%------------------------------------------------------------------------------
% 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    : Query_Optimization/0009_Dtree/prob_03474_148458__15164822_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1814 ( 563 unt; 545 typ;   0 def)
%            Number of atoms       : 3617 (2009 equ;   0 cnn)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives : 13324 ( 984   ~;  32   |; 188   &;10419   @)
%                                         (   0 <=>;1701  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Number of types       :  118 ( 117 usr)
%            Number of type conns  : 1011 (1011   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  429 ( 428 usr;  46 con; 0-3 aty)
%            Number of variables   : 4358 (  44   ^;4041   !; 273   ?;4358   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-18 16:06:38.313
%------------------------------------------------------------------------------
% Could-be-implicit typings (117)
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J_J,type,
    produc2679909195573480038od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc4669796033538812730od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc4732240729513732134od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2580745285611667110od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc3904047216122699628od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc8284565691568599343_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc2919045324072751003_a_b_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fset_P9180166578942778714od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc1627906242116850535od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J_J,type,
    produc375670372958830678_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc6844405789190802602od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc783859242544933067_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7239927097622659425od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc435541801560641583ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc442345915616064047_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_P5357134975691234797od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    fset_P271555816861255656_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_Pr8296264926188598114_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7338334792537277175od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_M_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc9140505053306170267_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc5332496565491608475ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3348719938592107239od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc2698676102954276518od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc1821044701915316840od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc8137180380982048514_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc9134726091994374893od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J_J,type,
    produc1280734032651800022ee_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fset_P5910908224067821594od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc8474099945245761646od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7795635294741998752od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    fset_P8532786667068971368_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_Pr1790600203756605154_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc4044292680377378282od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc4081214457754080642_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_P8094385941167427565od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J_J,type,
    produc5473036864866960214_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc566207910345494828od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc7218430402464555874od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc6081131995383004661_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc7582145809211085103ee_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    fset_P1087233464713034472ee_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_Pr3885137059925752418ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3334210663054469735od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    fset_P8869035697996476266od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    fset_P6924693328471822228od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_M_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc6760719095789406107ee_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    dtree_8339642294131873593od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc1688629678973589927od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc1961764714219340802ee_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    list_P7924273279524553179_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_Pr2755428042910921141_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J_J,type,
    produc8756840788158812374ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc229868702982719930od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc2878020351943352036od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_dt8691689324118462429_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc750211871370617675ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc8908337785154950741_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_P8601282865932132013od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    fset_P5991447722532490344ee_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr3015088788472578951od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_Pr8090914455431026146ee_a_b: $tType ).

thf(ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Ounit_J,type,
    pair_p6651462780844640539t_unit: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    dtree_6636540493345571111_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc5068203645811208070od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7397007428618769063od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc2168945239844811237_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc6260003399586931330ee_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    list_P3724575226198589275ee_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    list_P7142016109841313883_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_l7282425492883329843od_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    dtree_5519289247442030201od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_dt2836678144041639773ee_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_dt6254119027684364381_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc3685132500274331861ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc5339155667539881461ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc3392468160873345493_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_P3463435030753280173od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    set_Pr5493900063595384711od_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    dtree_8690448868185853351ee_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    dtree_8397784528784866983_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc2233330766403592615od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_P5700792096213675741od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    list_P7294506862534405595ee_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J_J,type,
    fset_P3031279327735363940_b_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_Pr8736279663640031669ee_a_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    list_l2608773801899484570_a_b_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_2253494508914376569od_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_dt5871847375752683485ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2639161875728825943od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc5177672665255943253ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J,type,
    produc5284372313782567166_b_b_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    list_l6443893005374362810od_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    list_P5360711134766023690_a_b_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    fset_P5281107635120001194_a_b_b: $tType ).

thf(ty_n_t__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    dtree_8545934391348768041od_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    dtree_1861073144021109543ee_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    set_Pr3012420139608375472_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_062_Itf__b_Mtf__a_J_J,type,
    produc1083523234014712191_b_b_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    list_l8778361445553822004od_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc4558475209616630778_a_b_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    list_list_dtree_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    list_P1467974523212632366od_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    fset_P9214369701362650254od_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_dtree_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    set_Product_prod_a_b: $tType ).

thf(ty_n_t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    list_dtree_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    fset_dtree_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    set_dtree_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    product_prod_a_b: $tType ).

thf(ty_n_t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_Itf__b_J,type,
    fset_b: $tType ).

thf(ty_n_t__FSet__Ofset_Itf__a_J,type,
    fset_a: $tType ).

thf(ty_n_t__Set__Oset_Itf__b_J,type,
    set_b: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (428)
thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    basic_3138169641471185194ee_a_b: produc6260003399586931330ee_a_b > set_dt5871847375752683485ee_a_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    basic_3992591041251291690_a_b_b: produc4081214457754080642_a_b_b > set_dt6254119027684364381_a_b_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    basic_2889154014856113066ee_a_b: produc1961764714219340802ee_a_b > set_dt2836678144041639773ee_a_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    basic_6594820288780307626_a_b_b: produc8137180380982048514_a_b_b > set_dt8691689324118462429_a_b_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    basic_7578771248400840636_a_b_b: produc4558475209616630778_a_b_b > set_dtree_a_b ).

thf(sy_c_Basic__BNFs_Osnds_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    basic_1877077703026942_a_b_b: produc4558475209616630778_a_b_b > set_b ).

thf(sy_c_Dtree_Odhead_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dhead_3390085853063673444ee_a_b: dtree_1861073144021109543ee_a_b > ( dtree_a_b > dtree_a_b ) > dtree_a_b > dtree_a_b ).

thf(sy_c_Dtree_Odhead_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dhead_5693685568992248292_a_b_b: dtree_8397784528784866983_a_b_b > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odhead_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dhead_3175603910144251108ee_a_b: dtree_8690448868185853351ee_a_b > ( dtree_a_b > produc4558475209616630778_a_b_b ) > dtree_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odhead_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dhead_6575884314179264612_a_b_b: dtree_6636540493345571111_a_b_b > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odhead_001tf__a_001tf__b,type,
    dhead_a_b: dtree_a_b > ( b > a ) > b > a ).

thf(sy_c_Dtree_Odtail_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtail_6577300080304104276ee_a_b: dtree_1861073144021109543ee_a_b > ( dtree_a_b > dtree_a_b ) > dtree_a_b > dtree_a_b ).

thf(sy_c_Dtree_Odtail_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtail_2974526391675993812_a_b_b: dtree_8397784528784866983_a_b_b > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odtail_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtail_456444732827996628ee_a_b: dtree_8690448868185853351ee_a_b > ( dtree_a_b > produc4558475209616630778_a_b_b ) > dtree_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odtail_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtail_367104560391499092_a_b_b: dtree_6636540493345571111_a_b_b > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odtail_001tf__a_001tf__b,type,
    dtail_a_b: dtree_a_b > ( b > a ) > b > a ).

thf(sy_c_Dtree_Odtree_ONode_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    node_P5897935084763704574od_a_b: ( product_prod_a_b > product_prod_a_b > $o ) > fset_P9180166578942778714od_a_b > dtree_8339642294131873593od_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    node_d7487230363575057332ee_a_b: dtree_a_b > fset_P5991447722532490344ee_a_b > dtree_1861073144021109543ee_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    node_d5271158820939511604_a_b_b: dtree_a_b > fset_P8532786667068971368_a_b_b > dtree_8397784528784866983_a_b_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    node_dtree_a_b_b: dtree_a_b > fset_P3031279327735363940_b_b_b > dtree_dtree_a_b_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    node_l1136085673055119934od_a_b: list_P1467974523212632366od_a_b > fset_P5910908224067821594od_a_b > dtree_5519289247442030201od_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    node_P2753077162091514420ee_a_b: produc4558475209616630778_a_b_b > fset_P1087233464713034472ee_a_b > dtree_8690448868185853351ee_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    node_P961815112480277940_a_b_b: produc4558475209616630778_a_b_b > fset_P271555816861255656_a_b_b > dtree_6636540493345571111_a_b_b ).

thf(sy_c_Dtree_Odtree_ONode_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    node_P1936840572307073598od_a_b: product_prod_a_b > fset_P6924693328471822228od_a_b > dtree_2253494508914376569od_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    node_a6325075177599301358od_a_b: a > fset_P8869035697996476266od_a_b > dtree_8545934391348768041od_a_b ).

thf(sy_c_Dtree_Odtree_ONode_001tf__a_001tf__b,type,
    node_a_b: a > fset_P5281107635120001194_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    darcs_1812195894409408735ee_a_b: dtree_1861073144021109543ee_a_b > set_dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    darcs_154907951296907615_a_b_b: dtree_8397784528784866983_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    darcs_6860198329303686239ee_a_b: dtree_8690448868185853351ee_a_b > set_dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    darcs_2805522099973010655_a_b_b: dtree_6636540493345571111_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001tf__a_001tf__b,type,
    darcs_a_b: dtree_a_b > set_b ).

thf(sy_c_Dtree_Odtree_Odverts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dverts2436977245124431984ee_a_b: dtree_1861073144021109543ee_a_b > set_dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odverts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dverts5490399362891984880_a_b_b: dtree_8397784528784866983_a_b_b > set_dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odverts_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dverts2972317704043987696ee_a_b: dtree_8690448868185853351ee_a_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Dtree_Odtree_Odverts_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dverts1640268204329280112_a_b_b: dtree_6636540493345571111_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Dtree_Odtree_Odverts_001tf__a_001tf__b,type,
    dverts_a_b: dtree_a_b > set_a ).

thf(sy_c_Dtree_Odtree_Oroot_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    root_P7917853640449190558od_a_b: dtree_8339642294131873593od_a_b > product_prod_a_b > product_prod_a_b > $o ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    root_d1746759089207908692ee_a_b: dtree_1861073144021109543ee_a_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    root_d8071547644108387540_a_b_b: dtree_8397784528784866983_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    root_dtree_a_b_b: dtree_dtree_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    root_l2497086882398443486od_a_b: dtree_5519289247442030201od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    root_P5553465985260390356ee_a_b: dtree_8690448868185853351ee_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    root_P204151722342556500_a_b_b: dtree_6636540493345571111_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Dtree_Odtree_Oroot_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    root_P6595957619955152862od_a_b: dtree_2253494508914376569od_a_b > product_prod_a_b ).

thf(sy_c_Dtree_Odtree_Oroot_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    root_a584603903232152718od_a_b: dtree_8545934391348768041od_a_b > a ).

thf(sy_c_Dtree_Odtree_Oroot_001tf__a_001tf__b,type,
    root_a_b: dtree_a_b > a ).

thf(sy_c_Dtree_Odtree_Osucs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    sucs_d5654203025177486372ee_a_b: dtree_1861073144021109543ee_a_b > fset_P5991447722532490344ee_a_b ).

thf(sy_c_Dtree_Odtree_Osucs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    sucs_d609074739952873380_a_b_b: dtree_8397784528784866983_a_b_b > fset_P8532786667068971368_a_b_b ).

thf(sy_c_Dtree_Odtree_Osucs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    sucs_P7314365117959652004ee_a_b: dtree_8690448868185853351ee_a_b > fset_P1087233464713034472ee_a_b ).

thf(sy_c_Dtree_Odtree_Osucs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    sucs_P6478368611001241124_a_b_b: dtree_6636540493345571111_a_b_b > fset_P271555816861255656_a_b_b ).

thf(sy_c_Dtree_Odtree_Osucs_001tf__a_001tf__b,type,
    sucs_a_b: dtree_a_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Dtree_Odtree__from__list_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_4383916385682046516od_a_b: ( product_prod_a_b > product_prod_a_b > $o ) > list_P8094385941167427565od_a_b > dtree_8339642294131873593od_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_7424119665891431146ee_a_b: dtree_a_b > list_P7294506862534405595ee_a_b > dtree_1861073144021109543ee_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_1144793476579453034_a_b_b: dtree_a_b > list_P7142016109841313883_a_b_b > dtree_8397784528784866983_a_b_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    dtree_5255521609252960911_a_b_b: dtree_a_b > list_P5360711134766023690_a_b_b > dtree_dtree_a_b_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_6507962483783174260od_a_b: list_P1467974523212632366od_a_b > list_P8601282865932132013od_a_b > dtree_5519289247442030201od_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_7850083854586231658ee_a_b: produc4558475209616630778_a_b_b > list_P3724575226198589275ee_a_b > dtree_8690448868185853351ee_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_450453658713739498_a_b_b: produc4558475209616630778_a_b_b > list_P7924273279524553179_a_b_b > dtree_6636540493345571111_a_b_b ).

thf(sy_c_Dtree_Odtree__from__list_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    dtree_1864022081312108148od_a_b: product_prod_a_b > list_P3463435030753280173od_a_b > dtree_2253494508914376569od_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_6261964479915675172od_a_b: a > list_P5700792096213675741od_a_b > dtree_8545934391348768041od_a_b ).

thf(sy_c_Dtree_Odtree__from__list_001tf__a_001tf__b,type,
    dtree_from_list_a_b: a > list_P1467974523212632366od_a_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree__from__list__rel_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_5744449417772980677od_a_b: produc2580745285611667110od_a_b > produc2580745285611667110od_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_678761158524876667ee_a_b: produc8756840788158812374ee_a_b > produc8756840788158812374ee_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_2165212018939139067_a_b_b: produc5473036864866960214_a_b_b > produc5473036864866960214_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    dtree_7549101302527828798_a_b_b: produc2168945239844811237_a_b_b > produc2168945239844811237_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_836713862541457285od_a_b: produc2698676102954276518od_a_b > produc2698676102954276518od_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_8870502396945917691ee_a_b: produc1280734032651800022ee_a_b > produc1280734032651800022ee_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_4572921241105318779_a_b_b: produc375670372958830678_a_b_b > produc375670372958830678_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    dtree_4985918624134698629od_a_b: produc566207910345494828od_a_b > produc566207910345494828od_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_8739978009403896501od_a_b: produc5068203645811208070od_a_b > produc5068203645811208070od_a_b > $o ).

thf(sy_c_Dtree_Odtree__from__list__rel_001tf__a_001tf__b,type,
    dtree_4965841467942179590el_a_b: produc2639161875728825943od_a_b > produc2639161875728825943od_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_2881821214123584869od_a_b: dtree_8339642294131873593od_a_b > list_P8094385941167427565od_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_5459410236902894363ee_a_b: dtree_1861073144021109543ee_a_b > list_P7294506862534405595ee_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_2482681192243439515_a_b_b: dtree_8397784528784866983_a_b_b > list_P7142016109841313883_a_b_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    dtree_29943561566189470_a_b_b: dtree_dtree_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_5213960014362835749od_a_b: dtree_5519289247442030201od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_9187971570250218139ee_a_b: dtree_8690448868185853351ee_a_b > list_P3724575226198589275ee_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_1768895223656068891_a_b_b: dtree_6636540493345571111_a_b_b > list_P7924273279524553179_a_b_b ).

thf(sy_c_Dtree_Odtree__to__list_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    dtree_983605638134528549od_a_b: dtree_2253494508914376569od_a_b > list_P3463435030753280173od_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_4297255050927138389od_a_b: dtree_8545934391348768041od_a_b > list_P5700792096213675741od_a_b ).

thf(sy_c_Dtree_Odtree__to__list_001tf__a_001tf__b,type,
    dtree_to_list_a_b: dtree_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_Dtree_Odtree__to__list__rel_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_4748084400063416276od_a_b: dtree_8339642294131873593od_a_b > dtree_8339642294131873593od_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_690707291460779146ee_a_b: dtree_1861073144021109543ee_a_b > dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_5851200291563680266_a_b_b: dtree_8397784528784866983_a_b_b > dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    dtree_7148473427102603503_a_b_b: dtree_dtree_a_b_b > dtree_dtree_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_1941884435189367316od_a_b: dtree_5519289247442030201od_a_b > dtree_5519289247442030201od_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_3333118632715683082ee_a_b: dtree_8690448868185853351ee_a_b > dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    dtree_5584907631894100618_a_b_b: dtree_6636540493345571111_a_b_b > dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    dtree_5602071207833618452od_a_b: dtree_2253494508914376569od_a_b > dtree_2253494508914376569od_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    dtree_8751924142339798980od_a_b: dtree_8545934391348768041od_a_b > dtree_8545934391348768041od_a_b > $o ).

thf(sy_c_Dtree_Odtree__to__list__rel_001tf__a_001tf__b,type,
    dtree_9180682678494368405el_a_b: dtree_a_b > dtree_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    is_sub9145550046624671838od_a_b: dtree_8339642294131873593od_a_b > dtree_8339642294131873593od_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    is_sub7866859304860047124ee_a_b: dtree_1861073144021109543ee_a_b > dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    is_sub3309389790737183380_a_b_b: dtree_8397784528784866983_a_b_b > dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    is_sub2776994699154135781_a_b_b: dtree_dtree_a_b_b > dtree_dtree_a_b_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    is_sub3969663741311890846od_a_b: dtree_5519289247442030201od_a_b > dtree_5519289247442030201od_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    is_sub791308131889186196ee_a_b: dtree_8690448868185853351ee_a_b > dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    is_sub6703628162287821076_a_b_b: dtree_6636540493345571111_a_b_b > dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    is_sub6933245819845350814od_a_b: dtree_2253494508914376569od_a_b > dtree_2253494508914376569od_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    is_sub6704704118884291150od_a_b: dtree_8545934391348768041od_a_b > dtree_8545934391348768041od_a_b > $o ).

thf(sy_c_Dtree_Ois__subtree_001tf__a_001tf__b,type,
    is_subtree_a_b: dtree_a_b > dtree_a_b > $o ).

thf(sy_c_Dtree_Omax__deg_001tf__a_001tf__b,type,
    max_deg_a_b: dtree_a_b > nat ).

thf(sy_c_Dtree_Onum__leaves_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    num_le762670902658651842ee_a_b: dtree_1861073144021109543ee_a_b > nat ).

thf(sy_c_Dtree_Onum__leaves_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    num_le3490100660955108418_a_b_b: dtree_8397784528784866983_a_b_b > nat ).

thf(sy_c_Dtree_Onum__leaves_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    num_le972019002107111234ee_a_b: dtree_8690448868185853351ee_a_b > nat ).

thf(sy_c_Dtree_Onum__leaves_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    num_le5032565032286201026_a_b_b: dtree_6636540493345571111_a_b_b > nat ).

thf(sy_c_Dtree_Onum__leaves_001tf__a_001tf__b,type,
    num_leaves_a_b: dtree_a_b > nat ).

thf(sy_c_Dtree_Ostrict__subtree_001tf__a_001tf__b,type,
    strict_subtree_a_b: dtree_a_b > dtree_a_b > $o ).

thf(sy_c_Dtree_Owf__darcs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dar7222114146661136918ee_a_b: dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Dtree_Owf__darcs_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dar5665471658239198102_a_b_b: dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Dtree_Owf__darcs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dar3147389999391200918ee_a_b: dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Dtree_Owf__darcs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dar8189686260367384598_a_b_b: dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Dtree_Owf__darcs_001tf__a_001tf__b,type,
    wf_darcs_a_b: dtree_a_b > $o ).

thf(sy_c_Dtree_Owf__dtree_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dtr6838629865543741107ee_a_b: dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Dtree_Owf__dtree_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dtr5498106988402938675_a_b_b: dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Dtree_Owf__dtree_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dtr2980025329554941491ee_a_b: dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Dtree_Owf__dtree_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dtr8395680321066191539_a_b_b: dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Dtree_Owf__dtree_001tf__a_001tf__b,type,
    wf_dtree_a_b: dtree_a_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dve9201916681887519993ee_a_b: dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dve1338770620977398649_a_b_b: dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    wf_dve8044060998984177273ee_a_b: dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    wf_dve6839618634935551225_a_b_b: dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001tf__a_001tf__b,type,
    wf_dverts_a_b: dtree_a_b > $o ).

thf(sy_c_Dtree_Owf__list__verts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    wf_lis4446142942163678948_a_b_b: list_P5360711134766023690_a_b_b > $o ).

thf(sy_c_Dtree_Owf__list__verts_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    wf_lis873957137097608799od_a_b: list_P3463435030753280173od_a_b > $o ).

thf(sy_c_Dtree_Owf__list__verts_001tf__a_001tf__b,type,
    wf_list_verts_a_b: list_P1467974523212632366od_a_b > $o ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    finser4631589853810920290od_a_b: produc6844405789190802602od_a_b > fset_P9180166578942778714od_a_b > fset_P9180166578942778714od_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    finser8516331313445392842ee_a_b: produc6260003399586931330ee_a_b > fset_P5991447722532490344ee_a_b > fset_P5991447722532490344ee_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    finser5778094437704840394_a_b_b: produc4081214457754080642_a_b_b > fset_P8532786667068971368_a_b_b > fset_P8532786667068971368_a_b_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J,type,
    finser6734551996811508806_b_b_b: produc5284372313782567166_b_b_b > fset_P3031279327735363940_b_b_b > fset_P3031279327735363940_b_b_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    finser4916530145793648802od_a_b: produc4044292680377378282od_a_b > fset_P5910908224067821594od_a_b > fset_P5910908224067821594od_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    finser7847761039489690442ee_a_b: produc1961764714219340802ee_a_b > fset_P1087233464713034472ee_a_b > fset_P1087233464713034472ee_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    finser3407669804807474762_a_b_b: produc8137180380982048514_a_b_b > fset_P271555816861255656_a_b_b > fset_P271555816861255656_a_b_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    finser5347476252697843100od_a_b: produc2878020351943352036od_a_b > fset_P6924693328471822228od_a_b > fset_P6924693328471822228od_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    finser2699324603737210994od_a_b: produc229868702982719930od_a_b > fset_P8869035697996476266od_a_b > fset_P8869035697996476266od_a_b ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    finser8437519239679886002_a_b_b: produc4558475209616630778_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_FSet_Ofmember_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    fmember_dtree_a_b: dtree_a_b > fset_dtree_a_b > $o ).

thf(sy_c_FSet_Ofmember_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fmembe3173364709796808819_a_b_b: produc4558475209616630778_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_FSet_Ofset_Ofset_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    fset_dtree_a_b2: fset_dtree_a_b > set_dtree_a_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    fset_P4845137164202167537ee_a_b: fset_P5991447722532490344ee_a_b > set_Pr8090914455431026146ee_a_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    fset_P4440376523358319089_a_b_b: fset_P8532786667068971368_a_b_b > set_Pr1790600203756605154_a_b_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    fset_P3182333368011040625ee_a_b: fset_P1087233464713034472ee_a_b > set_Pr3885137059925752418ee_a_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    fset_P8825802006873508977_a_b_b: fset_P271555816861255656_a_b_b > set_Pr8296264926188598114_a_b_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fset_P783253628892185035_a_b_b: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_FSet_Ofset_Ofset_001tf__a,type,
    fset_a2: fset_a > set_a ).

thf(sy_c_FSet_Ofset_Ofset_001tf__b,type,
    fset_b2: fset_b > set_b ).

thf(sy_c_FSet_Ofset__of__list_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    fset_o5204176837177470516ee_a_b: list_dtree_a_b > fset_dtree_a_b ).

thf(sy_c_FSet_Ofset__of__list_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fset_o8043272628024912308_a_b_b: list_P5360711134766023690_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_FSet_Ofset__of__list_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    fset_o3702720909373460334od_a_b: list_P1467974523212632366od_a_b > fset_P9214369701362650254od_a_b ).

thf(sy_c_FSet_Ofthe__elem_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fthe_e7442499522476018237_a_b_b: fset_P5281107635120001194_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    minus_1250967532242559235_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    minus_3445990907098541065ee_a_b: set_dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    minus_1392386589478415753_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
    minus_minus_set_a: set_a > set_a > set_a ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_Eo_J,type,
    inf_inf_dtree_a_b_o: ( dtree_a_b > $o ) > ( dtree_a_b > $o ) > dtree_a_b > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J,type,
    inf_in55627642082981827_b_b_o: ( produc4558475209616630778_a_b_b > $o ) > ( produc4558475209616630778_a_b_b > $o ) > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    inf_in7138637532943773244_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    inf_in5903708963019302594ee_a_b: set_dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    inf_in8710443480170685603ee_a_b: set_Pr8736279663640031669ee_a_b > set_Pr8736279663640031669ee_a_b > set_Pr8736279663640031669ee_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    inf_in6138156342456174402_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    inf_in1590458884271868277od_a_b: set_Pr3015088788472578951od_a_b > set_Pr3015088788472578951od_a_b > set_Pr3015088788472578951od_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    inf_in8976041639890736118od_a_b: set_Product_prod_a_b > set_Product_prod_a_b > set_Product_prod_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
    inf_inf_set_a: set_a > set_a > set_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__b_J,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    sup_su860928060825958358_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    sup_su8994539500306794332ee_a_b: set_dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    sup_su2887895092731772380_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__b_J,type,
    sup_sup_set_b: set_b > set_b > set_b ).

thf(sy_c_List_Oappend_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    append_dtree_a_b: list_dtree_a_b > list_dtree_a_b > list_dtree_a_b ).

thf(sy_c_List_Oappend_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    append7557446516274476873od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    append2461588412122937986od_a_b: list_P8094385941167427565od_a_b > list_P8094385941167427565od_a_b > list_P8094385941167427565od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    append5407404413692997488ee_a_b: list_P7294506862534405595ee_a_b > list_P7294506862534405595ee_a_b > list_P7294506862534405595ee_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    append8797929544692208_a_b_b: list_P7142016109841313883_a_b_b > list_P7142016109841313883_a_b_b > list_P7142016109841313883_a_b_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    append86853766581025439_a_b_b: list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    append5385366555182926146od_a_b: list_P8601282865932132013od_a_b > list_P8601282865932132013od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    append301462268945678576ee_a_b: list_P3724575226198589275ee_a_b > list_P3724575226198589275ee_a_b > list_P3724575226198589275ee_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    append7918683371861672816_a_b_b: list_P7924273279524553179_a_b_b > list_P7924273279524553179_a_b_b > list_P7924273279524553179_a_b_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    append3447563168971123522od_a_b: list_P3463435030753280173od_a_b > list_P3463435030753280173od_a_b > list_P3463435030753280173od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    append2868893624165880178od_a_b: list_P5700792096213675741od_a_b > list_P5700792096213675741od_a_b > list_P5700792096213675741od_a_b ).

thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    append5335208823350062147od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Obind_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    bind_P7003926910255595655od_a_b: list_P1467974523212632366od_a_b > ( product_prod_a_b > list_P1467974523212632366od_a_b ) > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Obutlast_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    butlast_dtree_a_b: list_dtree_a_b > list_dtree_a_b ).

thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    butlas7288446807591328296_a_b_b: list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    butlas8142365734376493050od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Odistinct__adj_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    distin2562679511629466758od_a_b: list_P1467974523212632366od_a_b > $o ).

thf(sy_c_List_Olast_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    last_dtree_a_b: list_dtree_a_b > dtree_a_b ).

thf(sy_c_List_Olast_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    last_P1593854145880039067_a_b_b: list_P5360711134766023690_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_List_Olast_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    last_P8790725272581694279od_a_b: list_P1467974523212632366od_a_b > product_prod_a_b ).

