Uv: product_unit] : product_Unity ) ) ).

% sup_unit_def
thf(fact_1224_bot__unit__def,axiom,
    bot_bot_Product_unit = product_Unity ).

% bot_unit_def
thf(fact_1225_Sup__unit__def,axiom,
    ( comple4687483117567863418t_unit
    = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).

% Sup_unit_def
thf(fact_1226_old_Ounit_Oexhaust,axiom,
    ! [Y: product_unit] : ( Y = product_Unity ) ).

% old.unit.exhaust
thf(fact_1227_inf__unit__def,axiom,
    ( inf_inf_Product_unit
    = ( ^ [Uu2: product_unit,Uv: product_unit] : product_Unity ) ) ).

% inf_unit_def
thf(fact_1228_default__unit__def,axiom,
    defaul566961228789861419t_unit = product_Unity ).

% default_unit_def

% Helper facts (3)
thf(help_If_3_1_If_001t__Set__Oset_Itf__v_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Set__Oset_Itf__v_J_T,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( if_set_v @ $false @ X2 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Set__Oset_Itf__v_J_T,axiom,
    ! [X2: set_v,Y: set_v] :
      ( ( if_set_v @ $true @ X2 @ Y )
      = X2 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    member_v @ m @ cc ).

%------------------------------------------------------------------------------