thf(sy_c_List_Olist_OCons_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    cons_dtree_a_b: dtree_a_b > list_dtree_a_b > list_dtree_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    cons_list_dtree_a_b: list_dtree_a_b > list_list_dtree_a_b > list_list_dtree_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_l4798275018037426410od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    cons_l8517938233221414356_a_b_b: list_P5360711134766023690_a_b_b > list_l2608773801899484570_a_b_b > list_l2608773801899484570_a_b_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_l5043155473145997155od_a_b: list_P3463435030753280173od_a_b > list_l7282425492883329843od_a_b > list_l7282425492883329843od_a_b ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    cons_l907386227682280420od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_P3561991119763190045od_a_b: produc3334210663054469735od_a_b > list_P8094385941167427565od_a_b > list_P8094385941167427565od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    cons_P1798951315401763083ee_a_b: produc5177672665255943253ee_a_b > list_P7294506862534405595ee_a_b > list_P7294506862534405595ee_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    cons_P4972188603266062475_a_b_b: produc3392468160873345493_a_b_b > list_P7142016109841313883_a_b_b > list_P7142016109841313883_a_b_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    cons_P2785074014425598660_a_b_b: produc4558475209616630778_a_b_b > list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_P1529385591390545501od_a_b: produc7397007428618769063od_a_b > list_P8601282865932132013od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    cons_P5264852942667048843ee_a_b: produc3685132500274331861ee_a_b > list_P3724575226198589275ee_a_b > list_P3724575226198589275ee_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    cons_P9068067167194404619_a_b_b: produc8908337785154950741_a_b_b > list_P7924273279524553179_a_b_b > list_P7924273279524553179_a_b_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_P5303771978918612125od_a_b: produc3348719938592107239od_a_b > list_P5357134975691234797od_a_b > list_P5357134975691234797od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    cons_P8222935586017696605od_a_b: produc2233330766403592615od_a_b > list_P3463435030753280173od_a_b > list_P3463435030753280173od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    cons_P8483812562729421581od_a_b: produc2639161875728825943od_a_b > list_P5700792096213675741od_a_b > list_P5700792096213675741od_a_b ).

thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    cons_P7316939131009794654od_a_b: product_prod_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    nil_dtree_a_b: list_dtree_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    nil_list_dtree_a_b: list_list_dtree_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_li2802039260981550394od_a_b: list_l6443893005374362810od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    nil_li143336474603867524_a_b_b: list_l2608773801899484570_a_b_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_li9150416971034547123od_a_b: list_l7282425492883329843od_a_b ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    nil_li8635777946366267444od_a_b: list_l8778361445553822004od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_Pr7311172237979606381od_a_b: list_P8094385941167427565od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    nil_Pr558572586965427547ee_a_b: list_P7294506862534405595ee_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    nil_Pr9079450101154612443_a_b_b: list_P7142016109841313883_a_b_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    nil_Pr5403147374433350260_a_b_b: list_P5360711134766023690_a_b_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_Pr2412700377486846637od_a_b: list_P8601282865932132013od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    nil_Pr148742403700823003ee_a_b: list_P3724575226198589275ee_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    nil_Pr5872703755862520667_a_b_b: list_P7924273279524553179_a_b_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_Pr1799676319544484077od_a_b: list_P5357134975691234797od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    nil_Pr906174322249854893od_a_b: list_P3463435030753280173od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    nil_Pr7243433834293086045od_a_b: list_P5700792096213675741od_a_b ).

thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    nil_Product_prod_a_b: list_P1467974523212632366od_a_b ).

thf(sy_c_List_Olist_Ohd_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    hd_dtree_a_b: list_dtree_a_b > dtree_a_b ).

thf(sy_c_List_Olist_Ohd_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    hd_Pro8093898422926754895_a_b_b: list_P5360711134766023690_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_List_Olist_Ohd_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    hd_Product_prod_a_b: list_P1467974523212632366od_a_b > product_prod_a_b ).

thf(sy_c_List_Olist_Oset_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    set_dtree_a_b2: list_dtree_a_b > set_dtree_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    set_Pr2725521476954953066ee_a_b: list_P7294506862534405595ee_a_b > set_Pr8736279663640031669ee_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    set_Pr8239206241032387877_a_b_b: list_P5360711134766023690_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    set_Pr1544013579528541546_a_b_b: list_P7924273279524553179_a_b_b > set_Pr2755428042910921141_a_b_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    set_Pr5228040199190236220od_a_b: list_P3463435030753280173od_a_b > set_Pr5493900063595384711od_a_b ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    set_Product_prod_a_b2: list_P1467974523212632366od_a_b > set_Product_prod_a_b ).

thf(sy_c_List_Olistrel1_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    listre2955263632500257159od_a_b: set_Pr5493900063595384711od_a_b > set_Pr3015088788472578951od_a_b ).

thf(sy_c_List_Omaps_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    maps_P4858162816583320641od_a_b: ( product_prod_a_b > list_P1467974523212632366od_a_b ) > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Opartition_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    partit8484945486742549543od_a_b: ( product_prod_a_b > $o ) > list_P1467974523212632366od_a_b > produc7397007428618769063od_a_b ).

thf(sy_c_List_Oproduct__lists_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc5544102775981650891ee_a_b: list_list_dtree_a_b > list_list_dtree_a_b ).

thf(sy_c_List_Oproduct__lists_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc4369083959415664285od_a_b: list_l6443893005374362810od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc8247723432148779083_a_b_b: list_l2608773801899484570_a_b_b > list_l2608773801899484570_a_b_b ).

thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc3864309093259441302od_a_b: list_l7282425492883329843od_a_b > list_l7282425492883329843od_a_b ).

thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    produc5891818806577749399od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_List_OremoveAll_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    removeAll_dtree_a_b: dtree_a_b > list_dtree_a_b > list_dtree_a_b ).

thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    remove1345892019315867374_a_b_b: produc4558475209616630778_a_b_b > list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    remove3678230900650767028od_a_b: product_prod_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_List_Osubseqs_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    subseqs_dtree_a_b: list_dtree_a_b > list_list_dtree_a_b ).

thf(sy_c_List_Osubseqs_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    subseq465733082264987907od_a_b: list_l8778361445553822004od_a_b > list_l6443893005374362810od_a_b ).

thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    subseq5611861847932087141_a_b_b: list_P5360711134766023690_a_b_b > list_l2608773801899484570_a_b_b ).

thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    subseq3833396900492357116od_a_b: list_P3463435030753280173od_a_b > list_l7282425492883329843od_a_b ).

thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    subseq3159716953272533757od_a_b: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    size_s6196567657804286395ee_a_b: dtree_1861073144021109543ee_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    size_s8990628085413054779_a_b_b: dtree_8397784528784866983_a_b_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    size_s59920387959265339ee_a_b: dtree_8690448868185853351ee_a_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    size_s5437551432765265851_a_b_b: dtree_6636540493345571111_a_b_b > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    size_size_dtree_a_b: dtree_a_b > nat ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_Eo_J,type,
    bot_bot_dtree_a_b_o: dtree_a_b > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J,type,
    bot_bo7321339186913516097_b_b_o: produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
    bot_bot_a_o: a > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__b_M_Eo_J,type,
    bot_bot_b_o: b > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
    bot_bot_o: $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    bot_bo4081095239089054910ee_a_b: fset_dtree_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo137739038786217454od_a_b: fset_P9180166578942778714od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    bot_bo5711572498106067156ee_a_b: fset_P5991447722532490344ee_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    bot_bo1493276529839087060_a_b_b: fset_P8532786667068971368_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J_J,type,
    bot_bo4737202254184417232_b_b_b: fset_P3031279327735363940_b_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo2863178955461725870od_a_b: fset_P5910908224067821594od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    bot_bo3079078458218859348ee_a_b: fset_P1087233464713034472ee_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    bot_bo6312180378851360852_a_b_b: fset_P271555816861255656_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    bot_bo7856883933444951080od_a_b: fset_P6924693328471822228od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo577854266114829310od_a_b: fset_P8869035697996476266od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    bot_bo2895716411488905534_a_b_b: fset_P5281107635120001194_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    bot_bo757577729753943290od_a_b: fset_P9214369701362650254od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_Itf__a_J,type,
    bot_bot_fset_a: fset_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_Itf__b_J,type,
    bot_bot_fset_b: fset_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    bot_bo8730652382759064772ee_a_b: set_dtree_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    bot_bo936214220562098254ee_a_b: set_Pr8090914455431026146ee_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    bot_bo3911397808570943822_a_b_b: set_Pr1790600203756605154_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    bot_bo6717195425869660366ee_a_b: set_Pr3885137059925752418ee_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    bot_bo5192956117685428686_a_b_b: set_Pr8296264926188598114_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    bot_bo6208222296400721441ee_a_b: set_Pr8736279663640031669ee_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    bot_bo3721250822024684356_a_b_b: set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    bot_bo5083760590458426867od_a_b: set_Pr3015088788472578951od_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    bot_bo3428410327501040244od_a_b: set_Product_prod_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
    bot_bot_set_b: set_b ).

thf(sy_c_Orderings_Oord__class_Oless_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le7001451600920047870_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    ord_le1844933027578805380ee_a_b: set_dtree_a_b > set_dtree_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le3723863380492978948_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
    ord_less_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__b_J,type,
    ord_less_set_b: set_b > set_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le789900035998834954_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    ord_le6340955050456522384ee_a_b: set_dtree_a_b > set_dtree_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le146215904626753808_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
    ord_less_eq_set_b: set_b > set_b > $o ).

thf(sy_c_Pair__Digraph_Opawalk__verts_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    pair_p1830641812483871010od_a_b: product_prod_a_b > list_P3463435030753280173od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc5314445973317677381ee_a_b: ( dtree_a_b > dtree_a_b > $o ) > list_dtree_a_b > produc750211871370617675ee_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc7760118425732869085od_a_b: ( list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ) > list_l8778361445553822004od_a_b > produc9134726091994374893od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc6413140877468432325_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o ) > list_P5360711134766023690_a_b_b > produc783859242544933067_a_b_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_062_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc1267148703545900054od_a_b: ( produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o ) > list_P3463435030753280173od_a_b > produc4732240729513732134od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc8832364399110542614od_a_b: ( product_prod_a_b > product_prod_a_b > $o ) > list_P8094385941167427565od_a_b > produc2580745285611667110od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc7704224619955794135od_a_b: ( product_prod_a_b > product_prod_a_b > $o ) > list_P1467974523212632366od_a_b > produc3334210663054469735od_a_b ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc9039425639929299113od_a_b: ( product_prod_a_b > product_prod_a_b ) > produc7397007428618769063od_a_b > produc7338334792537277175od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc3171423612928471772od_a_b: dtree_8339642294131873593od_a_b > list_P1467974523212632366od_a_b > produc6844405789190802602od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc6544956255868073555ee_a_b: dtree_1861073144021109543ee_a_b > ( dtree_a_b > dtree_a_b ) > produc6760719095789406107ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc4534897565878092007ee_a_b: dtree_1861073144021109543ee_a_b > dtree_1861073144021109543ee_a_b > produc7582145809211085103ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc2775200505768408122ee_a_b: dtree_1861073144021109543ee_a_b > dtree_a_b > produc6260003399586931330ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc7322284097139419219ee_a_b: dtree_8397784528784866983_a_b_b > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc5332496565491608475ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc1224323170490167271_a_b_b: dtree_8397784528784866983_a_b_b > dtree_8397784528784866983_a_b_b > produc442345915616064047_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc74755587182097722_a_b_b: dtree_8397784528784866983_a_b_b > produc4558475209616630778_a_b_b > produc4081214457754080642_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b,type,
    produc3612315917713105134_b_b_b: dtree_dtree_a_b_b > b > produc5284372313782567166_b_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc101167938378516380od_a_b: dtree_5519289247442030201od_a_b > list_P1467974523212632366od_a_b > produc4044292680377378282od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc7420187361910270035_a_b_b: dtree_8690448868185853351ee_a_b > ( dtree_a_b > produc4558475209616630778_a_b_b ) > produc9140505053306170267_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc4927624279478455783ee_a_b: dtree_8690448868185853351ee_a_b > dtree_8690448868185853351ee_a_b > produc435541801560641583ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc8867760425442229946ee_a_b: dtree_8690448868185853351ee_a_b > dtree_a_b > produc1961764714219340802ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc2908783650095110739_a_b_b: dtree_6636540493345571111_a_b_b > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc2919045324072751003_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc8054778519219240167_a_b_b: dtree_6636540493345571111_a_b_b > dtree_6636540493345571111_a_b_b > produc8284565691568599343_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc6281861845666676666_a_b_b: dtree_6636540493345571111_a_b_b > produc4558475209616630778_a_b_b > produc8137180380982048514_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    produc8904365110017546518od_a_b: dtree_2253494508914376569od_a_b > product_prod_a_b > produc2878020351943352036od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc8281931372741142764od_a_b: dtree_8545934391348768041od_a_b > list_P1467974523212632366od_a_b > produc229868702982719930od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    produc1993688775741047735_b_b_a: dtree_a_b > ( b > a ) > produc1083523234014712191_b_b_a ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc7805419539522982029ee_a_b: dtree_a_b > dtree_a_b > produc5177672665255943253ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc8306998211170319496ee_a_b: dtree_a_b > list_P7294506862534405595ee_a_b > produc8756840788158812374ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc6235741833889237512_a_b_b: dtree_a_b > list_P7142016109841313883_a_b_b > produc5473036864866960214_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc139389723908703645_a_b_b: dtree_a_b > list_P5360711134766023690_a_b_b > produc2168945239844811237_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc5178744004469394189_a_b_b: dtree_a_b > produc4558475209616630778_a_b_b > produc3392468160873345493_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc331601717337510060_a_b_b: dtree_a_b > b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc6019849452775264557ee_a_b: list_dtree_a_b > list_dtree_a_b > produc5339155667539881461ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3466467997744452247od_a_b: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > produc1688629678973589927od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc4608802955787333421_a_b_b: list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b > produc6081131995383004661_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc7754707808757098584od_a_b: list_P8601282865932132013od_a_b > list_P1467974523212632366od_a_b > produc1821044701915316840od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc3836617586516638167od_a_b: list_P3463435030753280173od_a_b > list_P3463435030753280173od_a_b > produc1627906242116850535od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    produc3641491676853602002od_a_b: list_P3463435030753280173od_a_b > product_prod_a_b > produc7218430402464555874od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc971229398454786070od_a_b: list_P1467974523212632366od_a_b > list_P8601282865932132013od_a_b > produc2698676102954276518od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc5288560138351607191od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > produc7397007428618769063od_a_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc2045222648701277328od_a_b: list_P1467974523212632366od_a_b > produc7397007428618769063od_a_b > produc7795635294741998752od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc4404387750691742122od_a_b: pair_p6651462780844640539t_unit > produc8474099945245761646od_a_b > produc4669796033538812730od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc2660662345621397005ee_a_b: produc4558475209616630778_a_b_b > dtree_a_b > produc3685132500274331861ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    produc7996648267824065416ee_a_b: produc4558475209616630778_a_b_b > list_P3724575226198589275ee_a_b > produc1280734032651800022ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc4858344343507073288_a_b_b: produc4558475209616630778_a_b_b > list_P7924273279524553179_a_b_b > produc375670372958830678_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc6533307410877503629_a_b_b: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc7345660473123082718od_a_b: produc7397007428618769063od_a_b > list_P1467974523212632366od_a_b > produc8474099945245761646od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    produc7680696477578383190od_a_b: produc7397007428618769063od_a_b > produc2698676102954276518od_a_b > produc2679909195573480038od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc6197409143109712604od_a_b: produc2233330766403592615od_a_b > produc566207910345494828od_a_b > produc3904047216122699628od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc8133154353881416535od_a_b: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > produc3348719938592107239od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    produc5088573426887569692od_a_b: product_prod_a_b > list_P3463435030753280173od_a_b > produc566207910345494828od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc4522856930405434833od_a_b: product_prod_a_b > produc7218430402464555874od_a_b > produc7239927097622659425od_a_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    produc6550459592057863831od_a_b: product_prod_a_b > product_prod_a_b > produc2233330766403592615od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    produc7441261679724955638od_a_b: a > list_P5700792096213675741od_a_b > produc5068203645811208070od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    produc6643264353547226055od_a_b: a > list_P1467974523212632366od_a_b > produc2639161875728825943od_a_b ).

thf(sy_c_Product__Type_OPair_001tf__a_001tf__b,type,
    product_Pair_a_b: a > b > product_prod_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc697780174058963904_a_b_b: produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__a_001tf__b,type,
    product_fst_a_b: product_prod_a_b > a ).

thf(sy_c_Relation_OField_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    field_dtree_a_b: set_Pr8736279663640031669ee_a_b > set_dtree_a_b ).

thf(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    field_2612910574630873453_a_b_b: set_Pr2755428042910921141_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Relation_Orefl__on_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    refl_on_dtree_a_b: set_dtree_a_b > set_Pr8736279663640031669ee_a_b > $o ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    refl_o6438828113603023419_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_Set_OCollect_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    collect_dtree_a_b: ( dtree_a_b > $o ) > set_dtree_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    collec1189380413810840640ee_a_b: ( produc5177672665255943253ee_a_b > $o ) > set_Pr8736279663640031669ee_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    collec1368399972772960719_a_b_b: ( produc4558475209616630778_a_b_b > $o ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    collec6173795731405551122od_a_b: ( produc7397007428618769063od_a_b > $o ) > set_Pr3015088788472578951od_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    collec3336397801687681299od_a_b: ( product_prod_a_b > $o ) > set_Product_prod_a_b ).

thf(sy_c_Set_OCollect_001tf__a,type,
    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_OCollect_001tf__b,type,
    collect_b: ( b > $o ) > set_b ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_1160270813240538107ee_a_b: ( dtree_a_b > dtree_a_b ) > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_360604450665336955_a_b_b: ( dtree_a_b > produc4558475209616630778_a_b_b ) > set_dtree_a_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_7065894828672115579ee_a_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > set_Pr3012420139608375472_a_b_b > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_6081965176830705659_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001tf__a,type,
    image_2802296252294471259_a_b_a: ( product_prod_a_b > a ) > set_Product_prod_a_b > set_a ).

thf(sy_c_Set_Oinsert_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    insert_dtree_a_b: dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    insert1613891728210272810_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    insert7668604973114392439od_a_b: produc2233330766403592615od_a_b > set_Pr5493900063595384711od_a_b > set_Pr5493900063595384711od_a_b ).

thf(sy_c_Set_Oinsert_001tf__a,type,
    insert_a: a > set_a > set_a ).

thf(sy_c_Set_Oinsert_001tf__b,type,
    insert_b: b > set_b > set_b ).

thf(sy_c_Set_Ois__singleton_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    is_sin1157029654344370822ee_a_b: set_dtree_a_b > $o ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    is_sin1118336051388392454_a_b_b: set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Set_Oremove_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    remove_dtree_a_b: dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    remove1850832869696284629_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    the_el4127461656392778949_a_b_b: set_Pr3012420139608375472_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    the_el8589169213296894365od_a_b: set_Product_prod_a_b > product_prod_a_b ).

thf(sy_c_Vertex__Walk_Ojoinable_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    vertex7469968122360900522od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o ).

thf(sy_c_Vertex__Walk_Ovwalk__arcs_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    vertex6757798842484198146ee_a_b: list_dtree_a_b > list_P7294506862534405595ee_a_b ).

thf(sy_c_Vertex__Walk_Ovwalk__arcs_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    vertex1682407011257858726od_a_b: list_l8778361445553822004od_a_b > list_P8601282865932132013od_a_b ).

thf(sy_c_Vertex__Walk_Ovwalk__arcs_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    vertex6010537929073084546_a_b_b: list_P5360711134766023690_a_b_b > list_P7924273279524553179_a_b_b ).

thf(sy_c_Vertex__Walk_Ovwalk__arcs_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    vertex6365343018446862111od_a_b: list_P3463435030753280173od_a_b > list_P5357134975691234797od_a_b ).

thf(sy_c_Vertex__Walk_Ovwalk__arcs_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    vertex3879532237292798496od_a_b: list_P1467974523212632366od_a_b > list_P3463435030753280173od_a_b ).

thf(sy_c_Vertex__Walk_Ovwalk__join_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    vertex7288003445438391211ee_a_b: list_dtree_a_b > list_dtree_a_b > list_dtree_a_b ).

thf(sy_c_Vertex__Walk_Ovwalk__join_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    vertex8382513469400993835_a_b_b: list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b > list_P5360711134766023690_a_b_b ).

thf(sy_c_Vertex__Walk_Ovwalk__join_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    vertex9110485820359517623od_a_b: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    accp_d5529011194741156464od_a_b: ( dtree_8339642294131873593od_a_b > dtree_8339642294131873593od_a_b > $o ) > dtree_8339642294131873593od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    accp_d5080589847971241310ee_a_b: ( dtree_1861073144021109543ee_a_b > dtree_1861073144021109543ee_a_b > $o ) > dtree_1861073144021109543ee_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    accp_d8404032630378873310_a_b_b: ( dtree_8397784528784866983_a_b_b > dtree_8397784528784866983_a_b_b > $o ) > dtree_8397784528784866983_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    accp_d7585430846279353905_a_b_b: ( dtree_dtree_a_b_b > dtree_dtree_a_b_b > $o ) > dtree_dtree_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    accp_d8312782500435053104od_a_b: ( dtree_5519289247442030201od_a_b > dtree_5519289247442030201od_a_b > $o ) > dtree_5519289247442030201od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    accp_d8696696969779859678ee_a_b: ( dtree_8690448868185853351ee_a_b > dtree_8690448868185853351ee_a_b > $o ) > dtree_8690448868185853351ee_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    accp_d2303357675354748254_a_b_b: ( dtree_6636540493345571111_a_b_b > dtree_6636540493345571111_a_b_b > $o ) > dtree_6636540493345571111_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    accp_d5695662582940224048od_a_b: ( dtree_2253494508914376569od_a_b > dtree_2253494508914376569od_a_b > $o ) > dtree_2253494508914376569od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    accp_d2542079058444124000od_a_b: ( dtree_8545934391348768041od_a_b > dtree_8545934391348768041od_a_b > $o ) > dtree_8545934391348768041od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    accp_dtree_a_b: ( dtree_a_b > dtree_a_b > $o ) > dtree_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_Itf__a_Mtf__b_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    accp_P8819943038680161455od_a_b: ( produc2580745285611667110od_a_b > produc2580745285611667110od_a_b > $o ) > produc2580745285611667110od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J_J,type,
    accp_P9118761241516785037ee_a_b: ( produc8756840788158812374ee_a_b > produc8756840788158812374ee_a_b > $o ) > produc8756840788158812374ee_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J_J,type,
    accp_P3938370695117152525_a_b_b: ( produc5473036864866960214_a_b_b > produc5473036864866960214_a_b_b > $o ) > produc5473036864866960214_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    accp_P6264444294748803566_a_b_b: ( produc2168945239844811237_a_b_b > produc2168945239844811237_a_b_b > $o ) > produc2168945239844811237_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    accp_P4877579601615922095od_a_b: ( produc2698676102954276518od_a_b > produc2698676102954276518od_a_b > $o ) > produc2698676102954276518od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J_J,type,
    accp_P1358717780819827853ee_a_b: ( produc1280734032651800022ee_a_b > produc1280734032651800022ee_a_b > $o ) > produc1280734032651800022ee_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J_J,type,
    accp_P883312628021968909_a_b_b: ( produc375670372958830678_a_b_b > produc375670372958830678_a_b_b > $o ) > produc375670372958830678_a_b_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J,type,
    accp_P4521695509574281141od_a_b: ( produc566207910345494828od_a_b > produc566207910345494828od_a_b > $o ) > produc566207910345494828od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J_J_J,type,
    accp_P9163702700715200399od_a_b: ( produc5068203645811208070od_a_b > produc5068203645811208070od_a_b > $o ) > produc5068203645811208070od_a_b > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    accp_P6845111368451614688od_a_b: ( produc2639161875728825943od_a_b > produc2639161875728825943od_a_b > $o ) > produc2639161875728825943od_a_b > $o ).

thf(sy_c_member_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member57152265779237438ee_a_b: dtree_1861073144021109543ee_a_b > set_dt5871847375752683485ee_a_b > $o ).

thf(sy_c_member_001t__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member1357683700308350654_a_b_b: dtree_8397784528784866983_a_b_b > set_dt6254119027684364381_a_b_b > $o ).

thf(sy_c_member_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member1650348039709337022ee_a_b: dtree_8690448868185853351ee_a_b > set_dt2836678144041639773ee_a_b > $o ).

thf(sy_c_member_001t__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member4384582438082964030_a_b_b: dtree_6636540493345571111_a_b_b > set_dt8691689324118462429_a_b_b > $o ).

thf(sy_c_member_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    member_dtree_a_b: dtree_a_b > set_dtree_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member1914986943068214699ee_a_b: produc6260003399586931330ee_a_b > set_Pr8090914455431026146ee_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member2386720262296790699_a_b_b: produc4081214457754080642_a_b_b > set_Pr1790600203756605154_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member5265136988498437675ee_a_b: produc1961764714219340802ee_a_b > set_Pr3885137059925752418ee_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member684607838164940587_a_b_b: produc8137180380982048514_a_b_b > set_Pr8296264926188598114_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member2060280516343777534ee_a_b: produc5177672665255943253ee_a_b > set_Pr8736279663640031669ee_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    member4380921116106875537_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__b_J_J_J,type,
    member3051990972100052432od_a_b: produc7397007428618769063od_a_b > set_Pr3015088788472578951od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member9171970031259705598_a_b_b: produc8908337785154950741_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_Itf__a_Mtf__b_J_J,type,
    member5065438833300252112od_a_b: produc2233330766403592615od_a_b > set_Pr5493900063595384711od_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    member1426531481828664017od_a_b: product_prod_a_b > set_Product_prod_a_b > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_v_r____,type,
    r: a ).

thf(sy_v_xs____,type,
    xs: fset_P5281107635120001194_a_b_b ).

% Relevant facts (1268)
thf(fact_0_True,axiom,
    ! [X: produc4558475209616630778_a_b_b] :
      ( xs
     != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) ) ).

% True
thf(fact_1_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P6924693328471822228od_a_b,R: product_prod_a_b] :
      ( ! [X2: produc2878020351943352036od_a_b] :
          ( Xs
         != ( finser5347476252697843100od_a_b @ X2 @ bot_bo7856883933444951080od_a_b ) )
     => ( ( dtree_983605638134528549od_a_b @ ( node_P1936840572307073598od_a_b @ R @ Xs ) )
        = nil_Pr906174322249854893od_a_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_2_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P3031279327735363940_b_b_b,R: dtree_a_b] :
      ( ! [X2: produc5284372313782567166_b_b_b] :
          ( Xs
         != ( finser6734551996811508806_b_b_b @ X2 @ bot_bo4737202254184417232_b_b_b ) )
     => ( ( dtree_29943561566189470_a_b_b @ ( node_dtree_a_b_b @ R @ Xs ) )
        = nil_Pr5403147374433350260_a_b_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_3_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P5991447722532490344ee_a_b,R: dtree_a_b] :
      ( ! [X2: produc6260003399586931330ee_a_b] :
          ( Xs
         != ( finser8516331313445392842ee_a_b @ X2 @ bot_bo5711572498106067156ee_a_b ) )
     => ( ( dtree_5459410236902894363ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
        = nil_Pr558572586965427547ee_a_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_4_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P1087233464713034472ee_a_b,R: produc4558475209616630778_a_b_b] :
      ( ! [X2: produc1961764714219340802ee_a_b] :
          ( Xs
         != ( finser7847761039489690442ee_a_b @ X2 @ bot_bo3079078458218859348ee_a_b ) )
     => ( ( dtree_9187971570250218139ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
        = nil_Pr148742403700823003ee_a_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_5_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P8532786667068971368_a_b_b,R: dtree_a_b] :
      ( ! [X2: produc4081214457754080642_a_b_b] :
          ( Xs
         != ( finser5778094437704840394_a_b_b @ X2 @ bot_bo1493276529839087060_a_b_b ) )
     => ( ( dtree_2482681192243439515_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
        = nil_Pr9079450101154612443_a_b_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_6_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P271555816861255656_a_b_b,R: produc4558475209616630778_a_b_b] :
      ( ! [X2: produc8137180380982048514_a_b_b] :
          ( Xs
         != ( finser3407669804807474762_a_b_b @ X2 @ bot_bo6312180378851360852_a_b_b ) )
     => ( ( dtree_1768895223656068891_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
        = nil_Pr5872703755862520667_a_b_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_7_dtree__to__list_Osimps_I2_J,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( Xs
         != ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) )
     => ( ( dtree_to_list_a_b @ ( node_a_b @ R @ Xs ) )
        = nil_Product_prod_a_b ) ) ).

% dtree_to_list.simps(2)
thf(fact_8_dtree_Oinject,axiom,
    ! [X1: dtree_a_b,X22: fset_P5991447722532490344ee_a_b,Y1: dtree_a_b,Y2: fset_P5991447722532490344ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ X1 @ X22 )
        = ( node_d7487230363575057332ee_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% dtree.inject
thf(fact_9_dtree_Oinject,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P1087233464713034472ee_a_b,Y1: produc4558475209616630778_a_b_b,Y2: fset_P1087233464713034472ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ X1 @ X22 )
        = ( node_P2753077162091514420ee_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% dtree.inject
thf(fact_10_dtree_Oinject,axiom,
    ! [X1: dtree_a_b,X22: fset_P8532786667068971368_a_b_b,Y1: dtree_a_b,Y2: fset_P8532786667068971368_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ X1 @ X22 )
        = ( node_d5271158820939511604_a_b_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% dtree.inject
thf(fact_11_dtree_Oinject,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P271555816861255656_a_b_b,Y1: produc4558475209616630778_a_b_b,Y2: fset_P271555816861255656_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ X1 @ X22 )
        = ( node_P961815112480277940_a_b_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% dtree.inject
thf(fact_12_dtree_Oinject,axiom,
    ! [X1: a,X22: fset_P5281107635120001194_a_b_b,Y1: a,Y2: fset_P5281107635120001194_a_b_b] :
      ( ( ( node_a_b @ X1 @ X22 )
        = ( node_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% dtree.inject
thf(fact_13_Node_Oprems,axiom,
    wf_dverts_a_b @ ( node_a_b @ r @ xs ) ).

% Node.prems
thf(fact_14_dtree_Oexhaust,axiom,
    ! [Y: dtree_1861073144021109543ee_a_b] :
      ~ ! [X12: dtree_a_b,X23: fset_P5991447722532490344ee_a_b] :
          ( Y
         != ( node_d7487230363575057332ee_a_b @ X12 @ X23 ) ) ).

% dtree.exhaust
thf(fact_15_dtree_Oexhaust,axiom,
    ! [Y: dtree_8690448868185853351ee_a_b] :
      ~ ! [X12: produc4558475209616630778_a_b_b,X23: fset_P1087233464713034472ee_a_b] :
          ( Y
         != ( node_P2753077162091514420ee_a_b @ X12 @ X23 ) ) ).

% dtree.exhaust
thf(fact_16_dtree_Oexhaust,axiom,
    ! [Y: dtree_8397784528784866983_a_b_b] :
      ~ ! [X12: dtree_a_b,X23: fset_P8532786667068971368_a_b_b] :
          ( Y
         != ( node_d5271158820939511604_a_b_b @ X12 @ X23 ) ) ).

% dtree.exhaust
thf(fact_17_dtree_Oexhaust,axiom,
    ! [Y: dtree_6636540493345571111_a_b_b] :
      ~ ! [X12: produc4558475209616630778_a_b_b,X23: fset_P271555816861255656_a_b_b] :
          ( Y
         != ( node_P961815112480277940_a_b_b @ X12 @ X23 ) ) ).

% dtree.exhaust
thf(fact_18_dtree_Oexhaust,axiom,
    ! [Y: dtree_a_b] :
      ~ ! [X12: a,X23: fset_P5281107635120001194_a_b_b] :
          ( Y
         != ( node_a_b @ X12 @ X23 ) ) ).

% dtree.exhaust
thf(fact_19_dverts__mset_Ocases,axiom,
    ! [X3: dtree_1861073144021109543ee_a_b] :
      ~ ! [R2: dtree_a_b,Xs2: fset_P5991447722532490344ee_a_b] :
          ( X3
         != ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ).

% dverts_mset.cases
thf(fact_20_dverts__mset_Ocases,axiom,
    ! [X3: dtree_8690448868185853351ee_a_b] :
      ~ ! [R2: produc4558475209616630778_a_b_b,Xs2: fset_P1087233464713034472ee_a_b] :
          ( X3
         != ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ).

% dverts_mset.cases
thf(fact_21_dverts__mset_Ocases,axiom,
    ! [X3: dtree_8397784528784866983_a_b_b] :
      ~ ! [R2: dtree_a_b,Xs2: fset_P8532786667068971368_a_b_b] :
          ( X3
         != ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ).

% dverts_mset.cases
thf(fact_22_dverts__mset_Ocases,axiom,
    ! [X3: dtree_6636540493345571111_a_b_b] :
      ~ ! [R2: produc4558475209616630778_a_b_b,Xs2: fset_P271555816861255656_a_b_b] :
          ( X3
         != ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ).

% dverts_mset.cases
thf(fact_23_dverts__mset_Ocases,axiom,
    ! [X3: dtree_a_b] :
      ~ ! [R2: a,Xs2: fset_P5281107635120001194_a_b_b] :
          ( X3
         != ( node_a_b @ R2 @ Xs2 ) ) ).

% dverts_mset.cases
thf(fact_24_wf__list__verts_Osimps_I1_J,axiom,
    wf_lis873957137097608799od_a_b @ nil_Pr906174322249854893od_a_b ).

% wf_list_verts.simps(1)
thf(fact_25_wf__list__verts_Osimps_I1_J,axiom,
    wf_lis4446142942163678948_a_b_b @ nil_Pr5403147374433350260_a_b_b ).

% wf_list_verts.simps(1)
thf(fact_26_wf__list__verts_Osimps_I1_J,axiom,
    wf_list_verts_a_b @ nil_Product_prod_a_b ).

% wf_list_verts.simps(1)
thf(fact_27_Node_OIH,axiom,
    ! [X2aa: produc4558475209616630778_a_b_b,X2aaa: dtree_a_b] :
      ( ( member4380921116106875537_a_b_b @ X2aa @ ( fset_P783253628892185035_a_b_b @ xs ) )
     => ( ( member_dtree_a_b @ X2aaa @ ( basic_7578771248400840636_a_b_b @ X2aa ) )
       => ( ( wf_dverts_a_b @ X2aaa )
         => ( wf_list_verts_a_b @ ( dtree_to_list_a_b @ X2aaa ) ) ) ) ) ).

% Node.IH
thf(fact_28_num__leaves__root,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,R3: dtree_a_b] :
      ( ( num_le762670902658651842ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
      = ( num_le762670902658651842ee_a_b @ ( node_d7487230363575057332ee_a_b @ R3 @ Xs ) ) ) ).

% num_leaves_root
thf(fact_29_num__leaves__root,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,R3: produc4558475209616630778_a_b_b] :
      ( ( num_le972019002107111234ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
      = ( num_le972019002107111234ee_a_b @ ( node_P2753077162091514420ee_a_b @ R3 @ Xs ) ) ) ).

% num_leaves_root
thf(fact_30_num__leaves__root,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,R3: dtree_a_b] :
      ( ( num_le3490100660955108418_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
      = ( num_le3490100660955108418_a_b_b @ ( node_d5271158820939511604_a_b_b @ R3 @ Xs ) ) ) ).

% num_leaves_root
thf(fact_31_num__leaves__root,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,R3: produc4558475209616630778_a_b_b] :
      ( ( num_le5032565032286201026_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
      = ( num_le5032565032286201026_a_b_b @ ( node_P961815112480277940_a_b_b @ R3 @ Xs ) ) ) ).

% num_leaves_root
thf(fact_32_num__leaves__root,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,R3: a] :
      ( ( num_leaves_a_b @ ( node_a_b @ R @ Xs ) )
      = ( num_leaves_a_b @ ( node_a_b @ R3 @ Xs ) ) ) ).

% num_leaves_root
thf(fact_33_dtree__to__from__list__id,axiom,
    ! [R: a,Xs: list_P1467974523212632366od_a_b] :
      ( ( dtree_to_list_a_b @ ( dtree_from_list_a_b @ R @ Xs ) )
      = Xs ) ).

% dtree_to_from_list_id
thf(fact_34_dtree__size__eq__root,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,R3: dtree_a_b] :
      ( ( size_s6196567657804286395ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
      = ( size_s6196567657804286395ee_a_b @ ( node_d7487230363575057332ee_a_b @ R3 @ Xs ) ) ) ).

% dtree_size_eq_root
thf(fact_35_dtree__size__eq__root,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,R3: produc4558475209616630778_a_b_b] :
      ( ( size_s59920387959265339ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
      = ( size_s59920387959265339ee_a_b @ ( node_P2753077162091514420ee_a_b @ R3 @ Xs ) ) ) ).

% dtree_size_eq_root
thf(fact_36_dtree__size__eq__root,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,R3: dtree_a_b] :
      ( ( size_s8990628085413054779_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
      = ( size_s8990628085413054779_a_b_b @ ( node_d5271158820939511604_a_b_b @ R3 @ Xs ) ) ) ).

% dtree_size_eq_root
thf(fact_37_dtree__size__eq__root,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,R3: produc4558475209616630778_a_b_b] :
      ( ( size_s5437551432765265851_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
      = ( size_s5437551432765265851_a_b_b @ ( node_P961815112480277940_a_b_b @ R3 @ Xs ) ) ) ).

% dtree_size_eq_root
thf(fact_38_dtree__size__eq__root,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,R3: a] :
      ( ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs ) )
      = ( size_size_dtree_a_b @ ( node_a_b @ R3 @ Xs ) ) ) ).

% dtree_size_eq_root
thf(fact_39_dtree__from__list__v__eq__r,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,V: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
        = ( dtree_7424119665891431146ee_a_b @ V @ Ys ) )
     => ( R = V ) ) ).

% dtree_from_list_v_eq_r
thf(fact_40_dtree__from__list__v__eq__r,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,V: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
        = ( dtree_7850083854586231658ee_a_b @ V @ Ys ) )
     => ( R = V ) ) ).

% dtree_from_list_v_eq_r
thf(fact_41_dtree__from__list__v__eq__r,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,V: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
        = ( dtree_1144793476579453034_a_b_b @ V @ Ys ) )
     => ( R = V ) ) ).

% dtree_from_list_v_eq_r
thf(fact_42_dtree__from__list__v__eq__r,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,V: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
        = ( dtree_450453658713739498_a_b_b @ V @ Ys ) )
     => ( R = V ) ) ).

% dtree_from_list_v_eq_r
thf(fact_43_dtree__from__list__v__eq__r,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( node_a_b @ R @ Xs )
        = ( dtree_from_list_a_b @ V @ Ys ) )
     => ( R = V ) ) ).

% dtree_from_list_v_eq_r
thf(fact_44_is__subtree_Ocases,axiom,
    ! [X3: produc7582145809211085103ee_a_b] :
      ~ ! [X2: dtree_1861073144021109543ee_a_b,R2: dtree_a_b,Xs2: fset_P5991447722532490344ee_a_b] :
          ( X3
         != ( produc4534897565878092007ee_a_b @ X2 @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ) ).

% is_subtree.cases
thf(fact_45_is__subtree_Ocases,axiom,
    ! [X3: produc435541801560641583ee_a_b] :
      ~ ! [X2: dtree_8690448868185853351ee_a_b,R2: produc4558475209616630778_a_b_b,Xs2: fset_P1087233464713034472ee_a_b] :
          ( X3
         != ( produc4927624279478455783ee_a_b @ X2 @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ) ).

% is_subtree.cases
thf(fact_46_is__subtree_Ocases,axiom,
    ! [X3: produc442345915616064047_a_b_b] :
      ~ ! [X2: dtree_8397784528784866983_a_b_b,R2: dtree_a_b,Xs2: fset_P8532786667068971368_a_b_b] :
          ( X3
         != ( produc1224323170490167271_a_b_b @ X2 @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ) ).

% is_subtree.cases
thf(fact_47_is__subtree_Ocases,axiom,
    ! [X3: produc8284565691568599343_a_b_b] :
      ~ ! [X2: dtree_6636540493345571111_a_b_b,R2: produc4558475209616630778_a_b_b,Xs2: fset_P271555816861255656_a_b_b] :
          ( X3
         != ( produc8054778519219240167_a_b_b @ X2 @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ) ).

% is_subtree.cases
thf(fact_48_is__subtree_Ocases,axiom,
    ! [X3: produc5177672665255943253ee_a_b] :
      ~ ! [X2: dtree_a_b,R2: a,Xs2: fset_P5281107635120001194_a_b_b] :
          ( X3
         != ( produc7805419539522982029ee_a_b @ X2 @ ( node_a_b @ R2 @ Xs2 ) ) ) ).

% is_subtree.cases
thf(fact_49_dtree_Osel_I2_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P5991447722532490344ee_a_b] :
      ( ( sucs_d5654203025177486372ee_a_b @ ( node_d7487230363575057332ee_a_b @ X1 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_50_dtree_Osel_I2_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P1087233464713034472ee_a_b] :
      ( ( sucs_P7314365117959652004ee_a_b @ ( node_P2753077162091514420ee_a_b @ X1 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_51_dtree_Osel_I2_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P8532786667068971368_a_b_b] :
      ( ( sucs_d609074739952873380_a_b_b @ ( node_d5271158820939511604_a_b_b @ X1 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_52_dtree_Osel_I2_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P271555816861255656_a_b_b] :
      ( ( sucs_P6478368611001241124_a_b_b @ ( node_P961815112480277940_a_b_b @ X1 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_53_dtree_Osel_I2_J,axiom,
    ! [X1: a,X22: fset_P5281107635120001194_a_b_b] :
      ( ( sucs_a_b @ ( node_a_b @ X1 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_54_dtail_Ocases,axiom,
    ! [X3: produc6760719095789406107ee_a_b] :
      ~ ! [R2: dtree_a_b,Xs2: fset_P5991447722532490344ee_a_b,Def: dtree_a_b > dtree_a_b] :
          ( X3
         != ( produc6544956255868073555ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) @ Def ) ) ).

% dtail.cases
thf(fact_55_dtail_Ocases,axiom,
    ! [X3: produc9140505053306170267_a_b_b] :
      ~ ! [R2: produc4558475209616630778_a_b_b,Xs2: fset_P1087233464713034472ee_a_b,Def: dtree_a_b > produc4558475209616630778_a_b_b] :
          ( X3
         != ( produc7420187361910270035_a_b_b @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) @ Def ) ) ).

% dtail.cases
thf(fact_56_dtail_Ocases,axiom,
    ! [X3: produc5332496565491608475ee_a_b] :
      ~ ! [R2: dtree_a_b,Xs2: fset_P8532786667068971368_a_b_b,Def: produc4558475209616630778_a_b_b > dtree_a_b] :
          ( X3
         != ( produc7322284097139419219ee_a_b @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) @ Def ) ) ).

% dtail.cases
thf(fact_57_dtail_Ocases,axiom,
    ! [X3: produc2919045324072751003_a_b_b] :
      ~ ! [R2: produc4558475209616630778_a_b_b,Xs2: fset_P271555816861255656_a_b_b,Def: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
          ( X3
         != ( produc2908783650095110739_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) @ Def ) ) ).

% dtail.cases
thf(fact_58_dtail_Ocases,axiom,
    ! [X3: produc1083523234014712191_b_b_a] :
      ~ ! [R2: a,Xs2: fset_P5281107635120001194_a_b_b,Def: b > a] :
          ( X3
         != ( produc1993688775741047735_b_b_a @ ( node_a_b @ R2 @ Xs2 ) @ Def ) ) ).

% dtail.cases
thf(fact_59_dtree_Oset__intros_I1_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P5991447722532490344ee_a_b] : ( member_dtree_a_b @ X1 @ ( dverts2436977245124431984ee_a_b @ ( node_d7487230363575057332ee_a_b @ X1 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_60_dtree_Oset__intros_I1_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P1087233464713034472ee_a_b] : ( member4380921116106875537_a_b_b @ X1 @ ( dverts2972317704043987696ee_a_b @ ( node_P2753077162091514420ee_a_b @ X1 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_61_dtree_Oset__intros_I1_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P8532786667068971368_a_b_b] : ( member_dtree_a_b @ X1 @ ( dverts5490399362891984880_a_b_b @ ( node_d5271158820939511604_a_b_b @ X1 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_62_dtree_Oset__intros_I1_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P271555816861255656_a_b_b] : ( member4380921116106875537_a_b_b @ X1 @ ( dverts1640268204329280112_a_b_b @ ( node_P961815112480277940_a_b_b @ X1 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_63_dtree_Oset__intros_I1_J,axiom,
    ! [X1: a,X22: fset_P5281107635120001194_a_b_b] : ( member_a @ X1 @ ( dverts_a_b @ ( node_a_b @ X1 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_64_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc6260003399586931330ee_a_b,A: dtree_1861073144021109543ee_a_b,Xa: dtree_1861073144021109543ee_a_b,Xb: dtree_a_b] :
      ( ( member1914986943068214699ee_a_b @ X3 @ ( fset_P4845137164202167537ee_a_b @ ( sucs_d5654203025177486372ee_a_b @ A ) ) )
     => ( ( member57152265779237438ee_a_b @ Xa @ ( basic_3138169641471185194ee_a_b @ X3 ) )
       => ( ( member_dtree_a_b @ Xb @ ( dverts2436977245124431984ee_a_b @ Xa ) )
         => ( member_dtree_a_b @ Xb @ ( dverts2436977245124431984ee_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_65_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc1961764714219340802ee_a_b,A: dtree_8690448868185853351ee_a_b,Xa: dtree_8690448868185853351ee_a_b,Xb: produc4558475209616630778_a_b_b] :
      ( ( member5265136988498437675ee_a_b @ X3 @ ( fset_P3182333368011040625ee_a_b @ ( sucs_P7314365117959652004ee_a_b @ A ) ) )
     => ( ( member1650348039709337022ee_a_b @ Xa @ ( basic_2889154014856113066ee_a_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ Xb @ ( dverts2972317704043987696ee_a_b @ Xa ) )
         => ( member4380921116106875537_a_b_b @ Xb @ ( dverts2972317704043987696ee_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_66_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc4081214457754080642_a_b_b,A: dtree_8397784528784866983_a_b_b,Xa: dtree_8397784528784866983_a_b_b,Xb: dtree_a_b] :
      ( ( member2386720262296790699_a_b_b @ X3 @ ( fset_P4440376523358319089_a_b_b @ ( sucs_d609074739952873380_a_b_b @ A ) ) )
     => ( ( member1357683700308350654_a_b_b @ Xa @ ( basic_3992591041251291690_a_b_b @ X3 ) )
       => ( ( member_dtree_a_b @ Xb @ ( dverts5490399362891984880_a_b_b @ Xa ) )
         => ( member_dtree_a_b @ Xb @ ( dverts5490399362891984880_a_b_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_67_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc8137180380982048514_a_b_b,A: dtree_6636540493345571111_a_b_b,Xa: dtree_6636540493345571111_a_b_b,Xb: produc4558475209616630778_a_b_b] :
      ( ( member684607838164940587_a_b_b @ X3 @ ( fset_P8825802006873508977_a_b_b @ ( sucs_P6478368611001241124_a_b_b @ A ) ) )
     => ( ( member4384582438082964030_a_b_b @ Xa @ ( basic_6594820288780307626_a_b_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ Xb @ ( dverts1640268204329280112_a_b_b @ Xa ) )
         => ( member4380921116106875537_a_b_b @ Xb @ ( dverts1640268204329280112_a_b_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_68_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A: dtree_a_b,Xa: dtree_a_b,Xb: a] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_dtree_a_b @ Xa @ ( basic_7578771248400840636_a_b_b @ X3 ) )
       => ( ( member_a @ Xb @ ( dverts_a_b @ Xa ) )
         => ( member_a @ Xb @ ( dverts_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_69_dtree_Oset__cases_I1_J,axiom,
    ! [E: dtree_a_b,A: dtree_1861073144021109543ee_a_b] :
      ( ( member_dtree_a_b @ E @ ( dverts2436977245124431984ee_a_b @ A ) )
     => ( ! [Z2: fset_P5991447722532490344ee_a_b] :
            ( A
           != ( node_d7487230363575057332ee_a_b @ E @ Z2 ) )
       => ~ ! [Z1: dtree_a_b,Z2: fset_P5991447722532490344ee_a_b] :
              ( ( A
                = ( node_d7487230363575057332ee_a_b @ Z1 @ Z2 ) )
             => ! [X2: produc6260003399586931330ee_a_b] :
                  ( ( member1914986943068214699ee_a_b @ X2 @ ( fset_P4845137164202167537ee_a_b @ Z2 ) )
                 => ! [Xa2: dtree_1861073144021109543ee_a_b] :
                      ( ( member57152265779237438ee_a_b @ Xa2 @ ( basic_3138169641471185194ee_a_b @ X2 ) )
                     => ~ ( member_dtree_a_b @ E @ ( dverts2436977245124431984ee_a_b @ Xa2 ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_70_dtree_Oset__cases_I1_J,axiom,
    ! [E: produc4558475209616630778_a_b_b,A: dtree_8690448868185853351ee_a_b] :
      ( ( member4380921116106875537_a_b_b @ E @ ( dverts2972317704043987696ee_a_b @ A ) )
     => ( ! [Z2: fset_P1087233464713034472ee_a_b] :
            ( A
           != ( node_P2753077162091514420ee_a_b @ E @ Z2 ) )
       => ~ ! [Z1: produc4558475209616630778_a_b_b,Z2: fset_P1087233464713034472ee_a_b] :
              ( ( A
                = ( node_P2753077162091514420ee_a_b @ Z1 @ Z2 ) )
             => ! [X2: produc1961764714219340802ee_a_b] :
                  ( ( member5265136988498437675ee_a_b @ X2 @ ( fset_P3182333368011040625ee_a_b @ Z2 ) )
                 => ! [Xa2: dtree_8690448868185853351ee_a_b] :
                      ( ( member1650348039709337022ee_a_b @ Xa2 @ ( basic_2889154014856113066ee_a_b @ X2 ) )
                     => ~ ( member4380921116106875537_a_b_b @ E @ ( dverts2972317704043987696ee_a_b @ Xa2 ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_71_dtree_Oset__cases_I1_J,axiom,
    ! [E: dtree_a_b,A: dtree_8397784528784866983_a_b_b] :
      ( ( member_dtree_a_b @ E @ ( dverts5490399362891984880_a_b_b @ A ) )
     => ( ! [Z2: fset_P8532786667068971368_a_b_b] :
            ( A
           != ( node_d5271158820939511604_a_b_b @ E @ Z2 ) )
       => ~ ! [Z1: dtree_a_b,Z2: fset_P8532786667068971368_a_b_b] :
              ( ( A
                = ( node_d5271158820939511604_a_b_b @ Z1 @ Z2 ) )
             => ! [X2: produc4081214457754080642_a_b_b] :
                  ( ( member2386720262296790699_a_b_b @ X2 @ ( fset_P4440376523358319089_a_b_b @ Z2 ) )
                 => ! [Xa2: dtree_8397784528784866983_a_b_b] :
                      ( ( member1357683700308350654_a_b_b @ Xa2 @ ( basic_3992591041251291690_a_b_b @ X2 ) )
                     => ~ ( member_dtree_a_b @ E @ ( dverts5490399362891984880_a_b_b @ Xa2 ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_72_dtree_Oset__cases_I1_J,axiom,
    ! [E: produc4558475209616630778_a_b_b,A: dtree_6636540493345571111_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ E @ ( dverts1640268204329280112_a_b_b @ A ) )
     => ( ! [Z2: fset_P271555816861255656_a_b_b] :
            ( A
           != ( node_P961815112480277940_a_b_b @ E @ Z2 ) )
       => ~ ! [Z1: produc4558475209616630778_a_b_b,Z2: fset_P271555816861255656_a_b_b] :
              ( ( A
                = ( node_P961815112480277940_a_b_b @ Z1 @ Z2 ) )
             => ! [X2: produc8137180380982048514_a_b_b] :
                  ( ( member684607838164940587_a_b_b @ X2 @ ( fset_P8825802006873508977_a_b_b @ Z2 ) )
                 => ! [Xa2: dtree_6636540493345571111_a_b_b] :
                      ( ( member4384582438082964030_a_b_b @ Xa2 @ ( basic_6594820288780307626_a_b_b @ X2 ) )
                     => ~ ( member4380921116106875537_a_b_b @ E @ ( dverts1640268204329280112_a_b_b @ Xa2 ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_73_dtree_Oset__cases_I1_J,axiom,
    ! [E: a,A: dtree_a_b] :
      ( ( member_a @ E @ ( dverts_a_b @ A ) )
     => ( ! [Z2: fset_P5281107635120001194_a_b_b] :
            ( A
           != ( node_a_b @ E @ Z2 ) )
       => ~ ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
              ( ( A
                = ( node_a_b @ Z1 @ Z2 ) )
             => ! [X2: produc4558475209616630778_a_b_b] :
                  ( ( member4380921116106875537_a_b_b @ X2 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
                 => ! [Xa2: dtree_a_b] :
                      ( ( member_dtree_a_b @ Xa2 @ ( basic_7578771248400840636_a_b_b @ X2 ) )
                     => ~ ( member_a @ E @ ( dverts_a_b @ Xa2 ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_74_dtree_Oset__intros_I2_J,axiom,
    ! [Y: produc6260003399586931330ee_a_b,X22: fset_P5991447722532490344ee_a_b,Ya: dtree_1861073144021109543ee_a_b,Yb: dtree_a_b,X1: dtree_a_b] :
      ( ( member1914986943068214699ee_a_b @ Y @ ( fset_P4845137164202167537ee_a_b @ X22 ) )
     => ( ( member57152265779237438ee_a_b @ Ya @ ( basic_3138169641471185194ee_a_b @ Y ) )
       => ( ( member_dtree_a_b @ Yb @ ( dverts2436977245124431984ee_a_b @ Ya ) )
         => ( member_dtree_a_b @ Yb @ ( dverts2436977245124431984ee_a_b @ ( node_d7487230363575057332ee_a_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_75_dtree_Oset__intros_I2_J,axiom,
    ! [Y: produc1961764714219340802ee_a_b,X22: fset_P1087233464713034472ee_a_b,Ya: dtree_8690448868185853351ee_a_b,Yb: produc4558475209616630778_a_b_b,X1: produc4558475209616630778_a_b_b] :
      ( ( member5265136988498437675ee_a_b @ Y @ ( fset_P3182333368011040625ee_a_b @ X22 ) )
     => ( ( member1650348039709337022ee_a_b @ Ya @ ( basic_2889154014856113066ee_a_b @ Y ) )
       => ( ( member4380921116106875537_a_b_b @ Yb @ ( dverts2972317704043987696ee_a_b @ Ya ) )
         => ( member4380921116106875537_a_b_b @ Yb @ ( dverts2972317704043987696ee_a_b @ ( node_P2753077162091514420ee_a_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_76_dtree_Oset__intros_I2_J,axiom,
    ! [Y: produc4081214457754080642_a_b_b,X22: fset_P8532786667068971368_a_b_b,Ya: dtree_8397784528784866983_a_b_b,Yb: dtree_a_b,X1: dtree_a_b] :
      ( ( member2386720262296790699_a_b_b @ Y @ ( fset_P4440376523358319089_a_b_b @ X22 ) )
     => ( ( member1357683700308350654_a_b_b @ Ya @ ( basic_3992591041251291690_a_b_b @ Y ) )
       => ( ( member_dtree_a_b @ Yb @ ( dverts5490399362891984880_a_b_b @ Ya ) )
         => ( member_dtree_a_b @ Yb @ ( dverts5490399362891984880_a_b_b @ ( node_d5271158820939511604_a_b_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_77_dtree_Oset__intros_I2_J,axiom,
    ! [Y: produc8137180380982048514_a_b_b,X22: fset_P271555816861255656_a_b_b,Ya: dtree_6636540493345571111_a_b_b,Yb: produc4558475209616630778_a_b_b,X1: produc4558475209616630778_a_b_b] :
      ( ( member684607838164940587_a_b_b @ Y @ ( fset_P8825802006873508977_a_b_b @ X22 ) )
     => ( ( member4384582438082964030_a_b_b @ Ya @ ( basic_6594820288780307626_a_b_b @ Y ) )
       => ( ( member4380921116106875537_a_b_b @ Yb @ ( dverts1640268204329280112_a_b_b @ Ya ) )
         => ( member4380921116106875537_a_b_b @ Yb @ ( dverts1640268204329280112_a_b_b @ ( node_P961815112480277940_a_b_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_78_dtree_Oset__intros_I2_J,axiom,
    ! [Y: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Ya: dtree_a_b,Yb: a,X1: a] :
      ( ( member4380921116106875537_a_b_b @ Y @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_dtree_a_b @ Ya @ ( basic_7578771248400840636_a_b_b @ Y ) )
       => ( ( member_a @ Yb @ ( dverts_a_b @ Ya ) )
         => ( member_a @ Yb @ ( dverts_a_b @ ( node_a_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_79_singleton__uneq_H,axiom,
    ! [R: dtree_a_b,T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,V: dtree_a_b] :
      ( ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) )
     != ( node_d7487230363575057332ee_a_b @ V @ ( sucs_d5654203025177486372ee_a_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_80_singleton__uneq_H,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,V: produc4558475209616630778_a_b_b] :
      ( ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) )
     != ( node_P2753077162091514420ee_a_b @ V @ ( sucs_P7314365117959652004ee_a_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_81_singleton__uneq_H,axiom,
    ! [R: dtree_a_b,T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,V: dtree_a_b] :
      ( ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) )
     != ( node_d5271158820939511604_a_b_b @ V @ ( sucs_d609074739952873380_a_b_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_82_singleton__uneq_H,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b] :
      ( ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) )
     != ( node_P961815112480277940_a_b_b @ V @ ( sucs_P6478368611001241124_a_b_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_83_singleton__uneq_H,axiom,
    ! [R: a,T: dtree_a_b,E: b,V: a] :
      ( ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) )
     != ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_84_dtree__from__list__singleton,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,R: product_prod_a_b] :
      ( ( Xs != nil_Pr906174322249854893od_a_b )
     => ? [T2: dtree_2253494508914376569od_a_b,E2: product_prod_a_b] :
          ( ( dtree_1864022081312108148od_a_b @ R @ Xs )
          = ( node_P1936840572307073598od_a_b @ R @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T2 @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_85_dtree__from__list__singleton,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,R: dtree_a_b] :
      ( ( Xs != nil_Pr5403147374433350260_a_b_b )
     => ? [T2: dtree_dtree_a_b_b,E2: b] :
          ( ( dtree_5255521609252960911_a_b_b @ R @ Xs )
          = ( node_dtree_a_b_b @ R @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T2 @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_86_dtree__from__list__singleton,axiom,
    ! [Xs: list_P7294506862534405595ee_a_b,R: dtree_a_b] :
      ( ( Xs != nil_Pr558572586965427547ee_a_b )
     => ? [T2: dtree_1861073144021109543ee_a_b,E2: dtree_a_b] :
          ( ( dtree_7424119665891431146ee_a_b @ R @ Xs )
          = ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_87_dtree__from__list__singleton,axiom,
    ! [Xs: list_P3724575226198589275ee_a_b,R: produc4558475209616630778_a_b_b] :
      ( ( Xs != nil_Pr148742403700823003ee_a_b )
     => ? [T2: dtree_8690448868185853351ee_a_b,E2: dtree_a_b] :
          ( ( dtree_7850083854586231658ee_a_b @ R @ Xs )
          = ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_88_dtree__from__list__singleton,axiom,
    ! [Xs: list_P7142016109841313883_a_b_b,R: dtree_a_b] :
      ( ( Xs != nil_Pr9079450101154612443_a_b_b )
     => ? [T2: dtree_8397784528784866983_a_b_b,E2: produc4558475209616630778_a_b_b] :
          ( ( dtree_1144793476579453034_a_b_b @ R @ Xs )
          = ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_89_dtree__from__list__singleton,axiom,
    ! [Xs: list_P7924273279524553179_a_b_b,R: produc4558475209616630778_a_b_b] :
      ( ( Xs != nil_Pr5872703755862520667_a_b_b )
     => ? [T2: dtree_6636540493345571111_a_b_b,E2: produc4558475209616630778_a_b_b] :
          ( ( dtree_450453658713739498_a_b_b @ R @ Xs )
          = ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_90_dtree__from__list__singleton,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,R: a] :
      ( ( Xs != nil_Product_prod_a_b )
     => ? [T2: dtree_a_b,E2: b] :
          ( ( dtree_from_list_a_b @ R @ Xs )
          = ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% dtree_from_list_singleton
thf(fact_91_root__not__child__if__wf__dverts,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,T1: dtree_1861073144021109543ee_a_b,E1: dtree_a_b] :
      ( ( wf_dve9201916681887519993ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
     => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ T1 @ E1 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
       => ~ ( member_dtree_a_b @ R @ ( dverts2436977245124431984ee_a_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_92_root__not__child__if__wf__dverts,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,T1: dtree_8690448868185853351ee_a_b,E1: dtree_a_b] :
      ( ( wf_dve8044060998984177273ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
     => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ T1 @ E1 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
       => ~ ( member4380921116106875537_a_b_b @ R @ ( dverts2972317704043987696ee_a_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_93_root__not__child__if__wf__dverts,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,T1: dtree_8397784528784866983_a_b_b,E1: produc4558475209616630778_a_b_b] :
      ( ( wf_dve1338770620977398649_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
     => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ T1 @ E1 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
       => ~ ( member_dtree_a_b @ R @ ( dverts5490399362891984880_a_b_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_94_root__not__child__if__wf__dverts,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,T1: dtree_6636540493345571111_a_b_b,E1: produc4558475209616630778_a_b_b] :
      ( ( wf_dve6839618634935551225_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
     => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ T1 @ E1 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
       => ~ ( member4380921116106875537_a_b_b @ R @ ( dverts1640268204329280112_a_b_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_95_root__not__child__if__wf__dverts,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ~ ( member_a @ R @ ( dverts_a_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_96_num__leaves__singleton,axiom,
    ! [R: dtree_a_b,T: dtree_1861073144021109543ee_a_b,E: dtree_a_b] :
      ( ( num_le762670902658651842ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) ) )
      = ( num_le762670902658651842ee_a_b @ T ) ) ).

% num_leaves_singleton
thf(fact_97_num__leaves__singleton,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b,E: dtree_a_b] :
      ( ( num_le972019002107111234ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) ) )
      = ( num_le972019002107111234ee_a_b @ T ) ) ).

% num_leaves_singleton
thf(fact_98_num__leaves__singleton,axiom,
    ! [R: dtree_a_b,T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( num_le3490100660955108418_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) ) )
      = ( num_le3490100660955108418_a_b_b @ T ) ) ).

% num_leaves_singleton
thf(fact_99_num__leaves__singleton,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( num_le5032565032286201026_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) ) )
      = ( num_le5032565032286201026_a_b_b @ T ) ) ).

% num_leaves_singleton
thf(fact_100_num__leaves__singleton,axiom,
    ! [R: a,T: dtree_a_b,E: b] :
      ( ( num_leaves_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) )
      = ( num_leaves_a_b @ T ) ) ).

% num_leaves_singleton
thf(fact_101_singleton__uneq,axiom,
    ! [R: dtree_a_b,T: dtree_1861073144021109543ee_a_b,E: dtree_a_b] :
      ( ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) )
     != T ) ).

% singleton_uneq
thf(fact_102_singleton__uneq,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b,E: dtree_a_b] :
      ( ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) )
     != T ) ).

% singleton_uneq
thf(fact_103_singleton__uneq,axiom,
    ! [R: dtree_a_b,T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) )
     != T ) ).

% singleton_uneq
thf(fact_104_singleton__uneq,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) )
     != T ) ).

% singleton_uneq
thf(fact_105_singleton__uneq,axiom,
    ! [R: a,T: dtree_a_b,E: b] :
      ( ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) )
     != T ) ).

% singleton_uneq
thf(fact_106_dtree__to__list_Ocases,axiom,
    ! [X3: dtree_1861073144021109543ee_a_b] :
      ( ! [R2: dtree_a_b,T2: dtree_1861073144021109543ee_a_b,E2: dtree_a_b] :
          ( X3
         != ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) )
     => ~ ! [Xs2: fset_P5991447722532490344ee_a_b] :
            ( ! [X: produc6260003399586931330ee_a_b] :
                ( Xs2
               != ( finser8516331313445392842ee_a_b @ X @ bot_bo5711572498106067156ee_a_b ) )
           => ! [R2: dtree_a_b] :
                ( X3
               != ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ) ) ).

% dtree_to_list.cases
thf(fact_107_dtree__to__list_Ocases,axiom,
    ! [X3: dtree_8690448868185853351ee_a_b] :
      ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_8690448868185853351ee_a_b,E2: dtree_a_b] :
          ( X3
         != ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) )
     => ~ ! [Xs2: fset_P1087233464713034472ee_a_b] :
            ( ! [X: produc1961764714219340802ee_a_b] :
                ( Xs2
               != ( finser7847761039489690442ee_a_b @ X @ bot_bo3079078458218859348ee_a_b ) )
           => ! [R2: produc4558475209616630778_a_b_b] :
                ( X3
               != ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ) ) ).

% dtree_to_list.cases
thf(fact_108_dtree__to__list_Ocases,axiom,
    ! [X3: dtree_8397784528784866983_a_b_b] :
      ( ! [R2: dtree_a_b,T2: dtree_8397784528784866983_a_b_b,E2: produc4558475209616630778_a_b_b] :
          ( X3
         != ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) )
     => ~ ! [Xs2: fset_P8532786667068971368_a_b_b] :
            ( ! [X: produc4081214457754080642_a_b_b] :
                ( Xs2
               != ( finser5778094437704840394_a_b_b @ X @ bot_bo1493276529839087060_a_b_b ) )
           => ! [R2: dtree_a_b] :
                ( X3
               != ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ) ) ).

% dtree_to_list.cases
thf(fact_109_dtree__to__list_Ocases,axiom,
    ! [X3: dtree_6636540493345571111_a_b_b] :
      ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_6636540493345571111_a_b_b,E2: produc4558475209616630778_a_b_b] :
          ( X3
         != ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) )
     => ~ ! [Xs2: fset_P271555816861255656_a_b_b] :
            ( ! [X: produc8137180380982048514_a_b_b] :
                ( Xs2
               != ( finser3407669804807474762_a_b_b @ X @ bot_bo6312180378851360852_a_b_b ) )
           => ! [R2: produc4558475209616630778_a_b_b] :
                ( X3
               != ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ) ) ).

% dtree_to_list.cases
thf(fact_110_dtree__to__list_Ocases,axiom,
    ! [X3: dtree_a_b] :
      ( ! [R2: a,T2: dtree_a_b,E2: b] :
          ( X3
         != ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) )
     => ~ ! [Xs2: fset_P5281107635120001194_a_b_b] :
            ( ! [X: produc4558475209616630778_a_b_b] :
                ( Xs2
               != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) )
           => ! [R2: a] :
                ( X3
               != ( node_a_b @ R2 @ Xs2 ) ) ) ) ).

% dtree_to_list.cases
thf(fact_111_dtree__from__list__sucs__cases,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,V: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
        = ( dtree_7424119665891431146ee_a_b @ V @ Ys ) )
     => ( ( Xs = bot_bo5711572498106067156ee_a_b )
        | ? [X2: produc6260003399586931330ee_a_b] :
            ( Xs
            = ( finser8516331313445392842ee_a_b @ X2 @ bot_bo5711572498106067156ee_a_b ) ) ) ) ).

% dtree_from_list_sucs_cases
thf(fact_112_dtree__from__list__sucs__cases,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,V: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
        = ( dtree_7850083854586231658ee_a_b @ V @ Ys ) )
     => ( ( Xs = bot_bo3079078458218859348ee_a_b )
        | ? [X2: produc1961764714219340802ee_a_b] :
            ( Xs
            = ( finser7847761039489690442ee_a_b @ X2 @ bot_bo3079078458218859348ee_a_b ) ) ) ) ).

% dtree_from_list_sucs_cases
thf(fact_113_dtree__from__list__sucs__cases,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,V: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
        = ( dtree_1144793476579453034_a_b_b @ V @ Ys ) )
     => ( ( Xs = bot_bo1493276529839087060_a_b_b )
        | ? [X2: produc4081214457754080642_a_b_b] :
            ( Xs
            = ( finser5778094437704840394_a_b_b @ X2 @ bot_bo1493276529839087060_a_b_b ) ) ) ) ).

% dtree_from_list_sucs_cases
thf(fact_114_dtree__from__list__sucs__cases,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,V: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
        = ( dtree_450453658713739498_a_b_b @ V @ Ys ) )
     => ( ( Xs = bot_bo6312180378851360852_a_b_b )
        | ? [X2: produc8137180380982048514_a_b_b] :
            ( Xs
            = ( finser3407669804807474762_a_b_b @ X2 @ bot_bo6312180378851360852_a_b_b ) ) ) ) ).

% dtree_from_list_sucs_cases
thf(fact_115_dtree__from__list__sucs__cases,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( node_a_b @ R @ Xs )
        = ( dtree_from_list_a_b @ V @ Ys ) )
     => ( ( Xs = bot_bo2895716411488905534_a_b_b )
        | ? [X2: produc4558475209616630778_a_b_b] :
            ( Xs
            = ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% dtree_from_list_sucs_cases
thf(fact_116_dtree__from__list__eq__empty,axiom,
    ! [R: product_prod_a_b,V: product_prod_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( ( node_P1936840572307073598od_a_b @ R @ bot_bo7856883933444951080od_a_b )
        = ( dtree_1864022081312108148od_a_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr906174322249854893od_a_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_117_dtree__from__list__eq__empty,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( node_dtree_a_b_b @ R @ bot_bo4737202254184417232_b_b_b )
        = ( dtree_5255521609252960911_a_b_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr5403147374433350260_a_b_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_118_dtree__from__list__eq__empty,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ R @ bot_bo5711572498106067156ee_a_b )
        = ( dtree_7424119665891431146ee_a_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr558572586965427547ee_a_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_119_dtree__from__list__eq__empty,axiom,
    ! [R: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ R @ bot_bo3079078458218859348ee_a_b )
        = ( dtree_7850083854586231658ee_a_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr148742403700823003ee_a_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_120_dtree__from__list__eq__empty,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ R @ bot_bo1493276529839087060_a_b_b )
        = ( dtree_1144793476579453034_a_b_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr9079450101154612443_a_b_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_121_dtree__from__list__eq__empty,axiom,
    ! [R: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ R @ bot_bo6312180378851360852_a_b_b )
        = ( dtree_450453658713739498_a_b_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Pr5872703755862520667_a_b_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_122_dtree__from__list__eq__empty,axiom,
    ! [R: a,V: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( node_a_b @ R @ bot_bo2895716411488905534_a_b_b )
        = ( dtree_from_list_a_b @ V @ Ys ) )
     => ( ( R = V )
        & ( Ys = nil_Product_prod_a_b ) ) ) ).

% dtree_from_list_eq_empty
thf(fact_123_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: product_prod_a_b] :
      ( ( dtree_1864022081312108148od_a_b @ R @ nil_Pr906174322249854893od_a_b )
      = ( node_P1936840572307073598od_a_b @ R @ bot_bo7856883933444951080od_a_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_124_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b] :
      ( ( dtree_5255521609252960911_a_b_b @ R @ nil_Pr5403147374433350260_a_b_b )
      = ( node_dtree_a_b_b @ R @ bot_bo4737202254184417232_b_b_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_125_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b] :
      ( ( dtree_7424119665891431146ee_a_b @ R @ nil_Pr558572586965427547ee_a_b )
      = ( node_d7487230363575057332ee_a_b @ R @ bot_bo5711572498106067156ee_a_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_126_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b] :
      ( ( dtree_7850083854586231658ee_a_b @ R @ nil_Pr148742403700823003ee_a_b )
      = ( node_P2753077162091514420ee_a_b @ R @ bot_bo3079078458218859348ee_a_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_127_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b] :
      ( ( dtree_1144793476579453034_a_b_b @ R @ nil_Pr9079450101154612443_a_b_b )
      = ( node_d5271158820939511604_a_b_b @ R @ bot_bo1493276529839087060_a_b_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_128_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b] :
      ( ( dtree_450453658713739498_a_b_b @ R @ nil_Pr5872703755862520667_a_b_b )
      = ( node_P961815112480277940_a_b_b @ R @ bot_bo6312180378851360852_a_b_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_129_dtree__from__list_Osimps_I1_J,axiom,
    ! [R: a] :
      ( ( dtree_from_list_a_b @ R @ nil_Product_prod_a_b )
      = ( node_a_b @ R @ bot_bo2895716411488905534_a_b_b ) ) ).

% dtree_from_list.simps(1)
thf(fact_130_finsert__absorb2,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( finser8437519239679886002_a_b_b @ X3 @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) )
      = ( finser8437519239679886002_a_b_b @ X3 @ A2 ) ) ).

% finsert_absorb2
thf(fact_131_bot__apply,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X4: produc4558475209616630778_a_b_b] : bot_bot_o ) ) ).

% bot_apply
thf(fact_132_bot__apply,axiom,
    ( bot_bot_dtree_a_b_o
    = ( ^ [X4: dtree_a_b] : bot_bot_o ) ) ).

% bot_apply
thf(fact_133_prod_Oinject,axiom,
    ! [X1: dtree_a_b,X22: b,Y1: dtree_a_b,Y2: b] :
      ( ( ( produc331601717337510060_a_b_b @ X1 @ X22 )
        = ( produc331601717337510060_a_b_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_134_prod_Oinject,axiom,
    ! [X1: list_P1467974523212632366od_a_b,X22: list_P1467974523212632366od_a_b,Y1: list_P1467974523212632366od_a_b,Y2: list_P1467974523212632366od_a_b] :
      ( ( ( produc5288560138351607191od_a_b @ X1 @ X22 )
        = ( produc5288560138351607191od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_135_prod_Oinject,axiom,
    ! [X1: product_prod_a_b > product_prod_a_b > $o,X22: list_P1467974523212632366od_a_b,Y1: product_prod_a_b > product_prod_a_b > $o,Y2: list_P1467974523212632366od_a_b] :
      ( ( ( produc7704224619955794135od_a_b @ X1 @ X22 )
        = ( produc7704224619955794135od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_136_prod_Oinject,axiom,
    ! [X1: a,X22: list_P1467974523212632366od_a_b,Y1: a,Y2: list_P1467974523212632366od_a_b] :
      ( ( ( produc6643264353547226055od_a_b @ X1 @ X22 )
        = ( produc6643264353547226055od_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_137_prod_Oinject,axiom,
    ! [X1: a,X22: b,Y1: a,Y2: b] :
      ( ( ( product_Pair_a_b @ X1 @ X22 )
        = ( product_Pair_a_b @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
thf(fact_138_old_Oprod_Oinject,axiom,
    ! [A: dtree_a_b,B: b,A3: dtree_a_b,B2: b] :
      ( ( ( produc331601717337510060_a_b_b @ A @ B )
        = ( produc331601717337510060_a_b_b @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_139_old_Oprod_Oinject,axiom,
    ! [A: list_P1467974523212632366od_a_b,B: list_P1467974523212632366od_a_b,A3: list_P1467974523212632366od_a_b,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc5288560138351607191od_a_b @ A @ B )
        = ( produc5288560138351607191od_a_b @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_140_old_Oprod_Oinject,axiom,
    ! [A: product_prod_a_b > product_prod_a_b > $o,B: list_P1467974523212632366od_a_b,A3: product_prod_a_b > product_prod_a_b > $o,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc7704224619955794135od_a_b @ A @ B )
        = ( produc7704224619955794135od_a_b @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_141_old_Oprod_Oinject,axiom,
    ! [A: a,B: list_P1467974523212632366od_a_b,A3: a,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc6643264353547226055od_a_b @ A @ B )
        = ( produc6643264353547226055od_a_b @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_142_old_Oprod_Oinject,axiom,
    ! [A: a,B: b,A3: a,B2: b] :
      ( ( ( product_Pair_a_b @ A @ B )
        = ( product_Pair_a_b @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_143_dtree__from__list_Oelims,axiom,
    ! [X3: product_prod_a_b,Xa: list_P3463435030753280173od_a_b,Y: dtree_2253494508914376569od_a_b] :
      ( ( ( dtree_1864022081312108148od_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr906174322249854893od_a_b )
         => ( Y
           != ( node_P1936840572307073598od_a_b @ X3 @ bot_bo7856883933444951080od_a_b ) ) )
       => ~ ! [V2: product_prod_a_b,E2: product_prod_a_b,Xs2: list_P3463435030753280173od_a_b] :
              ( ( Xa
                = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_P1936840572307073598od_a_b @ X3 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ ( dtree_1864022081312108148od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_144_dtree__from__list_Oelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P7294506862534405595ee_a_b,Y: dtree_1861073144021109543ee_a_b] :
      ( ( ( dtree_7424119665891431146ee_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr558572586965427547ee_a_b )
         => ( Y
           != ( node_d7487230363575057332ee_a_b @ X3 @ bot_bo5711572498106067156ee_a_b ) ) )
       => ~ ! [V2: dtree_a_b,E2: dtree_a_b,Xs2: list_P7294506862534405595ee_a_b] :
              ( ( Xa
                = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_d7487230363575057332ee_a_b @ X3 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ ( dtree_7424119665891431146ee_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_145_dtree__from__list_Oelims,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa: list_P3724575226198589275ee_a_b,Y: dtree_8690448868185853351ee_a_b] :
      ( ( ( dtree_7850083854586231658ee_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr148742403700823003ee_a_b )
         => ( Y
           != ( node_P2753077162091514420ee_a_b @ X3 @ bot_bo3079078458218859348ee_a_b ) ) )
       => ~ ! [V2: produc4558475209616630778_a_b_b,E2: dtree_a_b,Xs2: list_P3724575226198589275ee_a_b] :
              ( ( Xa
                = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_P2753077162091514420ee_a_b @ X3 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ ( dtree_7850083854586231658ee_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_146_dtree__from__list_Oelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P7142016109841313883_a_b_b,Y: dtree_8397784528784866983_a_b_b] :
      ( ( ( dtree_1144793476579453034_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr9079450101154612443_a_b_b )
         => ( Y
           != ( node_d5271158820939511604_a_b_b @ X3 @ bot_bo1493276529839087060_a_b_b ) ) )
       => ~ ! [V2: dtree_a_b,E2: produc4558475209616630778_a_b_b,Xs2: list_P7142016109841313883_a_b_b] :
              ( ( Xa
                = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_d5271158820939511604_a_b_b @ X3 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ ( dtree_1144793476579453034_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_147_dtree__from__list_Oelims,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa: list_P7924273279524553179_a_b_b,Y: dtree_6636540493345571111_a_b_b] :
      ( ( ( dtree_450453658713739498_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr5872703755862520667_a_b_b )
         => ( Y
           != ( node_P961815112480277940_a_b_b @ X3 @ bot_bo6312180378851360852_a_b_b ) ) )
       => ~ ! [V2: produc4558475209616630778_a_b_b,E2: produc4558475209616630778_a_b_b,Xs2: list_P7924273279524553179_a_b_b] :
              ( ( Xa
                = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_P961815112480277940_a_b_b @ X3 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ ( dtree_450453658713739498_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_148_dtree__from__list_Oelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P5360711134766023690_a_b_b,Y: dtree_dtree_a_b_b] :
      ( ( ( dtree_5255521609252960911_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr5403147374433350260_a_b_b )
         => ( Y
           != ( node_dtree_a_b_b @ X3 @ bot_bo4737202254184417232_b_b_b ) ) )
       => ~ ! [V2: dtree_a_b,E2: b,Xs2: list_P5360711134766023690_a_b_b] :
              ( ( Xa
                = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_dtree_a_b_b @ X3 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ ( dtree_5255521609252960911_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_149_dtree__from__list_Oelims,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xa: list_P8601282865932132013od_a_b,Y: dtree_5519289247442030201od_a_b] :
      ( ( ( dtree_6507962483783174260od_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr2412700377486846637od_a_b )
         => ( Y
           != ( node_l1136085673055119934od_a_b @ X3 @ bot_bo2863178955461725870od_a_b ) ) )
       => ~ ! [V2: list_P1467974523212632366od_a_b,E2: list_P1467974523212632366od_a_b,Xs2: list_P8601282865932132013od_a_b] :
              ( ( Xa
                = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_l1136085673055119934od_a_b @ X3 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ ( dtree_6507962483783174260od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo2863178955461725870od_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_150_dtree__from__list_Oelims,axiom,
    ! [X3: product_prod_a_b > product_prod_a_b > $o,Xa: list_P8094385941167427565od_a_b,Y: dtree_8339642294131873593od_a_b] :
      ( ( ( dtree_4383916385682046516od_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr7311172237979606381od_a_b )
         => ( Y
           != ( node_P5897935084763704574od_a_b @ X3 @ bot_bo137739038786217454od_a_b ) ) )
       => ~ ! [V2: product_prod_a_b > product_prod_a_b > $o,E2: list_P1467974523212632366od_a_b,Xs2: list_P8094385941167427565od_a_b] :
              ( ( Xa
                = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_P5897935084763704574od_a_b @ X3 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ ( dtree_4383916385682046516od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo137739038786217454od_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_151_dtree__from__list_Oelims,axiom,
    ! [X3: a,Xa: list_P5700792096213675741od_a_b,Y: dtree_8545934391348768041od_a_b] :
      ( ( ( dtree_6261964479915675172od_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Pr7243433834293086045od_a_b )
         => ( Y
           != ( node_a6325075177599301358od_a_b @ X3 @ bot_bo577854266114829310od_a_b ) ) )
       => ~ ! [V2: a,E2: list_P1467974523212632366od_a_b,Xs2: list_P5700792096213675741od_a_b] :
              ( ( Xa
                = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_a6325075177599301358od_a_b @ X3 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ ( dtree_6261964479915675172od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo577854266114829310od_a_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_152_dtree__from__list_Oelims,axiom,
    ! [X3: a,Xa: list_P1467974523212632366od_a_b,Y: dtree_a_b] :
      ( ( ( dtree_from_list_a_b @ X3 @ Xa )
        = Y )
     => ( ( ( Xa = nil_Product_prod_a_b )
         => ( Y
           != ( node_a_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) )
       => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
              ( ( Xa
                = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
               != ( node_a_b @ X3 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ ( dtree_from_list_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ) ).

% dtree_from_list.elims
thf(fact_153_FSet_Ofset__induct,axiom,
    ! [P: fset_P5281107635120001194_a_b_b > $o,S: fset_P5281107635120001194_a_b_b] :
      ( ( P @ bot_bo2895716411488905534_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b,S2: fset_P5281107635120001194_a_b_b] :
            ( ( P @ S2 )
           => ( P @ ( finser8437519239679886002_a_b_b @ X2 @ S2 ) ) )
       => ( P @ S ) ) ) ).

% FSet.fset_induct
thf(fact_154_fset__exhaust,axiom,
    ! [S: fset_P5281107635120001194_a_b_b] :
      ( ( S != bot_bo2895716411488905534_a_b_b )
     => ~ ! [X2: produc4558475209616630778_a_b_b,S3: fset_P5281107635120001194_a_b_b] :
            ( S
           != ( finser8437519239679886002_a_b_b @ X2 @ S3 ) ) ) ).

% fset_exhaust
thf(fact_155_fdoubleton__eq__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,C: produc4558475209616630778_a_b_b,D: produc4558475209616630778_a_b_b] :
      ( ( ( finser8437519239679886002_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ B @ bot_bo2895716411488905534_a_b_b ) )
        = ( finser8437519239679886002_a_b_b @ C @ ( finser8437519239679886002_a_b_b @ D @ bot_bo2895716411488905534_a_b_b ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ) ).

% fdoubleton_eq_iff
thf(fact_156_fsingleton__inject,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b )
        = ( finser8437519239679886002_a_b_b @ B @ bot_bo2895716411488905534_a_b_b ) )
     => ( A = B ) ) ).

% fsingleton_inject
thf(fact_157_finsert__not__fempty,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( finser8437519239679886002_a_b_b @ A @ A2 )
     != bot_bo2895716411488905534_a_b_b ) ).

% finsert_not_fempty
thf(fact_158_mem__Collect__eq,axiom,
    ! [A: produc5177672665255943253ee_a_b,P: produc5177672665255943253ee_a_b > $o] :
      ( ( member2060280516343777534ee_a_b @ A @ ( collec1189380413810840640ee_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_159_mem__Collect__eq,axiom,
    ! [A: produc7397007428618769063od_a_b,P: produc7397007428618769063od_a_b > $o] :
      ( ( member3051990972100052432od_a_b @ A @ ( collec6173795731405551122od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_160_mem__Collect__eq,axiom,
    ! [A: product_prod_a_b,P: product_prod_a_b > $o] :
      ( ( member1426531481828664017od_a_b @ A @ ( collec3336397801687681299od_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_161_mem__Collect__eq,axiom,
    ! [A: b,P: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_162_mem__Collect__eq,axiom,
    ! [A: a,P: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_163_mem__Collect__eq,axiom,
    ! [A: produc4558475209616630778_a_b_b,P: produc4558475209616630778_a_b_b > $o] :
      ( ( member4380921116106875537_a_b_b @ A @ ( collec1368399972772960719_a_b_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_164_mem__Collect__eq,axiom,
    ! [A: dtree_a_b,P: dtree_a_b > $o] :
      ( ( member_dtree_a_b @ A @ ( collect_dtree_a_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_165_Collect__mem__eq,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b] :
      ( ( collec1189380413810840640ee_a_b
        @ ^ [X4: produc5177672665255943253ee_a_b] : ( member2060280516343777534ee_a_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_166_Collect__mem__eq,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b] :
      ( ( collec6173795731405551122od_a_b
        @ ^ [X4: produc7397007428618769063od_a_b] : ( member3051990972100052432od_a_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_167_Collect__mem__eq,axiom,
    ! [A2: set_Product_prod_a_b] :
      ( ( collec3336397801687681299od_a_b
        @ ^ [X4: product_prod_a_b] : ( member1426531481828664017od_a_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_168_Collect__mem__eq,axiom,
    ! [A2: set_b] :
      ( ( collect_b
        @ ^ [X4: b] : ( member_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_169_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X4: a] : ( member_a @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_170_Collect__mem__eq,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( collec1368399972772960719_a_b_b
        @ ^ [X4: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_171_Collect__mem__eq,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( collect_dtree_a_b
        @ ^ [X4: dtree_a_b] : ( member_dtree_a_b @ X4 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_172_Collect__cong,axiom,
    ! [P: dtree_a_b > $o,Q: dtree_a_b > $o] :
      ( ! [X2: dtree_a_b] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_dtree_a_b @ P )
        = ( collect_dtree_a_b @ Q ) ) ) ).

% Collect_cong
thf(fact_173_Collect__cong,axiom,
    ! [P: produc4558475209616630778_a_b_b > $o,Q: produc4558475209616630778_a_b_b > $o] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collec1368399972772960719_a_b_b @ P )
        = ( collec1368399972772960719_a_b_b @ Q ) ) ) ).

% Collect_cong
thf(fact_174_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: product_prod_a_b,V: product_prod_a_b,E: product_prod_a_b,Xs: list_P3463435030753280173od_a_b] :
      ( ( dtree_1864022081312108148od_a_b @ R @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V @ E ) @ Xs ) )
      = ( node_P1936840572307073598od_a_b @ R @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ ( dtree_1864022081312108148od_a_b @ V @ Xs ) @ E ) @ bot_bo7856883933444951080od_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_175_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,E: dtree_a_b,Xs: list_P7294506862534405595ee_a_b] :
      ( ( dtree_7424119665891431146ee_a_b @ R @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ V @ E ) @ Xs ) )
      = ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ ( dtree_7424119665891431146ee_a_b @ V @ Xs ) @ E ) @ bot_bo5711572498106067156ee_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_176_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,E: dtree_a_b,Xs: list_P3724575226198589275ee_a_b] :
      ( ( dtree_7850083854586231658ee_a_b @ R @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ V @ E ) @ Xs ) )
      = ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ ( dtree_7850083854586231658ee_a_b @ V @ Xs ) @ E ) @ bot_bo3079078458218859348ee_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_177_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,E: produc4558475209616630778_a_b_b,Xs: list_P7142016109841313883_a_b_b] :
      ( ( dtree_1144793476579453034_a_b_b @ R @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ V @ E ) @ Xs ) )
      = ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ ( dtree_1144793476579453034_a_b_b @ V @ Xs ) @ E ) @ bot_bo1493276529839087060_a_b_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_178_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,E: produc4558475209616630778_a_b_b,Xs: list_P7924273279524553179_a_b_b] :
      ( ( dtree_450453658713739498_a_b_b @ R @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ V @ E ) @ Xs ) )
      = ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ ( dtree_450453658713739498_a_b_b @ V @ Xs ) @ E ) @ bot_bo6312180378851360852_a_b_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_179_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: dtree_a_b,V: dtree_a_b,E: b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( dtree_5255521609252960911_a_b_b @ R @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V @ E ) @ Xs ) )
      = ( node_dtree_a_b_b @ R @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ ( dtree_5255521609252960911_a_b_b @ V @ Xs ) @ E ) @ bot_bo4737202254184417232_b_b_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_180_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: list_P1467974523212632366od_a_b,V: list_P1467974523212632366od_a_b,E: list_P1467974523212632366od_a_b,Xs: list_P8601282865932132013od_a_b] :
      ( ( dtree_6507962483783174260od_a_b @ R @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V @ E ) @ Xs ) )
      = ( node_l1136085673055119934od_a_b @ R @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ ( dtree_6507962483783174260od_a_b @ V @ Xs ) @ E ) @ bot_bo2863178955461725870od_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_181_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: product_prod_a_b > product_prod_a_b > $o,V: product_prod_a_b > product_prod_a_b > $o,E: list_P1467974523212632366od_a_b,Xs: list_P8094385941167427565od_a_b] :
      ( ( dtree_4383916385682046516od_a_b @ R @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V @ E ) @ Xs ) )
      = ( node_P5897935084763704574od_a_b @ R @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ ( dtree_4383916385682046516od_a_b @ V @ Xs ) @ E ) @ bot_bo137739038786217454od_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_182_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: a,V: a,E: list_P1467974523212632366od_a_b,Xs: list_P5700792096213675741od_a_b] :
      ( ( dtree_6261964479915675172od_a_b @ R @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V @ E ) @ Xs ) )
      = ( node_a6325075177599301358od_a_b @ R @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ ( dtree_6261964479915675172od_a_b @ V @ Xs ) @ E ) @ bot_bo577854266114829310od_a_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_183_dtree__from__list_Osimps_I2_J,axiom,
    ! [R: a,V: a,E: b,Xs: list_P1467974523212632366od_a_b] :
      ( ( dtree_from_list_a_b @ R @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V @ E ) @ Xs ) )
      = ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ ( dtree_from_list_a_b @ V @ Xs ) @ E ) @ bot_bo2895716411488905534_a_b_b ) ) ) ).

% dtree_from_list.simps(2)
thf(fact_184_wf__darcs__sucs,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,X3: produc6260003399586931330ee_a_b,R: dtree_a_b] :
      ( ( wf_dar7222114146661136918ee_a_b @ T )
     => ( ( member1914986943068214699ee_a_b @ X3 @ ( fset_P4845137164202167537ee_a_b @ ( sucs_d5654203025177486372ee_a_b @ T ) ) )
       => ( wf_dar7222114146661136918ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ X3 @ bot_bo5711572498106067156ee_a_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_185_wf__darcs__sucs,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,X3: produc1961764714219340802ee_a_b,R: produc4558475209616630778_a_b_b] :
      ( ( wf_dar3147389999391200918ee_a_b @ T )
     => ( ( member5265136988498437675ee_a_b @ X3 @ ( fset_P3182333368011040625ee_a_b @ ( sucs_P7314365117959652004ee_a_b @ T ) ) )
       => ( wf_dar3147389999391200918ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ X3 @ bot_bo3079078458218859348ee_a_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_186_wf__darcs__sucs,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,X3: produc4081214457754080642_a_b_b,R: dtree_a_b] :
      ( ( wf_dar5665471658239198102_a_b_b @ T )
     => ( ( member2386720262296790699_a_b_b @ X3 @ ( fset_P4440376523358319089_a_b_b @ ( sucs_d609074739952873380_a_b_b @ T ) ) )
       => ( wf_dar5665471658239198102_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ X3 @ bot_bo1493276529839087060_a_b_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_187_wf__darcs__sucs,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,X3: produc8137180380982048514_a_b_b,R: produc4558475209616630778_a_b_b] :
      ( ( wf_dar8189686260367384598_a_b_b @ T )
     => ( ( member684607838164940587_a_b_b @ X3 @ ( fset_P8825802006873508977_a_b_b @ ( sucs_P6478368611001241124_a_b_b @ T ) ) )
       => ( wf_dar8189686260367384598_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ X3 @ bot_bo6312180378851360852_a_b_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_188_wf__darcs__sucs,axiom,
    ! [T: dtree_a_b,X3: produc4558475209616630778_a_b_b,R: a] :
      ( ( wf_darcs_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) )
       => ( wf_darcs_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_189_bot__fset_Orep__eq,axiom,
    ( ( fset_P4845137164202167537ee_a_b @ bot_bo5711572498106067156ee_a_b )
    = bot_bo936214220562098254ee_a_b ) ).

% bot_fset.rep_eq
thf(fact_190_bot__fset_Orep__eq,axiom,
    ( ( fset_P3182333368011040625ee_a_b @ bot_bo3079078458218859348ee_a_b )
    = bot_bo6717195425869660366ee_a_b ) ).

% bot_fset.rep_eq
thf(fact_191_bot__fset_Orep__eq,axiom,
    ( ( fset_P4440376523358319089_a_b_b @ bot_bo1493276529839087060_a_b_b )
    = bot_bo3911397808570943822_a_b_b ) ).

% bot_fset.rep_eq
thf(fact_192_bot__fset_Orep__eq,axiom,
    ( ( fset_P8825802006873508977_a_b_b @ bot_bo6312180378851360852_a_b_b )
    = bot_bo5192956117685428686_a_b_b ) ).

% bot_fset.rep_eq
thf(fact_193_bot__fset_Orep__eq,axiom,
    ( ( fset_dtree_a_b2 @ bot_bo4081095239089054910ee_a_b )
    = bot_bo8730652382759064772ee_a_b ) ).

% bot_fset.rep_eq
thf(fact_194_bot__fset_Orep__eq,axiom,
    ( ( fset_b2 @ bot_bot_fset_b )
    = bot_bot_set_b ) ).

% bot_fset.rep_eq
thf(fact_195_bot__fset_Orep__eq,axiom,
    ( ( fset_a2 @ bot_bot_fset_a )
    = bot_bot_set_a ) ).

% bot_fset.rep_eq
thf(fact_196_bot__fset_Orep__eq,axiom,
    ( ( fset_P783253628892185035_a_b_b @ bot_bo2895716411488905534_a_b_b )
    = bot_bo3721250822024684356_a_b_b ) ).

% bot_fset.rep_eq
thf(fact_197_dtree__from__list_Ocases,axiom,
    ! [X3: produc566207910345494828od_a_b] :
      ( ! [R2: product_prod_a_b] :
          ( X3
         != ( produc5088573426887569692od_a_b @ R2 @ nil_Pr906174322249854893od_a_b ) )
     => ~ ! [R2: product_prod_a_b,V2: product_prod_a_b,E2: product_prod_a_b,Xs2: list_P3463435030753280173od_a_b] :
            ( X3
           != ( produc5088573426887569692od_a_b @ R2 @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_198_dtree__from__list_Ocases,axiom,
    ! [X3: produc2168945239844811237_a_b_b] :
      ( ! [R2: dtree_a_b] :
          ( X3
         != ( produc139389723908703645_a_b_b @ R2 @ nil_Pr5403147374433350260_a_b_b ) )
     => ~ ! [R2: dtree_a_b,V2: dtree_a_b,E2: b,Xs2: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( produc139389723908703645_a_b_b @ R2 @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_199_dtree__from__list_Ocases,axiom,
    ! [X3: produc2698676102954276518od_a_b] :
      ( ! [R2: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc971229398454786070od_a_b @ R2 @ nil_Pr2412700377486846637od_a_b ) )
     => ~ ! [R2: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,E2: list_P1467974523212632366od_a_b,Xs2: list_P8601282865932132013od_a_b] :
            ( X3
           != ( produc971229398454786070od_a_b @ R2 @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_200_dtree__from__list_Ocases,axiom,
    ! [X3: produc2580745285611667110od_a_b] :
      ( ! [R2: product_prod_a_b > product_prod_a_b > $o] :
          ( X3
         != ( produc8832364399110542614od_a_b @ R2 @ nil_Pr7311172237979606381od_a_b ) )
     => ~ ! [R2: product_prod_a_b > product_prod_a_b > $o,V2: product_prod_a_b > product_prod_a_b > $o,E2: list_P1467974523212632366od_a_b,Xs2: list_P8094385941167427565od_a_b] :
            ( X3
           != ( produc8832364399110542614od_a_b @ R2 @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_201_dtree__from__list_Ocases,axiom,
    ! [X3: produc5068203645811208070od_a_b] :
      ( ! [R2: a] :
          ( X3
         != ( produc7441261679724955638od_a_b @ R2 @ nil_Pr7243433834293086045od_a_b ) )
     => ~ ! [R2: a,V2: a,E2: list_P1467974523212632366od_a_b,Xs2: list_P5700792096213675741od_a_b] :
            ( X3
           != ( produc7441261679724955638od_a_b @ R2 @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_202_dtree__from__list_Ocases,axiom,
    ! [X3: produc2639161875728825943od_a_b] :
      ( ! [R2: a] :
          ( X3
         != ( produc6643264353547226055od_a_b @ R2 @ nil_Product_prod_a_b ) )
     => ~ ! [R2: a,V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc6643264353547226055od_a_b @ R2 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ).

% dtree_from_list.cases
thf(fact_203_wf__list__verts_Ocases,axiom,
    ! [X3: list_P3463435030753280173od_a_b] :
      ( ( X3 != nil_Pr906174322249854893od_a_b )
     => ~ ! [V2: product_prod_a_b,E2: product_prod_a_b,Xs2: list_P3463435030753280173od_a_b] :
            ( X3
           != ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_204_wf__list__verts_Ocases,axiom,
    ! [X3: list_P5360711134766023690_a_b_b] :
      ( ( X3 != nil_Pr5403147374433350260_a_b_b )
     => ~ ! [V2: dtree_a_b,E2: b,Xs2: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_205_wf__list__verts_Ocases,axiom,
    ! [X3: list_P8601282865932132013od_a_b] :
      ( ( X3 != nil_Pr2412700377486846637od_a_b )
     => ~ ! [V2: list_P1467974523212632366od_a_b,E2: list_P1467974523212632366od_a_b,Xs2: list_P8601282865932132013od_a_b] :
            ( X3
           != ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_206_wf__list__verts_Ocases,axiom,
    ! [X3: list_P8094385941167427565od_a_b] :
      ( ( X3 != nil_Pr7311172237979606381od_a_b )
     => ~ ! [V2: product_prod_a_b > product_prod_a_b > $o,E2: list_P1467974523212632366od_a_b,Xs2: list_P8094385941167427565od_a_b] :
            ( X3
           != ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_207_wf__list__verts_Ocases,axiom,
    ! [X3: list_P5700792096213675741od_a_b] :
      ( ( X3 != nil_Pr7243433834293086045od_a_b )
     => ~ ! [V2: a,E2: list_P1467974523212632366od_a_b,Xs2: list_P5700792096213675741od_a_b] :
            ( X3
           != ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_208_wf__list__verts_Ocases,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( X3 != nil_Product_prod_a_b )
     => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ).

% wf_list_verts.cases
thf(fact_209_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,T1: dtree_1861073144021109543ee_a_b,E1: dtree_a_b,T22: dtree_1861073144021109543ee_a_b,E22: dtree_a_b] :
      ( ( wf_dar7222114146661136918ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
     => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ T1 @ E1 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
       => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ T22 @ E22 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
         => ( ( ( produc2775200505768408122ee_a_b @ T1 @ E1 )
             != ( produc2775200505768408122ee_a_b @ T22 @ E22 ) )
           => ( E1 != E22 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_210_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,T1: dtree_8690448868185853351ee_a_b,E1: dtree_a_b,T22: dtree_8690448868185853351ee_a_b,E22: dtree_a_b] :
      ( ( wf_dar3147389999391200918ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
     => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ T1 @ E1 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
       => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ T22 @ E22 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
         => ( ( ( produc8867760425442229946ee_a_b @ T1 @ E1 )
             != ( produc8867760425442229946ee_a_b @ T22 @ E22 ) )
           => ( E1 != E22 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_211_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,T1: dtree_8397784528784866983_a_b_b,E1: produc4558475209616630778_a_b_b,T22: dtree_8397784528784866983_a_b_b,E22: produc4558475209616630778_a_b_b] :
      ( ( wf_dar5665471658239198102_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
     => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ T1 @ E1 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
       => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ T22 @ E22 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
         => ( ( ( produc74755587182097722_a_b_b @ T1 @ E1 )
             != ( produc74755587182097722_a_b_b @ T22 @ E22 ) )
           => ( E1 != E22 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_212_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,T1: dtree_6636540493345571111_a_b_b,E1: produc4558475209616630778_a_b_b,T22: dtree_6636540493345571111_a_b_b,E22: produc4558475209616630778_a_b_b] :
      ( ( wf_dar8189686260367384598_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
     => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ T1 @ E1 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
       => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ T22 @ E22 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
         => ( ( ( produc6281861845666676666_a_b_b @ T1 @ E1 )
             != ( produc6281861845666676666_a_b_b @ T22 @ E22 ) )
           => ( E1 != E22 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_213_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T22: dtree_a_b,E22: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T22 @ E22 ) )
           => ( E1 != E22 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_214_Pair__inject,axiom,
    ! [A: dtree_a_b,B: b,A3: dtree_a_b,B2: b] :
      ( ( ( produc331601717337510060_a_b_b @ A @ B )
        = ( produc331601717337510060_a_b_b @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_215_Pair__inject,axiom,
    ! [A: list_P1467974523212632366od_a_b,B: list_P1467974523212632366od_a_b,A3: list_P1467974523212632366od_a_b,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc5288560138351607191od_a_b @ A @ B )
        = ( produc5288560138351607191od_a_b @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_216_Pair__inject,axiom,
    ! [A: product_prod_a_b > product_prod_a_b > $o,B: list_P1467974523212632366od_a_b,A3: product_prod_a_b > product_prod_a_b > $o,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc7704224619955794135od_a_b @ A @ B )
        = ( produc7704224619955794135od_a_b @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_217_Pair__inject,axiom,
    ! [A: a,B: list_P1467974523212632366od_a_b,A3: a,B2: list_P1467974523212632366od_a_b] :
      ( ( ( produc6643264353547226055od_a_b @ A @ B )
        = ( produc6643264353547226055od_a_b @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_218_Pair__inject,axiom,
    ! [A: a,B: b,A3: a,B2: b] :
      ( ( ( product_Pair_a_b @ A @ B )
        = ( product_Pair_a_b @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_219_prod__cases,axiom,
    ! [P: produc4558475209616630778_a_b_b > $o,P2: produc4558475209616630778_a_b_b] :
      ( ! [A4: dtree_a_b,B3: b] : ( P @ ( produc331601717337510060_a_b_b @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_220_prod__cases,axiom,
    ! [P: produc7397007428618769063od_a_b > $o,P2: produc7397007428618769063od_a_b] :
      ( ! [A4: list_P1467974523212632366od_a_b,B3: list_P1467974523212632366od_a_b] : ( P @ ( produc5288560138351607191od_a_b @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_221_prod__cases,axiom,
    ! [P: produc3334210663054469735od_a_b > $o,P2: produc3334210663054469735od_a_b] :
      ( ! [A4: product_prod_a_b > product_prod_a_b > $o,B3: list_P1467974523212632366od_a_b] : ( P @ ( produc7704224619955794135od_a_b @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_222_prod__cases,axiom,
    ! [P: produc2639161875728825943od_a_b > $o,P2: produc2639161875728825943od_a_b] :
      ( ! [A4: a,B3: list_P1467974523212632366od_a_b] : ( P @ ( produc6643264353547226055od_a_b @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_223_prod__cases,axiom,
    ! [P: product_prod_a_b > $o,P2: product_prod_a_b] :
      ( ! [A4: a,B3: b] : ( P @ ( product_Pair_a_b @ A4 @ B3 ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_224_surj__pair,axiom,
    ! [P2: produc4558475209616630778_a_b_b] :
    ? [X2: dtree_a_b,Y3: b] :
      ( P2
      = ( produc331601717337510060_a_b_b @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_225_surj__pair,axiom,
    ! [P2: produc7397007428618769063od_a_b] :
    ? [X2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b] :
      ( P2
      = ( produc5288560138351607191od_a_b @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_226_surj__pair,axiom,
    ! [P2: produc3334210663054469735od_a_b] :
    ? [X2: product_prod_a_b > product_prod_a_b > $o,Y3: list_P1467974523212632366od_a_b] :
      ( P2
      = ( produc7704224619955794135od_a_b @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_227_surj__pair,axiom,
    ! [P2: produc2639161875728825943od_a_b] :
    ? [X2: a,Y3: list_P1467974523212632366od_a_b] :
      ( P2
      = ( produc6643264353547226055od_a_b @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_228_surj__pair,axiom,
    ! [P2: product_prod_a_b] :
    ? [X2: a,Y3: b] :
      ( P2
      = ( product_Pair_a_b @ X2 @ Y3 ) ) ).

% surj_pair
thf(fact_229_old_Oprod_Oexhaust,axiom,
    ! [Y: produc4558475209616630778_a_b_b] :
      ~ ! [A4: dtree_a_b,B3: b] :
          ( Y
         != ( produc331601717337510060_a_b_b @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_230_old_Oprod_Oexhaust,axiom,
    ! [Y: produc7397007428618769063od_a_b] :
      ~ ! [A4: list_P1467974523212632366od_a_b,B3: list_P1467974523212632366od_a_b] :
          ( Y
         != ( produc5288560138351607191od_a_b @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_231_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3334210663054469735od_a_b] :
      ~ ! [A4: product_prod_a_b > product_prod_a_b > $o,B3: list_P1467974523212632366od_a_b] :
          ( Y
         != ( produc7704224619955794135od_a_b @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_232_old_Oprod_Oexhaust,axiom,
    ! [Y: produc2639161875728825943od_a_b] :
      ~ ! [A4: a,B3: list_P1467974523212632366od_a_b] :
          ( Y
         != ( produc6643264353547226055od_a_b @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_233_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_a_b] :
      ~ ! [A4: a,B3: b] :
          ( Y
         != ( product_Pair_a_b @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_234_bot__fun__def,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X4: produc4558475209616630778_a_b_b] : bot_bot_o ) ) ).

% bot_fun_def
thf(fact_235_bot__fun__def,axiom,
    ( bot_bot_dtree_a_b_o
    = ( ^ [X4: dtree_a_b] : bot_bot_o ) ) ).

% bot_fun_def
thf(fact_236_fset__cong,axiom,
    ! [X3: fset_P5991447722532490344ee_a_b,Y: fset_P5991447722532490344ee_a_b] :
      ( ( ( fset_P4845137164202167537ee_a_b @ X3 )
        = ( fset_P4845137164202167537ee_a_b @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_237_fset__cong,axiom,
    ! [X3: fset_P1087233464713034472ee_a_b,Y: fset_P1087233464713034472ee_a_b] :
      ( ( ( fset_P3182333368011040625ee_a_b @ X3 )
        = ( fset_P3182333368011040625ee_a_b @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_238_fset__cong,axiom,
    ! [X3: fset_P8532786667068971368_a_b_b,Y: fset_P8532786667068971368_a_b_b] :
      ( ( ( fset_P4440376523358319089_a_b_b @ X3 )
        = ( fset_P4440376523358319089_a_b_b @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_239_fset__cong,axiom,
    ! [X3: fset_P271555816861255656_a_b_b,Y: fset_P271555816861255656_a_b_b] :
      ( ( ( fset_P8825802006873508977_a_b_b @ X3 )
        = ( fset_P8825802006873508977_a_b_b @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_240_fset__cong,axiom,
    ! [X3: fset_dtree_a_b,Y: fset_dtree_a_b] :
      ( ( ( fset_dtree_a_b2 @ X3 )
        = ( fset_dtree_a_b2 @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_241_fset__cong,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y: fset_P5281107635120001194_a_b_b] :
      ( ( ( fset_P783253628892185035_a_b_b @ X3 )
        = ( fset_P783253628892185035_a_b_b @ Y ) )
      = ( X3 = Y ) ) ).

% fset_cong
thf(fact_242_finsert__commute,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( finser8437519239679886002_a_b_b @ X3 @ ( finser8437519239679886002_a_b_b @ Y @ A2 ) )
      = ( finser8437519239679886002_a_b_b @ Y @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) ) ) ).

% finsert_commute
thf(fact_243_inverse__permutation__of__list_Ocases,axiom,
    ! [X3: produc7218430402464555874od_a_b] :
      ( ! [X2: product_prod_a_b] :
          ( X3
         != ( produc3641491676853602002od_a_b @ nil_Pr906174322249854893od_a_b @ X2 ) )
     => ~ ! [Y3: product_prod_a_b,X5: product_prod_a_b,Xs2: list_P3463435030753280173od_a_b,X2: product_prod_a_b] :
            ( X3
           != ( produc3641491676853602002od_a_b @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ Y3 @ X5 ) @ Xs2 ) @ X2 ) ) ) ).

% inverse_permutation_of_list.cases
thf(fact_244_inverse__permutation__of__list_Ocases,axiom,
    ! [X3: produc1821044701915316840od_a_b] :
      ( ! [X2: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc7754707808757098584od_a_b @ nil_Pr2412700377486846637od_a_b @ X2 ) )
     => ~ ! [Y3: list_P1467974523212632366od_a_b,X5: list_P1467974523212632366od_a_b,Xs2: list_P8601282865932132013od_a_b,X2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc7754707808757098584od_a_b @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ Y3 @ X5 ) @ Xs2 ) @ X2 ) ) ) ).

% inverse_permutation_of_list.cases
thf(fact_245_sd__path_Ocases,axiom,
    ! [X3: produc3904047216122699628od_a_b] :
      ( ! [Uu: produc2233330766403592615od_a_b,Uv: product_prod_a_b] :
          ( X3
         != ( produc6197409143109712604od_a_b @ Uu @ ( produc5088573426887569692od_a_b @ Uv @ nil_Pr906174322249854893od_a_b ) ) )
     => ~ ! [U: product_prod_a_b,V2: product_prod_a_b,W: product_prod_a_b,E2: produc2233330766403592615od_a_b,Es: list_P3463435030753280173od_a_b] :
            ( X3
           != ( produc6197409143109712604od_a_b @ ( produc6550459592057863831od_a_b @ U @ V2 ) @ ( produc5088573426887569692od_a_b @ W @ ( cons_P8222935586017696605od_a_b @ E2 @ Es ) ) ) ) ) ).

% sd_path.cases
thf(fact_246_sd__path_Ocases,axiom,
    ! [X3: produc2679909195573480038od_a_b] :
      ( ! [Uu: produc7397007428618769063od_a_b,Uv: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc7680696477578383190od_a_b @ Uu @ ( produc971229398454786070od_a_b @ Uv @ nil_Pr2412700377486846637od_a_b ) ) )
     => ~ ! [U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b,E2: produc7397007428618769063od_a_b,Es: list_P8601282865932132013od_a_b] :
            ( X3
           != ( produc7680696477578383190od_a_b @ ( produc5288560138351607191od_a_b @ U @ V2 ) @ ( produc971229398454786070od_a_b @ W @ ( cons_P1529385591390545501od_a_b @ E2 @ Es ) ) ) ) ) ).

% sd_path.cases
thf(fact_247_co__path_Ocases,axiom,
    ! [X3: produc3904047216122699628od_a_b] :
      ( ! [Uu: produc2233330766403592615od_a_b,Uv: product_prod_a_b] :
          ( X3
         != ( produc6197409143109712604od_a_b @ Uu @ ( produc5088573426887569692od_a_b @ Uv @ nil_Pr906174322249854893od_a_b ) ) )
     => ( ! [Uw: produc2233330766403592615od_a_b,Ux: product_prod_a_b,E2: produc2233330766403592615od_a_b] :
            ( X3
           != ( produc6197409143109712604od_a_b @ Uw @ ( produc5088573426887569692od_a_b @ Ux @ ( cons_P8222935586017696605od_a_b @ E2 @ nil_Pr906174322249854893od_a_b ) ) ) )
       => ~ ! [U: product_prod_a_b,V2: product_prod_a_b,W: product_prod_a_b,E12: produc2233330766403592615od_a_b,E23: produc2233330766403592615od_a_b,Es: list_P3463435030753280173od_a_b] :
              ( X3
             != ( produc6197409143109712604od_a_b @ ( produc6550459592057863831od_a_b @ U @ V2 ) @ ( produc5088573426887569692od_a_b @ W @ ( cons_P8222935586017696605od_a_b @ E12 @ ( cons_P8222935586017696605od_a_b @ E23 @ Es ) ) ) ) ) ) ) ).

% co_path.cases
thf(fact_248_co__path_Ocases,axiom,
    ! [X3: produc2679909195573480038od_a_b] :
      ( ! [Uu: produc7397007428618769063od_a_b,Uv: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc7680696477578383190od_a_b @ Uu @ ( produc971229398454786070od_a_b @ Uv @ nil_Pr2412700377486846637od_a_b ) ) )
     => ( ! [Uw: produc7397007428618769063od_a_b,Ux: list_P1467974523212632366od_a_b,E2: produc7397007428618769063od_a_b] :
            ( X3
           != ( produc7680696477578383190od_a_b @ Uw @ ( produc971229398454786070od_a_b @ Ux @ ( cons_P1529385591390545501od_a_b @ E2 @ nil_Pr2412700377486846637od_a_b ) ) ) )
       => ~ ! [U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b,E12: produc7397007428618769063od_a_b,E23: produc7397007428618769063od_a_b,Es: list_P8601282865932132013od_a_b] :
              ( X3
             != ( produc7680696477578383190od_a_b @ ( produc5288560138351607191od_a_b @ U @ V2 ) @ ( produc971229398454786070od_a_b @ W @ ( cons_P1529385591390545501od_a_b @ E12 @ ( cons_P1529385591390545501od_a_b @ E23 @ Es ) ) ) ) ) ) ) ).

% co_path.cases
thf(fact_249_fthe__felem__eq,axiom,
    ! [X3: produc4558475209616630778_a_b_b] :
      ( ( fthe_e7442499522476018237_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
      = X3 ) ).

% fthe_felem_eq
thf(fact_250_list_Oinject,axiom,
    ! [X21: product_prod_a_b,X222: list_P1467974523212632366od_a_b,Y21: product_prod_a_b,Y22: list_P1467974523212632366od_a_b] :
      ( ( ( cons_P7316939131009794654od_a_b @ X21 @ X222 )
        = ( cons_P7316939131009794654od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_251_list_Oinject,axiom,
    ! [X21: list_P1467974523212632366od_a_b,X222: list_l8778361445553822004od_a_b,Y21: list_P1467974523212632366od_a_b,Y22: list_l8778361445553822004od_a_b] :
      ( ( ( cons_l907386227682280420od_a_b @ X21 @ X222 )
        = ( cons_l907386227682280420od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_252_list_Oinject,axiom,
    ! [X21: produc2233330766403592615od_a_b,X222: list_P3463435030753280173od_a_b,Y21: produc2233330766403592615od_a_b,Y22: list_P3463435030753280173od_a_b] :
      ( ( ( cons_P8222935586017696605od_a_b @ X21 @ X222 )
        = ( cons_P8222935586017696605od_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_253_list_Oinject,axiom,
    ! [X21: dtree_a_b,X222: list_dtree_a_b,Y21: dtree_a_b,Y22: list_dtree_a_b] :
      ( ( ( cons_dtree_a_b @ X21 @ X222 )
        = ( cons_dtree_a_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_254_list_Oinject,axiom,
    ! [X21: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b,Y21: produc4558475209616630778_a_b_b,Y22: list_P5360711134766023690_a_b_b] :
      ( ( ( cons_P2785074014425598660_a_b_b @ X21 @ X222 )
        = ( cons_P2785074014425598660_a_b_b @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_255_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_2253494508914376569od_a_b,Y: list_P3463435030753280173od_a_b] :
      ( ( ( dtree_983605638134528549od_a_b @ X3 )
        = Y )
     => ( ! [R2: product_prod_a_b,T2: dtree_2253494508914376569od_a_b,E2: product_prod_a_b] :
            ( ( X3
              = ( node_P1936840572307073598od_a_b @ R2 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T2 @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) )
           => ( Y
             != ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T2 ) @ E2 ) @ ( dtree_983605638134528549od_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P6924693328471822228od_a_b] :
              ( ! [X: produc2878020351943352036od_a_b] :
                  ( Xs2
                 != ( finser5347476252697843100od_a_b @ X @ bot_bo7856883933444951080od_a_b ) )
             => ( ? [R2: product_prod_a_b] :
                    ( X3
                    = ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr906174322249854893od_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_256_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_1861073144021109543ee_a_b,Y: list_P7294506862534405595ee_a_b] :
      ( ( ( dtree_5459410236902894363ee_a_b @ X3 )
        = Y )
     => ( ! [R2: dtree_a_b,T2: dtree_1861073144021109543ee_a_b,E2: dtree_a_b] :
            ( ( X3
              = ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) )
           => ( Y
             != ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T2 ) @ E2 ) @ ( dtree_5459410236902894363ee_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P5991447722532490344ee_a_b] :
              ( ! [X: produc6260003399586931330ee_a_b] :
                  ( Xs2
                 != ( finser8516331313445392842ee_a_b @ X @ bot_bo5711572498106067156ee_a_b ) )
             => ( ? [R2: dtree_a_b] :
                    ( X3
                    = ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr558572586965427547ee_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_257_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_8690448868185853351ee_a_b,Y: list_P3724575226198589275ee_a_b] :
      ( ( ( dtree_9187971570250218139ee_a_b @ X3 )
        = Y )
     => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_8690448868185853351ee_a_b,E2: dtree_a_b] :
            ( ( X3
              = ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) )
           => ( Y
             != ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T2 ) @ E2 ) @ ( dtree_9187971570250218139ee_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P1087233464713034472ee_a_b] :
              ( ! [X: produc1961764714219340802ee_a_b] :
                  ( Xs2
                 != ( finser7847761039489690442ee_a_b @ X @ bot_bo3079078458218859348ee_a_b ) )
             => ( ? [R2: produc4558475209616630778_a_b_b] :
                    ( X3
                    = ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr148742403700823003ee_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_258_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_8397784528784866983_a_b_b,Y: list_P7142016109841313883_a_b_b] :
      ( ( ( dtree_2482681192243439515_a_b_b @ X3 )
        = Y )
     => ( ! [R2: dtree_a_b,T2: dtree_8397784528784866983_a_b_b,E2: produc4558475209616630778_a_b_b] :
            ( ( X3
              = ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) )
           => ( Y
             != ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T2 ) @ E2 ) @ ( dtree_2482681192243439515_a_b_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P8532786667068971368_a_b_b] :
              ( ! [X: produc4081214457754080642_a_b_b] :
                  ( Xs2
                 != ( finser5778094437704840394_a_b_b @ X @ bot_bo1493276529839087060_a_b_b ) )
             => ( ? [R2: dtree_a_b] :
                    ( X3
                    = ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr9079450101154612443_a_b_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_259_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_6636540493345571111_a_b_b,Y: list_P7924273279524553179_a_b_b] :
      ( ( ( dtree_1768895223656068891_a_b_b @ X3 )
        = Y )
     => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_6636540493345571111_a_b_b,E2: produc4558475209616630778_a_b_b] :
            ( ( X3
              = ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) )
           => ( Y
             != ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T2 ) @ E2 ) @ ( dtree_1768895223656068891_a_b_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P271555816861255656_a_b_b] :
              ( ! [X: produc8137180380982048514_a_b_b] :
                  ( Xs2
                 != ( finser3407669804807474762_a_b_b @ X @ bot_bo6312180378851360852_a_b_b ) )
             => ( ? [R2: produc4558475209616630778_a_b_b] :
                    ( X3
                    = ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr5872703755862520667_a_b_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_260_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_dtree_a_b_b,Y: list_P5360711134766023690_a_b_b] :
      ( ( ( dtree_29943561566189470_a_b_b @ X3 )
        = Y )
     => ( ! [R2: dtree_a_b,T2: dtree_dtree_a_b_b,E2: b] :
            ( ( X3
              = ( node_dtree_a_b_b @ R2 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T2 @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) )
           => ( Y
             != ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T2 ) @ E2 ) @ ( dtree_29943561566189470_a_b_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P3031279327735363940_b_b_b] :
              ( ! [X: produc5284372313782567166_b_b_b] :
                  ( Xs2
                 != ( finser6734551996811508806_b_b_b @ X @ bot_bo4737202254184417232_b_b_b ) )
             => ( ? [R2: dtree_a_b] :
                    ( X3
                    = ( node_dtree_a_b_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr5403147374433350260_a_b_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_261_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_5519289247442030201od_a_b,Y: list_P8601282865932132013od_a_b] :
      ( ( ( dtree_5213960014362835749od_a_b @ X3 )
        = Y )
     => ( ! [R2: list_P1467974523212632366od_a_b,T2: dtree_5519289247442030201od_a_b,E2: list_P1467974523212632366od_a_b] :
            ( ( X3
              = ( node_l1136085673055119934od_a_b @ R2 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T2 @ E2 ) @ bot_bo2863178955461725870od_a_b ) ) )
           => ( Y
             != ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T2 ) @ E2 ) @ ( dtree_5213960014362835749od_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P5910908224067821594od_a_b] :
              ( ! [X: produc4044292680377378282od_a_b] :
                  ( Xs2
                 != ( finser4916530145793648802od_a_b @ X @ bot_bo2863178955461725870od_a_b ) )
             => ( ? [R2: list_P1467974523212632366od_a_b] :
                    ( X3
                    = ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr2412700377486846637od_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_262_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_8339642294131873593od_a_b,Y: list_P8094385941167427565od_a_b] :
      ( ( ( dtree_2881821214123584869od_a_b @ X3 )
        = Y )
     => ( ! [R2: product_prod_a_b > product_prod_a_b > $o,T2: dtree_8339642294131873593od_a_b,E2: list_P1467974523212632366od_a_b] :
            ( ( X3
              = ( node_P5897935084763704574od_a_b @ R2 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T2 @ E2 ) @ bot_bo137739038786217454od_a_b ) ) )
           => ( Y
             != ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T2 ) @ E2 ) @ ( dtree_2881821214123584869od_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P9180166578942778714od_a_b] :
              ( ! [X: produc6844405789190802602od_a_b] :
                  ( Xs2
                 != ( finser4631589853810920290od_a_b @ X @ bot_bo137739038786217454od_a_b ) )
             => ( ? [R2: product_prod_a_b > product_prod_a_b > $o] :
                    ( X3
                    = ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr7311172237979606381od_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_263_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_8545934391348768041od_a_b,Y: list_P5700792096213675741od_a_b] :
      ( ( ( dtree_4297255050927138389od_a_b @ X3 )
        = Y )
     => ( ! [R2: a,T2: dtree_8545934391348768041od_a_b,E2: list_P1467974523212632366od_a_b] :
            ( ( X3
              = ( node_a6325075177599301358od_a_b @ R2 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T2 @ E2 ) @ bot_bo577854266114829310od_a_b ) ) )
           => ( Y
             != ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T2 ) @ E2 ) @ ( dtree_4297255050927138389od_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P8869035697996476266od_a_b] :
              ( ! [X: produc229868702982719930od_a_b] :
                  ( Xs2
                 != ( finser2699324603737210994od_a_b @ X @ bot_bo577854266114829310od_a_b ) )
             => ( ? [R2: a] :
                    ( X3
                    = ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Pr7243433834293086045od_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_264_dtree__to__list_Oelims,axiom,
    ! [X3: dtree_a_b,Y: list_P1467974523212632366od_a_b] :
      ( ( ( dtree_to_list_a_b @ X3 )
        = Y )
     => ( ! [R2: a,T2: dtree_a_b,E2: b] :
            ( ( X3
              = ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) )
           => ( Y
             != ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T2 ) @ E2 ) @ ( dtree_to_list_a_b @ T2 ) ) ) )
       => ~ ! [Xs2: fset_P5281107635120001194_a_b_b] :
              ( ! [X: produc4558475209616630778_a_b_b] :
                  ( Xs2
                 != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) )
             => ( ? [R2: a] :
                    ( X3
                    = ( node_a_b @ R2 @ Xs2 ) )
               => ( Y != nil_Product_prod_a_b ) ) ) ) ) ).

% dtree_to_list.elims
thf(fact_265_pcas_Ocases,axiom,
    ! [X3: produc7239927097622659425od_a_b] :
      ( ! [U: product_prod_a_b,V2: product_prod_a_b] :
          ( X3
         != ( produc4522856930405434833od_a_b @ U @ ( produc3641491676853602002od_a_b @ nil_Pr906174322249854893od_a_b @ V2 ) ) )
     => ~ ! [U: product_prod_a_b,E2: produc2233330766403592615od_a_b,Es: list_P3463435030753280173od_a_b,V2: product_prod_a_b] :
            ( X3
           != ( produc4522856930405434833od_a_b @ U @ ( produc3641491676853602002od_a_b @ ( cons_P8222935586017696605od_a_b @ E2 @ Es ) @ V2 ) ) ) ) ).

% pcas.cases
thf(fact_266_dtree__from__list__root__r,axiom,
    ! [R: dtree_a_b,Xs: list_P7294506862534405595ee_a_b] :
      ( ( root_d1746759089207908692ee_a_b @ ( dtree_7424119665891431146ee_a_b @ R @ Xs ) )
      = R ) ).

% dtree_from_list_root_r
thf(fact_267_dtree__from__list__root__r,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: list_P3724575226198589275ee_a_b] :
      ( ( root_P5553465985260390356ee_a_b @ ( dtree_7850083854586231658ee_a_b @ R @ Xs ) )
      = R ) ).

% dtree_from_list_root_r
thf(fact_268_dtree__from__list__root__r,axiom,
    ! [R: dtree_a_b,Xs: list_P7142016109841313883_a_b_b] :
      ( ( root_d8071547644108387540_a_b_b @ ( dtree_1144793476579453034_a_b_b @ R @ Xs ) )
      = R ) ).

% dtree_from_list_root_r
thf(fact_269_dtree__from__list__root__r,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: list_P7924273279524553179_a_b_b] :
      ( ( root_P204151722342556500_a_b_b @ ( dtree_450453658713739498_a_b_b @ R @ Xs ) )
      = R ) ).

% dtree_from_list_root_r
thf(fact_270_dtree__from__list__root__r,axiom,
    ! [R: a,Xs: list_P1467974523212632366od_a_b] :
      ( ( root_a_b @ ( dtree_from_list_a_b @ R @ Xs ) )
      = R ) ).

% dtree_from_list_root_r
thf(fact_271_dtree_Ocollapse,axiom,
    ! [Dtree: dtree_1861073144021109543ee_a_b] :
      ( ( node_d7487230363575057332ee_a_b @ ( root_d1746759089207908692ee_a_b @ Dtree ) @ ( sucs_d5654203025177486372ee_a_b @ Dtree ) )
      = Dtree ) ).

% dtree.collapse
thf(fact_272_dtree_Ocollapse,axiom,
    ! [Dtree: dtree_8690448868185853351ee_a_b] :
      ( ( node_P2753077162091514420ee_a_b @ ( root_P5553465985260390356ee_a_b @ Dtree ) @ ( sucs_P7314365117959652004ee_a_b @ Dtree ) )
      = Dtree ) ).

% dtree.collapse
thf(fact_273_dtree_Ocollapse,axiom,
    ! [Dtree: dtree_8397784528784866983_a_b_b] :
      ( ( node_d5271158820939511604_a_b_b @ ( root_d8071547644108387540_a_b_b @ Dtree ) @ ( sucs_d609074739952873380_a_b_b @ Dtree ) )
      = Dtree ) ).

% dtree.collapse
thf(fact_274_dtree_Ocollapse,axiom,
    ! [Dtree: dtree_6636540493345571111_a_b_b] :
      ( ( node_P961815112480277940_a_b_b @ ( root_P204151722342556500_a_b_b @ Dtree ) @ ( sucs_P6478368611001241124_a_b_b @ Dtree ) )
      = Dtree ) ).

% dtree.collapse
thf(fact_275_dtree_Ocollapse,axiom,
    ! [Dtree: dtree_a_b] :
      ( ( node_a_b @ ( root_a_b @ Dtree ) @ ( sucs_a_b @ Dtree ) )
      = Dtree ) ).

% dtree.collapse
thf(fact_276_dtree_Osel_I1_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P5991447722532490344ee_a_b] :
      ( ( root_d1746759089207908692ee_a_b @ ( node_d7487230363575057332ee_a_b @ X1 @ X22 ) )
      = X1 ) ).

% dtree.sel(1)
thf(fact_277_dtree_Osel_I1_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P1087233464713034472ee_a_b] :
      ( ( root_P5553465985260390356ee_a_b @ ( node_P2753077162091514420ee_a_b @ X1 @ X22 ) )
      = X1 ) ).

% dtree.sel(1)
thf(fact_278_dtree_Osel_I1_J,axiom,
    ! [X1: dtree_a_b,X22: fset_P8532786667068971368_a_b_b] :
      ( ( root_d8071547644108387540_a_b_b @ ( node_d5271158820939511604_a_b_b @ X1 @ X22 ) )
      = X1 ) ).

% dtree.sel(1)
thf(fact_279_dtree_Osel_I1_J,axiom,
    ! [X1: produc4558475209616630778_a_b_b,X22: fset_P271555816861255656_a_b_b] :
      ( ( root_P204151722342556500_a_b_b @ ( node_P961815112480277940_a_b_b @ X1 @ X22 ) )
      = X1 ) ).

% dtree.sel(1)
thf(fact_280_dtree_Osel_I1_J,axiom,
    ! [X1: a,X22: fset_P5281107635120001194_a_b_b] :
      ( ( root_a_b @ ( node_a_b @ X1 @ X22 ) )
      = X1 ) ).

% dtree.sel(1)
thf(fact_281_dtree_Oset__sel_I1_J,axiom,
    ! [A: dtree_a_b] : ( member_a @ ( root_a_b @ A ) @ ( dverts_a_b @ A ) ) ).

% dtree.set_sel(1)
thf(fact_282_dtree_Oset__sel_I1_J,axiom,
    ! [A: dtree_1861073144021109543ee_a_b] : ( member_dtree_a_b @ ( root_d1746759089207908692ee_a_b @ A ) @ ( dverts2436977245124431984ee_a_b @ A ) ) ).

% dtree.set_sel(1)
thf(fact_283_dtree_Oset__sel_I1_J,axiom,
    ! [A: dtree_8690448868185853351ee_a_b] : ( member4380921116106875537_a_b_b @ ( root_P5553465985260390356ee_a_b @ A ) @ ( dverts2972317704043987696ee_a_b @ A ) ) ).

% dtree.set_sel(1)
thf(fact_284_dtree_Oset__sel_I1_J,axiom,
    ! [A: dtree_8397784528784866983_a_b_b] : ( member_dtree_a_b @ ( root_d8071547644108387540_a_b_b @ A ) @ ( dverts5490399362891984880_a_b_b @ A ) ) ).

% dtree.set_sel(1)
thf(fact_285_dtree_Oset__sel_I1_J,axiom,
    ! [A: dtree_6636540493345571111_a_b_b] : ( member4380921116106875537_a_b_b @ ( root_P204151722342556500_a_b_b @ A ) @ ( dverts1640268204329280112_a_b_b @ A ) ) ).

% dtree.set_sel(1)
thf(fact_286_dtree_Oexpand,axiom,
    ! [Dtree: dtree_1861073144021109543ee_a_b,Dtree2: dtree_1861073144021109543ee_a_b] :
      ( ( ( ( root_d1746759089207908692ee_a_b @ Dtree )
          = ( root_d1746759089207908692ee_a_b @ Dtree2 ) )
        & ( ( sucs_d5654203025177486372ee_a_b @ Dtree )
          = ( sucs_d5654203025177486372ee_a_b @ Dtree2 ) ) )
     => ( Dtree = Dtree2 ) ) ).

% dtree.expand
thf(fact_287_dtree_Oexpand,axiom,
    ! [Dtree: dtree_8690448868185853351ee_a_b,Dtree2: dtree_8690448868185853351ee_a_b] :
      ( ( ( ( root_P5553465985260390356ee_a_b @ Dtree )
          = ( root_P5553465985260390356ee_a_b @ Dtree2 ) )
        & ( ( sucs_P7314365117959652004ee_a_b @ Dtree )
          = ( sucs_P7314365117959652004ee_a_b @ Dtree2 ) ) )
     => ( Dtree = Dtree2 ) ) ).

% dtree.expand
thf(fact_288_dtree_Oexpand,axiom,
    ! [Dtree: dtree_8397784528784866983_a_b_b,Dtree2: dtree_8397784528784866983_a_b_b] :
      ( ( ( ( root_d8071547644108387540_a_b_b @ Dtree )
          = ( root_d8071547644108387540_a_b_b @ Dtree2 ) )
        & ( ( sucs_d609074739952873380_a_b_b @ Dtree )
          = ( sucs_d609074739952873380_a_b_b @ Dtree2 ) ) )
     => ( Dtree = Dtree2 ) ) ).

% dtree.expand
thf(fact_289_dtree_Oexpand,axiom,
    ! [Dtree: dtree_6636540493345571111_a_b_b,Dtree2: dtree_6636540493345571111_a_b_b] :
      ( ( ( ( root_P204151722342556500_a_b_b @ Dtree )
          = ( root_P204151722342556500_a_b_b @ Dtree2 ) )
        & ( ( sucs_P6478368611001241124_a_b_b @ Dtree )
          = ( sucs_P6478368611001241124_a_b_b @ Dtree2 ) ) )
     => ( Dtree = Dtree2 ) ) ).

% dtree.expand
thf(fact_290_dtree_Oexpand,axiom,
    ! [Dtree: dtree_a_b,Dtree2: dtree_a_b] :
      ( ( ( ( root_a_b @ Dtree )
          = ( root_a_b @ Dtree2 ) )
        & ( ( sucs_a_b @ Dtree )
          = ( sucs_a_b @ Dtree2 ) ) )
     => ( Dtree = Dtree2 ) ) ).

% dtree.expand
thf(fact_291_dtree_Oexhaust__sel,axiom,
    ! [Dtree: dtree_1861073144021109543ee_a_b] :
      ( Dtree
      = ( node_d7487230363575057332ee_a_b @ ( root_d1746759089207908692ee_a_b @ Dtree ) @ ( sucs_d5654203025177486372ee_a_b @ Dtree ) ) ) ).

% dtree.exhaust_sel
thf(fact_292_dtree_Oexhaust__sel,axiom,
    ! [Dtree: dtree_8690448868185853351ee_a_b] :
      ( Dtree
      = ( node_P2753077162091514420ee_a_b @ ( root_P5553465985260390356ee_a_b @ Dtree ) @ ( sucs_P7314365117959652004ee_a_b @ Dtree ) ) ) ).

% dtree.exhaust_sel
thf(fact_293_dtree_Oexhaust__sel,axiom,
    ! [Dtree: dtree_8397784528784866983_a_b_b] :
      ( Dtree
      = ( node_d5271158820939511604_a_b_b @ ( root_d8071547644108387540_a_b_b @ Dtree ) @ ( sucs_d609074739952873380_a_b_b @ Dtree ) ) ) ).

% dtree.exhaust_sel
thf(fact_294_dtree_Oexhaust__sel,axiom,
    ! [Dtree: dtree_6636540493345571111_a_b_b] :
      ( Dtree
      = ( node_P961815112480277940_a_b_b @ ( root_P204151722342556500_a_b_b @ Dtree ) @ ( sucs_P6478368611001241124_a_b_b @ Dtree ) ) ) ).

% dtree.exhaust_sel
thf(fact_295_dtree_Oexhaust__sel,axiom,
    ! [Dtree: dtree_a_b] :
      ( Dtree
      = ( node_a_b @ ( root_a_b @ Dtree ) @ ( sucs_a_b @ Dtree ) ) ) ).

% dtree.exhaust_sel
thf(fact_296_subdivide_Ocases,axiom,
    ! [X3: produc4669796033538812730od_a_b] :
      ~ ! [G: pair_p6651462780844640539t_unit,U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b,W: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc4404387750691742122od_a_b @ G @ ( produc7345660473123082718od_a_b @ ( produc5288560138351607191od_a_b @ U @ V2 ) @ W ) ) ) ).

% subdivide.cases
thf(fact_297_not__Cons__self2,axiom,
    ! [X3: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( cons_P7316939131009794654od_a_b @ X3 @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_298_not__Cons__self2,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xs: list_l8778361445553822004od_a_b] :
      ( ( cons_l907386227682280420od_a_b @ X3 @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_299_not__Cons__self2,axiom,
    ! [X3: produc2233330766403592615od_a_b,Xs: list_P3463435030753280173od_a_b] :
      ( ( cons_P8222935586017696605od_a_b @ X3 @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_300_not__Cons__self2,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( cons_dtree_a_b @ X3 @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_301_not__Cons__self2,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( cons_P2785074014425598660_a_b_b @ X3 @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_302_list_Odistinct_I1_J,axiom,
    ! [X21: list_P1467974523212632366od_a_b,X222: list_l8778361445553822004od_a_b] :
      ( nil_li8635777946366267444od_a_b
     != ( cons_l907386227682280420od_a_b @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_303_list_Odistinct_I1_J,axiom,
    ! [X21: produc2233330766403592615od_a_b,X222: list_P3463435030753280173od_a_b] :
      ( nil_Pr906174322249854893od_a_b
     != ( cons_P8222935586017696605od_a_b @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_304_list_Odistinct_I1_J,axiom,
    ! [X21: dtree_a_b,X222: list_dtree_a_b] :
      ( nil_dtree_a_b
     != ( cons_dtree_a_b @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_305_list_Odistinct_I1_J,axiom,
    ! [X21: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b] :
      ( nil_Pr5403147374433350260_a_b_b
     != ( cons_P2785074014425598660_a_b_b @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_306_list_Odistinct_I1_J,axiom,
    ! [X21: product_prod_a_b,X222: list_P1467974523212632366od_a_b] :
      ( nil_Product_prod_a_b
     != ( cons_P7316939131009794654od_a_b @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_307_list_OdiscI,axiom,
    ! [List: list_l8778361445553822004od_a_b,X21: list_P1467974523212632366od_a_b,X222: list_l8778361445553822004od_a_b] :
      ( ( List
        = ( cons_l907386227682280420od_a_b @ X21 @ X222 ) )
     => ( List != nil_li8635777946366267444od_a_b ) ) ).

% list.discI
thf(fact_308_list_OdiscI,axiom,
    ! [List: list_P3463435030753280173od_a_b,X21: produc2233330766403592615od_a_b,X222: list_P3463435030753280173od_a_b] :
      ( ( List
        = ( cons_P8222935586017696605od_a_b @ X21 @ X222 ) )
     => ( List != nil_Pr906174322249854893od_a_b ) ) ).

% list.discI
thf(fact_309_list_OdiscI,axiom,
    ! [List: list_dtree_a_b,X21: dtree_a_b,X222: list_dtree_a_b] :
      ( ( List
        = ( cons_dtree_a_b @ X21 @ X222 ) )
     => ( List != nil_dtree_a_b ) ) ).

% list.discI
thf(fact_310_list_OdiscI,axiom,
    ! [List: list_P5360711134766023690_a_b_b,X21: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b] :
      ( ( List
        = ( cons_P2785074014425598660_a_b_b @ X21 @ X222 ) )
     => ( List != nil_Pr5403147374433350260_a_b_b ) ) ).

% list.discI
thf(fact_311_list_OdiscI,axiom,
    ! [List: list_P1467974523212632366od_a_b,X21: product_prod_a_b,X222: list_P1467974523212632366od_a_b] :
      ( ( List
        = ( cons_P7316939131009794654od_a_b @ X21 @ X222 ) )
     => ( List != nil_Product_prod_a_b ) ) ).

% list.discI
thf(fact_312_list_Oexhaust,axiom,
    ! [Y: list_l8778361445553822004od_a_b] :
      ( ( Y != nil_li8635777946366267444od_a_b )
     => ~ ! [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
            ( Y
           != ( cons_l907386227682280420od_a_b @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_313_list_Oexhaust,axiom,
    ! [Y: list_P3463435030753280173od_a_b] :
      ( ( Y != nil_Pr906174322249854893od_a_b )
     => ~ ! [X212: produc2233330766403592615od_a_b,X223: list_P3463435030753280173od_a_b] :
            ( Y
           != ( cons_P8222935586017696605od_a_b @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_314_list_Oexhaust,axiom,
    ! [Y: list_dtree_a_b] :
      ( ( Y != nil_dtree_a_b )
     => ~ ! [X212: dtree_a_b,X223: list_dtree_a_b] :
            ( Y
           != ( cons_dtree_a_b @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_315_list_Oexhaust,axiom,
    ! [Y: list_P5360711134766023690_a_b_b] :
      ( ( Y != nil_Pr5403147374433350260_a_b_b )
     => ~ ! [X212: produc4558475209616630778_a_b_b,X223: list_P5360711134766023690_a_b_b] :
            ( Y
           != ( cons_P2785074014425598660_a_b_b @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_316_list_Oexhaust,axiom,
    ! [Y: list_P1467974523212632366od_a_b] :
      ( ( Y != nil_Product_prod_a_b )
     => ~ ! [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
            ( Y
           != ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_317_neq__Nil__conv,axiom,
    ! [Xs: list_l8778361445553822004od_a_b] :
      ( ( Xs != nil_li8635777946366267444od_a_b )
      = ( ? [Y4: list_P1467974523212632366od_a_b,Ys2: list_l8778361445553822004od_a_b] :
            ( Xs
            = ( cons_l907386227682280420od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_318_neq__Nil__conv,axiom,
    ! [Xs: list_P3463435030753280173od_a_b] :
      ( ( Xs != nil_Pr906174322249854893od_a_b )
      = ( ? [Y4: produc2233330766403592615od_a_b,Ys2: list_P3463435030753280173od_a_b] :
            ( Xs
            = ( cons_P8222935586017696605od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_319_neq__Nil__conv,axiom,
    ! [Xs: list_dtree_a_b] :
      ( ( Xs != nil_dtree_a_b )
      = ( ? [Y4: dtree_a_b,Ys2: list_dtree_a_b] :
            ( Xs
            = ( cons_dtree_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_320_neq__Nil__conv,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b] :
      ( ( Xs != nil_Pr5403147374433350260_a_b_b )
      = ( ? [Y4: produc4558475209616630778_a_b_b,Ys2: list_P5360711134766023690_a_b_b] :
            ( Xs
            = ( cons_P2785074014425598660_a_b_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_321_neq__Nil__conv,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
      = ( ? [Y4: product_prod_a_b,Ys2: list_P1467974523212632366od_a_b] :
            ( Xs
            = ( cons_P7316939131009794654od_a_b @ Y4 @ Ys2 ) ) ) ) ).

% neq_Nil_conv
thf(fact_322_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_Product_prod_a_b @ nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ nil_Product_prod_a_b )
       => ( ! [Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] : ( P @ nil_Product_prod_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_323_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_dtree_a_b > $o,Xs: list_P1467974523212632366od_a_b,Ys: list_dtree_a_b] :
      ( ( P @ nil_Product_prod_a_b @ nil_dtree_a_b )
     => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ nil_dtree_a_b )
       => ( ! [Y3: dtree_a_b,Ys3: list_dtree_a_b] : ( P @ nil_Product_prod_a_b @ ( cons_dtree_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: dtree_a_b,Ys3: list_dtree_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ ( cons_dtree_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_324_list__induct2_H,axiom,
    ! [P: list_dtree_a_b > list_P1467974523212632366od_a_b > $o,Xs: list_dtree_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_dtree_a_b @ nil_Product_prod_a_b )
     => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b] : ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ nil_Product_prod_a_b )
       => ( ! [Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] : ( P @ nil_dtree_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_325_list__induct2_H,axiom,
    ! [P: list_dtree_a_b > list_dtree_a_b > $o,Xs: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( P @ nil_dtree_a_b @ nil_dtree_a_b )
     => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b] : ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ nil_dtree_a_b )
       => ( ! [Y3: dtree_a_b,Ys3: list_dtree_a_b] : ( P @ nil_dtree_a_b @ ( cons_dtree_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Y3: dtree_a_b,Ys3: list_dtree_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ ( cons_dtree_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_326_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_l8778361445553822004od_a_b > $o,Xs: list_P1467974523212632366od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( P @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b )
     => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ nil_li8635777946366267444od_a_b )
       => ( ! [Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] : ( P @ nil_Product_prod_a_b @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_327_list__induct2_H,axiom,
    ! [P: list_l8778361445553822004od_a_b > list_P1467974523212632366od_a_b > $o,Xs: list_l8778361445553822004od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_li8635777946366267444od_a_b @ nil_Product_prod_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ nil_Product_prod_a_b )
       => ( ! [Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] : ( P @ nil_li8635777946366267444od_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_328_list__induct2_H,axiom,
    ! [P: list_l8778361445553822004od_a_b > list_dtree_a_b > $o,Xs: list_l8778361445553822004od_a_b,Ys: list_dtree_a_b] :
      ( ( P @ nil_li8635777946366267444od_a_b @ nil_dtree_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ nil_dtree_a_b )
       => ( ! [Y3: dtree_a_b,Ys3: list_dtree_a_b] : ( P @ nil_li8635777946366267444od_a_b @ ( cons_dtree_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: dtree_a_b,Ys3: list_dtree_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ ( cons_dtree_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_329_list__induct2_H,axiom,
    ! [P: list_dtree_a_b > list_l8778361445553822004od_a_b > $o,Xs: list_dtree_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( P @ nil_dtree_a_b @ nil_li8635777946366267444od_a_b )
     => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b] : ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ nil_li8635777946366267444od_a_b )
       => ( ! [Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] : ( P @ nil_dtree_a_b @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_330_list__induct2_H,axiom,
    ! [P: list_P1467974523212632366od_a_b > list_P5360711134766023690_a_b_b > $o,Xs: list_P1467974523212632366od_a_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( P @ nil_Product_prod_a_b @ nil_Pr5403147374433350260_a_b_b )
     => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ nil_Pr5403147374433350260_a_b_b )
       => ( ! [Y3: produc4558475209616630778_a_b_b,Ys3: list_P5360711134766023690_a_b_b] : ( P @ nil_Product_prod_a_b @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Ys3 ) )
         => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: produc4558475209616630778_a_b_b,Ys3: list_P5360711134766023690_a_b_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_331_list__induct2_H,axiom,
    ! [P: list_l8778361445553822004od_a_b > list_l8778361445553822004od_a_b > $o,Xs: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( P @ nil_li8635777946366267444od_a_b @ nil_li8635777946366267444od_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ nil_li8635777946366267444od_a_b )
       => ( ! [Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] : ( P @ nil_li8635777946366267444od_a_b @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) )
         => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_332_list__nonempty__induct,axiom,
    ! [Xs: list_l8778361445553822004od_a_b,P: list_l8778361445553822004od_a_b > $o] :
      ( ( Xs != nil_li8635777946366267444od_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b] : ( P @ ( cons_l907386227682280420od_a_b @ X2 @ nil_li8635777946366267444od_a_b ) )
       => ( ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
              ( ( Xs2 != nil_li8635777946366267444od_a_b )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_333_list__nonempty__induct,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,P: list_P3463435030753280173od_a_b > $o] :
      ( ( Xs != nil_Pr906174322249854893od_a_b )
     => ( ! [X2: produc2233330766403592615od_a_b] : ( P @ ( cons_P8222935586017696605od_a_b @ X2 @ nil_Pr906174322249854893od_a_b ) )
       => ( ! [X2: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b] :
              ( ( Xs2 != nil_Pr906174322249854893od_a_b )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P8222935586017696605od_a_b @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_334_list__nonempty__induct,axiom,
    ! [Xs: list_dtree_a_b,P: list_dtree_a_b > $o] :
      ( ( Xs != nil_dtree_a_b )
     => ( ! [X2: dtree_a_b] : ( P @ ( cons_dtree_a_b @ X2 @ nil_dtree_a_b ) )
       => ( ! [X2: dtree_a_b,Xs2: list_dtree_a_b] :
              ( ( Xs2 != nil_dtree_a_b )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_dtree_a_b @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_335_list__nonempty__induct,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,P: list_P5360711134766023690_a_b_b > $o] :
      ( ( Xs != nil_Pr5403147374433350260_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b] : ( P @ ( cons_P2785074014425598660_a_b_b @ X2 @ nil_Pr5403147374433350260_a_b_b ) )
       => ( ! [X2: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b] :
              ( ( Xs2 != nil_Pr5403147374433350260_a_b_b )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P2785074014425598660_a_b_b @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_336_list__nonempty__induct,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,P: list_P1467974523212632366od_a_b > $o] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) )
       => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
              ( ( Xs2 != nil_Product_prod_a_b )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_337_map__tailrec__rev_Ocases,axiom,
    ! [X3: produc7338334792537277175od_a_b] :
      ( ! [F: product_prod_a_b > product_prod_a_b,Bs: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc9039425639929299113od_a_b @ F @ ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Bs ) ) )
     => ~ ! [F: product_prod_a_b > product_prod_a_b,A4: product_prod_a_b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc9039425639929299113od_a_b @ F @ ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ A4 @ As ) @ Bs ) ) ) ) ).

% map_tailrec_rev.cases
thf(fact_338_successively_Ocases,axiom,
    ! [X3: produc9134726091994374893od_a_b] :
      ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o] :
          ( X3
         != ( produc7760118425732869085od_a_b @ P3 @ nil_li8635777946366267444od_a_b ) )
     => ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X2 @ nil_li8635777946366267444od_a_b ) ) )
       => ~ ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X2 @ ( cons_l907386227682280420od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_339_successively_Ocases,axiom,
    ! [X3: produc4732240729513732134od_a_b] :
      ( ! [P3: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o] :
          ( X3
         != ( produc1267148703545900054od_a_b @ P3 @ nil_Pr906174322249854893od_a_b ) )
     => ( ! [P3: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o,X2: produc2233330766403592615od_a_b] :
            ( X3
           != ( produc1267148703545900054od_a_b @ P3 @ ( cons_P8222935586017696605od_a_b @ X2 @ nil_Pr906174322249854893od_a_b ) ) )
       => ~ ! [P3: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o,X2: produc2233330766403592615od_a_b,Y3: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b] :
              ( X3
             != ( produc1267148703545900054od_a_b @ P3 @ ( cons_P8222935586017696605od_a_b @ X2 @ ( cons_P8222935586017696605od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_340_successively_Ocases,axiom,
    ! [X3: produc750211871370617675ee_a_b] :
      ( ! [P3: dtree_a_b > dtree_a_b > $o] :
          ( X3
         != ( produc5314445973317677381ee_a_b @ P3 @ nil_dtree_a_b ) )
     => ( ! [P3: dtree_a_b > dtree_a_b > $o,X2: dtree_a_b] :
            ( X3
           != ( produc5314445973317677381ee_a_b @ P3 @ ( cons_dtree_a_b @ X2 @ nil_dtree_a_b ) ) )
       => ~ ! [P3: dtree_a_b > dtree_a_b > $o,X2: dtree_a_b,Y3: dtree_a_b,Xs2: list_dtree_a_b] :
              ( X3
             != ( produc5314445973317677381ee_a_b @ P3 @ ( cons_dtree_a_b @ X2 @ ( cons_dtree_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_341_successively_Ocases,axiom,
    ! [X3: produc783859242544933067_a_b_b] :
      ( ! [P3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o] :
          ( X3
         != ( produc6413140877468432325_a_b_b @ P3 @ nil_Pr5403147374433350260_a_b_b ) )
     => ( ! [P3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o,X2: produc4558475209616630778_a_b_b] :
            ( X3
           != ( produc6413140877468432325_a_b_b @ P3 @ ( cons_P2785074014425598660_a_b_b @ X2 @ nil_Pr5403147374433350260_a_b_b ) ) )
       => ~ ! [P3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o,X2: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b] :
              ( X3
             != ( produc6413140877468432325_a_b_b @ P3 @ ( cons_P2785074014425598660_a_b_b @ X2 @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_342_successively_Ocases,axiom,
    ! [X3: produc3334210663054469735od_a_b] :
      ( ! [P3: product_prod_a_b > product_prod_a_b > $o] :
          ( X3
         != ( produc7704224619955794135od_a_b @ P3 @ nil_Product_prod_a_b ) )
     => ( ! [P3: product_prod_a_b > product_prod_a_b > $o,X2: product_prod_a_b] :
            ( X3
           != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) ) )
       => ~ ! [P3: product_prod_a_b > product_prod_a_b > $o,X2: product_prod_a_b,Y3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X2 @ ( cons_P7316939131009794654od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_343_sorted__wrt_Ocases,axiom,
    ! [X3: produc9134726091994374893od_a_b] :
      ( ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o] :
          ( X3
         != ( produc7760118425732869085od_a_b @ P3 @ nil_li8635777946366267444od_a_b ) )
     => ~ ! [P3: list_P1467974523212632366od_a_b > list_P1467974523212632366od_a_b > $o,X2: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc7760118425732869085od_a_b @ P3 @ ( cons_l907386227682280420od_a_b @ X2 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_344_sorted__wrt_Ocases,axiom,
    ! [X3: produc4732240729513732134od_a_b] :
      ( ! [P3: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o] :
          ( X3
         != ( produc1267148703545900054od_a_b @ P3 @ nil_Pr906174322249854893od_a_b ) )
     => ~ ! [P3: produc2233330766403592615od_a_b > produc2233330766403592615od_a_b > $o,X2: produc2233330766403592615od_a_b,Ys3: list_P3463435030753280173od_a_b] :
            ( X3
           != ( produc1267148703545900054od_a_b @ P3 @ ( cons_P8222935586017696605od_a_b @ X2 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_345_sorted__wrt_Ocases,axiom,
    ! [X3: produc750211871370617675ee_a_b] :
      ( ! [P3: dtree_a_b > dtree_a_b > $o] :
          ( X3
         != ( produc5314445973317677381ee_a_b @ P3 @ nil_dtree_a_b ) )
     => ~ ! [P3: dtree_a_b > dtree_a_b > $o,X2: dtree_a_b,Ys3: list_dtree_a_b] :
            ( X3
           != ( produc5314445973317677381ee_a_b @ P3 @ ( cons_dtree_a_b @ X2 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_346_sorted__wrt_Ocases,axiom,
    ! [X3: produc783859242544933067_a_b_b] :
      ( ! [P3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o] :
          ( X3
         != ( produc6413140877468432325_a_b_b @ P3 @ nil_Pr5403147374433350260_a_b_b ) )
     => ~ ! [P3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o,X2: produc4558475209616630778_a_b_b,Ys3: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( produc6413140877468432325_a_b_b @ P3 @ ( cons_P2785074014425598660_a_b_b @ X2 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_347_sorted__wrt_Ocases,axiom,
    ! [X3: produc3334210663054469735od_a_b] :
      ( ! [P3: product_prod_a_b > product_prod_a_b > $o] :
          ( X3
         != ( produc7704224619955794135od_a_b @ P3 @ nil_Product_prod_a_b ) )
     => ~ ! [P3: product_prod_a_b > product_prod_a_b > $o,X2: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc7704224619955794135od_a_b @ P3 @ ( cons_P7316939131009794654od_a_b @ X2 @ Ys3 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_348_transpose_Ocases,axiom,
    ! [X3: list_l6443893005374362810od_a_b] :
      ( ( X3 != nil_li2802039260981550394od_a_b )
     => ( ! [Xss: list_l6443893005374362810od_a_b] :
            ( X3
           != ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ Xss ) )
       => ~ ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Xss: list_l6443893005374362810od_a_b] :
              ( X3
             != ( cons_l4798275018037426410od_a_b @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_349_transpose_Ocases,axiom,
    ! [X3: list_l7282425492883329843od_a_b] :
      ( ( X3 != nil_li9150416971034547123od_a_b )
     => ( ! [Xss: list_l7282425492883329843od_a_b] :
            ( X3
           != ( cons_l5043155473145997155od_a_b @ nil_Pr906174322249854893od_a_b @ Xss ) )
       => ~ ! [X2: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b,Xss: list_l7282425492883329843od_a_b] :
              ( X3
             != ( cons_l5043155473145997155od_a_b @ ( cons_P8222935586017696605od_a_b @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_350_transpose_Ocases,axiom,
    ! [X3: list_list_dtree_a_b] :
      ( ( X3 != nil_list_dtree_a_b )
     => ( ! [Xss: list_list_dtree_a_b] :
            ( X3
           != ( cons_list_dtree_a_b @ nil_dtree_a_b @ Xss ) )
       => ~ ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Xss: list_list_dtree_a_b] :
              ( X3
             != ( cons_list_dtree_a_b @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_351_transpose_Ocases,axiom,
    ! [X3: list_l2608773801899484570_a_b_b] :
      ( ( X3 != nil_li143336474603867524_a_b_b )
     => ( ! [Xss: list_l2608773801899484570_a_b_b] :
            ( X3
           != ( cons_l8517938233221414356_a_b_b @ nil_Pr5403147374433350260_a_b_b @ Xss ) )
       => ~ ! [X2: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b,Xss: list_l2608773801899484570_a_b_b] :
              ( X3
             != ( cons_l8517938233221414356_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_352_transpose_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ( ! [Xss: list_l8778361445553822004od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ Xss ) )
       => ~ ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Xss: list_l8778361445553822004od_a_b] :
              ( X3
             != ( cons_l907386227682280420od_a_b @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_353_shuffles_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [Ys3: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Ys3 ) )
     => ( ! [Xs2: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ Xs2 @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
              ( X3
             != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_354_shuffles_Ocases,axiom,
    ! [X3: produc1627906242116850535od_a_b] :
      ( ! [Ys3: list_P3463435030753280173od_a_b] :
          ( X3
         != ( produc3836617586516638167od_a_b @ nil_Pr906174322249854893od_a_b @ Ys3 ) )
     => ( ! [Xs2: list_P3463435030753280173od_a_b] :
            ( X3
           != ( produc3836617586516638167od_a_b @ Xs2 @ nil_Pr906174322249854893od_a_b ) )
       => ~ ! [X2: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b,Y3: produc2233330766403592615od_a_b,Ys3: list_P3463435030753280173od_a_b] :
              ( X3
             != ( produc3836617586516638167od_a_b @ ( cons_P8222935586017696605od_a_b @ X2 @ Xs2 ) @ ( cons_P8222935586017696605od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_355_shuffles_Ocases,axiom,
    ! [X3: produc5339155667539881461ee_a_b] :
      ( ! [Ys3: list_dtree_a_b] :
          ( X3
         != ( produc6019849452775264557ee_a_b @ nil_dtree_a_b @ Ys3 ) )
     => ( ! [Xs2: list_dtree_a_b] :
            ( X3
           != ( produc6019849452775264557ee_a_b @ Xs2 @ nil_dtree_a_b ) )
       => ~ ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Y3: dtree_a_b,Ys3: list_dtree_a_b] :
              ( X3
             != ( produc6019849452775264557ee_a_b @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ ( cons_dtree_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_356_shuffles_Ocases,axiom,
    ! [X3: produc6081131995383004661_a_b_b] :
      ( ! [Ys3: list_P5360711134766023690_a_b_b] :
          ( X3
         != ( produc4608802955787333421_a_b_b @ nil_Pr5403147374433350260_a_b_b @ Ys3 ) )
     => ( ! [Xs2: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( produc4608802955787333421_a_b_b @ Xs2 @ nil_Pr5403147374433350260_a_b_b ) )
       => ~ ! [X2: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b,Y3: produc4558475209616630778_a_b_b,Ys3: list_P5360711134766023690_a_b_b] :
              ( X3
             != ( produc4608802955787333421_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X2 @ Xs2 ) @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_357_shuffles_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [Ys3: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Ys3 ) )
     => ( ! [Xs2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ Xs2 @ nil_Product_prod_a_b ) )
       => ~ ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
              ( X3
             != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% shuffles.cases
thf(fact_358_dtree__from__list__eq__singleton,axiom,
    ! [R0: product_prod_a_b,T0: dtree_2253494508914376569od_a_b,E0: product_prod_a_b,V1: product_prod_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( ( node_P1936840572307073598od_a_b @ R0 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T0 @ E0 ) @ bot_bo7856883933444951080od_a_b ) )
        = ( dtree_1864022081312108148od_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P3463435030753280173od_a_b] :
            ( ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_359_dtree__from__list__eq__singleton,axiom,
    ! [R0: dtree_a_b,T0: dtree_1861073144021109543ee_a_b,E0: dtree_a_b,V1: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ R0 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T0 @ E0 ) @ bot_bo5711572498106067156ee_a_b ) )
        = ( dtree_7424119665891431146ee_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P7294506862534405595ee_a_b] :
            ( ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_360_dtree__from__list__eq__singleton,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_8690448868185853351ee_a_b,E0: dtree_a_b,V1: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ R0 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T0 @ E0 ) @ bot_bo3079078458218859348ee_a_b ) )
        = ( dtree_7850083854586231658ee_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P3724575226198589275ee_a_b] :
            ( ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_361_dtree__from__list__eq__singleton,axiom,
    ! [R0: dtree_a_b,T0: dtree_8397784528784866983_a_b_b,E0: produc4558475209616630778_a_b_b,V1: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ R0 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T0 @ E0 ) @ bot_bo1493276529839087060_a_b_b ) )
        = ( dtree_1144793476579453034_a_b_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P7142016109841313883_a_b_b] :
            ( ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_362_dtree__from__list__eq__singleton,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_6636540493345571111_a_b_b,E0: produc4558475209616630778_a_b_b,V1: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ R0 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T0 @ E0 ) @ bot_bo6312180378851360852_a_b_b ) )
        = ( dtree_450453658713739498_a_b_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P7924273279524553179_a_b_b] :
            ( ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_363_dtree__from__list__eq__singleton,axiom,
    ! [R0: dtree_a_b,T0: dtree_dtree_a_b_b,E0: b,V1: dtree_a_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( node_dtree_a_b_b @ R0 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T0 @ E0 ) @ bot_bo4737202254184417232_b_b_b ) )
        = ( dtree_5255521609252960911_a_b_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P5360711134766023690_a_b_b] :
            ( ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_364_dtree__from__list__eq__singleton,axiom,
    ! [R0: list_P1467974523212632366od_a_b,T0: dtree_5519289247442030201od_a_b,E0: list_P1467974523212632366od_a_b,V1: list_P1467974523212632366od_a_b,Ys: list_P8601282865932132013od_a_b] :
      ( ( ( node_l1136085673055119934od_a_b @ R0 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T0 @ E0 ) @ bot_bo2863178955461725870od_a_b ) )
        = ( dtree_6507962483783174260od_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P8601282865932132013od_a_b] :
            ( ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_365_dtree__from__list__eq__singleton,axiom,
    ! [R0: product_prod_a_b > product_prod_a_b > $o,T0: dtree_8339642294131873593od_a_b,E0: list_P1467974523212632366od_a_b,V1: product_prod_a_b > product_prod_a_b > $o,Ys: list_P8094385941167427565od_a_b] :
      ( ( ( node_P5897935084763704574od_a_b @ R0 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T0 @ E0 ) @ bot_bo137739038786217454od_a_b ) )
        = ( dtree_4383916385682046516od_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P8094385941167427565od_a_b] :
            ( ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_366_dtree__from__list__eq__singleton,axiom,
    ! [R0: a,T0: dtree_8545934391348768041od_a_b,E0: list_P1467974523212632366od_a_b,V1: a,Ys: list_P5700792096213675741od_a_b] :
      ( ( ( node_a6325075177599301358od_a_b @ R0 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T0 @ E0 ) @ bot_bo577854266114829310od_a_b ) )
        = ( dtree_6261964479915675172od_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P5700792096213675741od_a_b] :
            ( ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_367_dtree__from__list__eq__singleton,axiom,
    ! [R0: a,T0: dtree_a_b,E0: b,V1: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( node_a_b @ R0 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T0 @ E0 ) @ bot_bo2895716411488905534_a_b_b ) )
        = ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ( ( R0 = V1 )
        & ? [Xs2: list_P1467974523212632366od_a_b] :
            ( ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T0 ) @ E0 ) @ Xs2 )
            = Ys ) ) ) ).

% dtree_from_list_eq_singleton
thf(fact_368_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: product_prod_a_b,T0: dtree_2253494508914376569od_a_b,E0: product_prod_a_b,V1: product_prod_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( ( node_P1936840572307073598od_a_b @ R0 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T0 @ E0 ) @ bot_bo7856883933444951080od_a_b ) )
        = ( dtree_1864022081312108148od_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P3463435030753280173od_a_b] :
          ( ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_369_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: dtree_a_b,T0: dtree_1861073144021109543ee_a_b,E0: dtree_a_b,V1: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( ( node_d7487230363575057332ee_a_b @ R0 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T0 @ E0 ) @ bot_bo5711572498106067156ee_a_b ) )
        = ( dtree_7424119665891431146ee_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P7294506862534405595ee_a_b] :
          ( ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_370_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_8690448868185853351ee_a_b,E0: dtree_a_b,V1: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( ( node_P2753077162091514420ee_a_b @ R0 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T0 @ E0 ) @ bot_bo3079078458218859348ee_a_b ) )
        = ( dtree_7850083854586231658ee_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P3724575226198589275ee_a_b] :
          ( ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_371_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: dtree_a_b,T0: dtree_8397784528784866983_a_b_b,E0: produc4558475209616630778_a_b_b,V1: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( ( node_d5271158820939511604_a_b_b @ R0 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T0 @ E0 ) @ bot_bo1493276529839087060_a_b_b ) )
        = ( dtree_1144793476579453034_a_b_b @ V1 @ Ys ) )
     => ? [Xs2: list_P7142016109841313883_a_b_b] :
          ( ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_372_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_6636540493345571111_a_b_b,E0: produc4558475209616630778_a_b_b,V1: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( ( node_P961815112480277940_a_b_b @ R0 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T0 @ E0 ) @ bot_bo6312180378851360852_a_b_b ) )
        = ( dtree_450453658713739498_a_b_b @ V1 @ Ys ) )
     => ? [Xs2: list_P7924273279524553179_a_b_b] :
          ( ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_373_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: dtree_a_b,T0: dtree_dtree_a_b_b,E0: b,V1: dtree_a_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( node_dtree_a_b_b @ R0 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T0 @ E0 ) @ bot_bo4737202254184417232_b_b_b ) )
        = ( dtree_5255521609252960911_a_b_b @ V1 @ Ys ) )
     => ? [Xs2: list_P5360711134766023690_a_b_b] :
          ( ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_374_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: list_P1467974523212632366od_a_b,T0: dtree_5519289247442030201od_a_b,E0: list_P1467974523212632366od_a_b,V1: list_P1467974523212632366od_a_b,Ys: list_P8601282865932132013od_a_b] :
      ( ( ( node_l1136085673055119934od_a_b @ R0 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T0 @ E0 ) @ bot_bo2863178955461725870od_a_b ) )
        = ( dtree_6507962483783174260od_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P8601282865932132013od_a_b] :
          ( ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_375_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: product_prod_a_b > product_prod_a_b > $o,T0: dtree_8339642294131873593od_a_b,E0: list_P1467974523212632366od_a_b,V1: product_prod_a_b > product_prod_a_b > $o,Ys: list_P8094385941167427565od_a_b] :
      ( ( ( node_P5897935084763704574od_a_b @ R0 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T0 @ E0 ) @ bot_bo137739038786217454od_a_b ) )
        = ( dtree_4383916385682046516od_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P8094385941167427565od_a_b] :
          ( ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_376_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: a,T0: dtree_8545934391348768041od_a_b,E0: list_P1467974523212632366od_a_b,V1: a,Ys: list_P5700792096213675741od_a_b] :
      ( ( ( node_a6325075177599301358od_a_b @ R0 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T0 @ E0 ) @ bot_bo577854266114829310od_a_b ) )
        = ( dtree_6261964479915675172od_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P5700792096213675741od_a_b] :
          ( ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_377_dtree__from__list__eq__singleton__hd,axiom,
    ! [R0: a,T0: dtree_a_b,E0: b,V1: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( node_a_b @ R0 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T0 @ E0 ) @ bot_bo2895716411488905534_a_b_b ) )
        = ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ? [Xs2: list_P1467974523212632366od_a_b] :
          ( ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T0 ) @ E0 ) @ Xs2 )
          = Ys ) ) ).

% dtree_from_list_eq_singleton_hd
thf(fact_378_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: product_prod_a_b,T: dtree_2253494508914376569od_a_b,E: product_prod_a_b] :
      ( ( dtree_983605638134528549od_a_b @ ( node_P1936840572307073598od_a_b @ R @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T @ E ) @ bot_bo7856883933444951080od_a_b ) ) )
      = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T ) @ E ) @ ( dtree_983605638134528549od_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_379_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_1861073144021109543ee_a_b,E: dtree_a_b] :
      ( ( dtree_5459410236902894363ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) ) )
      = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T ) @ E ) @ ( dtree_5459410236902894363ee_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_380_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b,E: dtree_a_b] :
      ( ( dtree_9187971570250218139ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) ) )
      = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T ) @ E ) @ ( dtree_9187971570250218139ee_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_381_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( dtree_2482681192243439515_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) ) )
      = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T ) @ E ) @ ( dtree_2482681192243439515_a_b_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_382_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( dtree_1768895223656068891_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) ) )
      = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T ) @ E ) @ ( dtree_1768895223656068891_a_b_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_383_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_dtree_a_b_b,E: b] :
      ( ( dtree_29943561566189470_a_b_b @ ( node_dtree_a_b_b @ R @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T @ E ) @ bot_bo4737202254184417232_b_b_b ) ) )
      = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T ) @ E ) @ ( dtree_29943561566189470_a_b_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_384_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: list_P1467974523212632366od_a_b,T: dtree_5519289247442030201od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( dtree_5213960014362835749od_a_b @ ( node_l1136085673055119934od_a_b @ R @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T @ E ) @ bot_bo2863178955461725870od_a_b ) ) )
      = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T ) @ E ) @ ( dtree_5213960014362835749od_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_385_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: product_prod_a_b > product_prod_a_b > $o,T: dtree_8339642294131873593od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( dtree_2881821214123584869od_a_b @ ( node_P5897935084763704574od_a_b @ R @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T @ E ) @ bot_bo137739038786217454od_a_b ) ) )
      = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T ) @ E ) @ ( dtree_2881821214123584869od_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_386_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: a,T: dtree_8545934391348768041od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( dtree_4297255050927138389od_a_b @ ( node_a6325075177599301358od_a_b @ R @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T @ E ) @ bot_bo577854266114829310od_a_b ) ) )
      = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T ) @ E ) @ ( dtree_4297255050927138389od_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_387_dtree__to__list_Osimps_I1_J,axiom,
    ! [R: a,T: dtree_a_b,E: b] :
      ( ( dtree_to_list_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) )
      = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T ) @ E ) @ ( dtree_to_list_a_b @ T ) ) ) ).

% dtree_to_list.simps(1)
thf(fact_388_pre__digraph_Ocas_Ocases,axiom,
    ! [X3: produc7795635294741998752od_a_b] :
      ( ! [U: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc2045222648701277328od_a_b @ U @ ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ V2 ) ) )
     => ~ ! [U: list_P1467974523212632366od_a_b,E2: product_prod_a_b,Es: list_P1467974523212632366od_a_b,V2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc2045222648701277328od_a_b @ U @ ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ E2 @ Es ) @ V2 ) ) ) ) ).

% pre_digraph.cas.cases
thf(fact_389_empty__iff,axiom,
    ! [C: produc5177672665255943253ee_a_b] :
      ~ ( member2060280516343777534ee_a_b @ C @ bot_bo6208222296400721441ee_a_b ) ).

% empty_iff
thf(fact_390_empty__iff,axiom,
    ! [C: produc7397007428618769063od_a_b] :
      ~ ( member3051990972100052432od_a_b @ C @ bot_bo5083760590458426867od_a_b ) ).

% empty_iff
thf(fact_391_empty__iff,axiom,
    ! [C: product_prod_a_b] :
      ~ ( member1426531481828664017od_a_b @ C @ bot_bo3428410327501040244od_a_b ) ).

% empty_iff
thf(fact_392_empty__iff,axiom,
    ! [C: b] :
      ~ ( member_b @ C @ bot_bot_set_b ) ).

% empty_iff
thf(fact_393_empty__iff,axiom,
    ! [C: a] :
      ~ ( member_a @ C @ bot_bot_set_a ) ).

% empty_iff
thf(fact_394_empty__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b] :
      ~ ( member4380921116106875537_a_b_b @ C @ bot_bo3721250822024684356_a_b_b ) ).

% empty_iff
thf(fact_395_empty__iff,axiom,
    ! [C: dtree_a_b] :
      ~ ( member_dtree_a_b @ C @ bot_bo8730652382759064772ee_a_b ) ).

% empty_iff
thf(fact_396_all__not__in__conv,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b] :
      ( ( ! [X4: produc5177672665255943253ee_a_b] :
            ~ ( member2060280516343777534ee_a_b @ X4 @ A2 ) )
      = ( A2 = bot_bo6208222296400721441ee_a_b ) ) ).

% all_not_in_conv
thf(fact_397_all__not__in__conv,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b] :
      ( ( ! [X4: produc7397007428618769063od_a_b] :
            ~ ( member3051990972100052432od_a_b @ X4 @ A2 ) )
      = ( A2 = bot_bo5083760590458426867od_a_b ) ) ).

% all_not_in_conv
thf(fact_398_all__not__in__conv,axiom,
    ! [A2: set_Product_prod_a_b] :
      ( ( ! [X4: product_prod_a_b] :
            ~ ( member1426531481828664017od_a_b @ X4 @ A2 ) )
      = ( A2 = bot_bo3428410327501040244od_a_b ) ) ).

% all_not_in_conv
thf(fact_399_all__not__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ! [X4: b] :
            ~ ( member_b @ X4 @ A2 ) )
      = ( A2 = bot_bot_set_b ) ) ).

% all_not_in_conv
thf(fact_400_all__not__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ! [X4: a] :
            ~ ( member_a @ X4 @ A2 ) )
      = ( A2 = bot_bot_set_a ) ) ).

% all_not_in_conv
thf(fact_401_all__not__in__conv,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( ! [X4: produc4558475209616630778_a_b_b] :
            ~ ( member4380921116106875537_a_b_b @ X4 @ A2 ) )
      = ( A2 = bot_bo3721250822024684356_a_b_b ) ) ).

% all_not_in_conv
thf(fact_402_all__not__in__conv,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( ! [X4: dtree_a_b] :
            ~ ( member_dtree_a_b @ X4 @ A2 ) )
      = ( A2 = bot_bo8730652382759064772ee_a_b ) ) ).

% all_not_in_conv
thf(fact_403_Collect__empty__eq,axiom,
    ! [P: produc4558475209616630778_a_b_b > $o] :
      ( ( ( collec1368399972772960719_a_b_b @ P )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X4: produc4558475209616630778_a_b_b] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_404_Collect__empty__eq,axiom,
    ! [P: dtree_a_b > $o] :
      ( ( ( collect_dtree_a_b @ P )
        = bot_bo8730652382759064772ee_a_b )
      = ( ! [X4: dtree_a_b] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_405_Collect__empty__eq,axiom,
    ! [P: b > $o] :
      ( ( ( collect_b @ P )
        = bot_bot_set_b )
      = ( ! [X4: b] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_406_Collect__empty__eq,axiom,
    ! [P: a > $o] :
      ( ( ( collect_a @ P )
        = bot_bot_set_a )
      = ( ! [X4: a] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_407_empty__Collect__eq,axiom,
    ! [P: produc4558475209616630778_a_b_b > $o] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( collec1368399972772960719_a_b_b @ P ) )
      = ( ! [X4: produc4558475209616630778_a_b_b] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_408_empty__Collect__eq,axiom,
    ! [P: dtree_a_b > $o] :
      ( ( bot_bo8730652382759064772ee_a_b
        = ( collect_dtree_a_b @ P ) )
      = ( ! [X4: dtree_a_b] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_409_empty__Collect__eq,axiom,
    ! [P: b > $o] :
      ( ( bot_bot_set_b
        = ( collect_b @ P ) )
      = ( ! [X4: b] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_410_empty__Collect__eq,axiom,
    ! [P: a > $o] :
      ( ( bot_bot_set_a
        = ( collect_a @ P ) )
      = ( ! [X4: a] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_411_dtree__from__list_Opelims,axiom,
    ! [X3: product_prod_a_b,Xa: list_P3463435030753280173od_a_b,Y: dtree_2253494508914376569od_a_b] :
      ( ( ( dtree_1864022081312108148od_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P4521695509574281141od_a_b @ dtree_4985918624134698629od_a_b @ ( produc5088573426887569692od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr906174322249854893od_a_b )
           => ( ( Y
                = ( node_P1936840572307073598od_a_b @ X3 @ bot_bo7856883933444951080od_a_b ) )
             => ~ ( accp_P4521695509574281141od_a_b @ dtree_4985918624134698629od_a_b @ ( produc5088573426887569692od_a_b @ X3 @ nil_Pr906174322249854893od_a_b ) ) ) )
         => ~ ! [V2: product_prod_a_b,E2: product_prod_a_b,Xs2: list_P3463435030753280173od_a_b] :
                ( ( Xa
                  = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_P1936840572307073598od_a_b @ X3 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ ( dtree_1864022081312108148od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) )
                 => ~ ( accp_P4521695509574281141od_a_b @ dtree_4985918624134698629od_a_b @ ( produc5088573426887569692od_a_b @ X3 @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_412_dtree__from__list_Opelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P7294506862534405595ee_a_b,Y: dtree_1861073144021109543ee_a_b] :
      ( ( ( dtree_7424119665891431146ee_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P9118761241516785037ee_a_b @ dtree_678761158524876667ee_a_b @ ( produc8306998211170319496ee_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr558572586965427547ee_a_b )
           => ( ( Y
                = ( node_d7487230363575057332ee_a_b @ X3 @ bot_bo5711572498106067156ee_a_b ) )
             => ~ ( accp_P9118761241516785037ee_a_b @ dtree_678761158524876667ee_a_b @ ( produc8306998211170319496ee_a_b @ X3 @ nil_Pr558572586965427547ee_a_b ) ) ) )
         => ~ ! [V2: dtree_a_b,E2: dtree_a_b,Xs2: list_P7294506862534405595ee_a_b] :
                ( ( Xa
                  = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_d7487230363575057332ee_a_b @ X3 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ ( dtree_7424119665891431146ee_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) )
                 => ~ ( accp_P9118761241516785037ee_a_b @ dtree_678761158524876667ee_a_b @ ( produc8306998211170319496ee_a_b @ X3 @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_413_dtree__from__list_Opelims,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa: list_P3724575226198589275ee_a_b,Y: dtree_8690448868185853351ee_a_b] :
      ( ( ( dtree_7850083854586231658ee_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P1358717780819827853ee_a_b @ dtree_8870502396945917691ee_a_b @ ( produc7996648267824065416ee_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr148742403700823003ee_a_b )
           => ( ( Y
                = ( node_P2753077162091514420ee_a_b @ X3 @ bot_bo3079078458218859348ee_a_b ) )
             => ~ ( accp_P1358717780819827853ee_a_b @ dtree_8870502396945917691ee_a_b @ ( produc7996648267824065416ee_a_b @ X3 @ nil_Pr148742403700823003ee_a_b ) ) ) )
         => ~ ! [V2: produc4558475209616630778_a_b_b,E2: dtree_a_b,Xs2: list_P3724575226198589275ee_a_b] :
                ( ( Xa
                  = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_P2753077162091514420ee_a_b @ X3 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ ( dtree_7850083854586231658ee_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) )
                 => ~ ( accp_P1358717780819827853ee_a_b @ dtree_8870502396945917691ee_a_b @ ( produc7996648267824065416ee_a_b @ X3 @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_414_dtree__from__list_Opelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P7142016109841313883_a_b_b,Y: dtree_8397784528784866983_a_b_b] :
      ( ( ( dtree_1144793476579453034_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P3938370695117152525_a_b_b @ dtree_2165212018939139067_a_b_b @ ( produc6235741833889237512_a_b_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr9079450101154612443_a_b_b )
           => ( ( Y
                = ( node_d5271158820939511604_a_b_b @ X3 @ bot_bo1493276529839087060_a_b_b ) )
             => ~ ( accp_P3938370695117152525_a_b_b @ dtree_2165212018939139067_a_b_b @ ( produc6235741833889237512_a_b_b @ X3 @ nil_Pr9079450101154612443_a_b_b ) ) ) )
         => ~ ! [V2: dtree_a_b,E2: produc4558475209616630778_a_b_b,Xs2: list_P7142016109841313883_a_b_b] :
                ( ( Xa
                  = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_d5271158820939511604_a_b_b @ X3 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ ( dtree_1144793476579453034_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) )
                 => ~ ( accp_P3938370695117152525_a_b_b @ dtree_2165212018939139067_a_b_b @ ( produc6235741833889237512_a_b_b @ X3 @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_415_dtree__from__list_Opelims,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa: list_P7924273279524553179_a_b_b,Y: dtree_6636540493345571111_a_b_b] :
      ( ( ( dtree_450453658713739498_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P883312628021968909_a_b_b @ dtree_4572921241105318779_a_b_b @ ( produc4858344343507073288_a_b_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr5872703755862520667_a_b_b )
           => ( ( Y
                = ( node_P961815112480277940_a_b_b @ X3 @ bot_bo6312180378851360852_a_b_b ) )
             => ~ ( accp_P883312628021968909_a_b_b @ dtree_4572921241105318779_a_b_b @ ( produc4858344343507073288_a_b_b @ X3 @ nil_Pr5872703755862520667_a_b_b ) ) ) )
         => ~ ! [V2: produc4558475209616630778_a_b_b,E2: produc4558475209616630778_a_b_b,Xs2: list_P7924273279524553179_a_b_b] :
                ( ( Xa
                  = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_P961815112480277940_a_b_b @ X3 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ ( dtree_450453658713739498_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) )
                 => ~ ( accp_P883312628021968909_a_b_b @ dtree_4572921241105318779_a_b_b @ ( produc4858344343507073288_a_b_b @ X3 @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_416_dtree__from__list_Opelims,axiom,
    ! [X3: dtree_a_b,Xa: list_P5360711134766023690_a_b_b,Y: dtree_dtree_a_b_b] :
      ( ( ( dtree_5255521609252960911_a_b_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P6264444294748803566_a_b_b @ dtree_7549101302527828798_a_b_b @ ( produc139389723908703645_a_b_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr5403147374433350260_a_b_b )
           => ( ( Y
                = ( node_dtree_a_b_b @ X3 @ bot_bo4737202254184417232_b_b_b ) )
             => ~ ( accp_P6264444294748803566_a_b_b @ dtree_7549101302527828798_a_b_b @ ( produc139389723908703645_a_b_b @ X3 @ nil_Pr5403147374433350260_a_b_b ) ) ) )
         => ~ ! [V2: dtree_a_b,E2: b,Xs2: list_P5360711134766023690_a_b_b] :
                ( ( Xa
                  = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_dtree_a_b_b @ X3 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ ( dtree_5255521609252960911_a_b_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) )
                 => ~ ( accp_P6264444294748803566_a_b_b @ dtree_7549101302527828798_a_b_b @ ( produc139389723908703645_a_b_b @ X3 @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_417_dtree__from__list_Opelims,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Xa: list_P8601282865932132013od_a_b,Y: dtree_5519289247442030201od_a_b] :
      ( ( ( dtree_6507962483783174260od_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P4877579601615922095od_a_b @ dtree_836713862541457285od_a_b @ ( produc971229398454786070od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr2412700377486846637od_a_b )
           => ( ( Y
                = ( node_l1136085673055119934od_a_b @ X3 @ bot_bo2863178955461725870od_a_b ) )
             => ~ ( accp_P4877579601615922095od_a_b @ dtree_836713862541457285od_a_b @ ( produc971229398454786070od_a_b @ X3 @ nil_Pr2412700377486846637od_a_b ) ) ) )
         => ~ ! [V2: list_P1467974523212632366od_a_b,E2: list_P1467974523212632366od_a_b,Xs2: list_P8601282865932132013od_a_b] :
                ( ( Xa
                  = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_l1136085673055119934od_a_b @ X3 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ ( dtree_6507962483783174260od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo2863178955461725870od_a_b ) ) )
                 => ~ ( accp_P4877579601615922095od_a_b @ dtree_836713862541457285od_a_b @ ( produc971229398454786070od_a_b @ X3 @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_418_dtree__from__list_Opelims,axiom,
    ! [X3: product_prod_a_b > product_prod_a_b > $o,Xa: list_P8094385941167427565od_a_b,Y: dtree_8339642294131873593od_a_b] :
      ( ( ( dtree_4383916385682046516od_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P8819943038680161455od_a_b @ dtree_5744449417772980677od_a_b @ ( produc8832364399110542614od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr7311172237979606381od_a_b )
           => ( ( Y
                = ( node_P5897935084763704574od_a_b @ X3 @ bot_bo137739038786217454od_a_b ) )
             => ~ ( accp_P8819943038680161455od_a_b @ dtree_5744449417772980677od_a_b @ ( produc8832364399110542614od_a_b @ X3 @ nil_Pr7311172237979606381od_a_b ) ) ) )
         => ~ ! [V2: product_prod_a_b > product_prod_a_b > $o,E2: list_P1467974523212632366od_a_b,Xs2: list_P8094385941167427565od_a_b] :
                ( ( Xa
                  = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_P5897935084763704574od_a_b @ X3 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ ( dtree_4383916385682046516od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo137739038786217454od_a_b ) ) )
                 => ~ ( accp_P8819943038680161455od_a_b @ dtree_5744449417772980677od_a_b @ ( produc8832364399110542614od_a_b @ X3 @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_419_dtree__from__list_Opelims,axiom,
    ! [X3: a,Xa: list_P5700792096213675741od_a_b,Y: dtree_8545934391348768041od_a_b] :
      ( ( ( dtree_6261964479915675172od_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P9163702700715200399od_a_b @ dtree_8739978009403896501od_a_b @ ( produc7441261679724955638od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Pr7243433834293086045od_a_b )
           => ( ( Y
                = ( node_a6325075177599301358od_a_b @ X3 @ bot_bo577854266114829310od_a_b ) )
             => ~ ( accp_P9163702700715200399od_a_b @ dtree_8739978009403896501od_a_b @ ( produc7441261679724955638od_a_b @ X3 @ nil_Pr7243433834293086045od_a_b ) ) ) )
         => ~ ! [V2: a,E2: list_P1467974523212632366od_a_b,Xs2: list_P5700792096213675741od_a_b] :
                ( ( Xa
                  = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_a6325075177599301358od_a_b @ X3 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ ( dtree_6261964479915675172od_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo577854266114829310od_a_b ) ) )
                 => ~ ( accp_P9163702700715200399od_a_b @ dtree_8739978009403896501od_a_b @ ( produc7441261679724955638od_a_b @ X3 @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_420_dtree__from__list_Opelims,axiom,
    ! [X3: a,Xa: list_P1467974523212632366od_a_b,Y: dtree_a_b] :
      ( ( ( dtree_from_list_a_b @ X3 @ Xa )
        = Y )
     => ( ( accp_P6845111368451614688od_a_b @ dtree_4965841467942179590el_a_b @ ( produc6643264353547226055od_a_b @ X3 @ Xa ) )
       => ( ( ( Xa = nil_Product_prod_a_b )
           => ( ( Y
                = ( node_a_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
             => ~ ( accp_P6845111368451614688od_a_b @ dtree_4965841467942179590el_a_b @ ( produc6643264353547226055od_a_b @ X3 @ nil_Product_prod_a_b ) ) ) )
         => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
                ( ( Xa
                  = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) )
               => ( ( Y
                    = ( node_a_b @ X3 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ ( dtree_from_list_a_b @ V2 @ Xs2 ) @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) )
                 => ~ ( accp_P6845111368451614688od_a_b @ dtree_4965841467942179590el_a_b @ ( produc6643264353547226055od_a_b @ X3 @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) ) ) ) ) ) ) ) ).

% dtree_from_list.pelims
thf(fact_421_vwalk__arcs_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ X2 @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
              ( X3
             != ( cons_l907386227682280420od_a_b @ X2 @ ( cons_l907386227682280420od_a_b @ Y3 @ Xs2 ) ) ) ) ) ).

% vwalk_arcs.cases
thf(fact_422_vwalk__arcs_Ocases,axiom,
    ! [X3: list_P3463435030753280173od_a_b] :
      ( ( X3 != nil_Pr906174322249854893od_a_b )
     => ( ! [X2: produc2233330766403592615od_a_b] :
            ( X3
           != ( cons_P8222935586017696605od_a_b @ X2 @ nil_Pr906174322249854893od_a_b ) )
       => ~ ! [X2: produc2233330766403592615od_a_b,Y3: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b] :
              ( X3
             != ( cons_P8222935586017696605od_a_b @ X2 @ ( cons_P8222935586017696605od_a_b @ Y3 @ Xs2 ) ) ) ) ) ).

% vwalk_arcs.cases
thf(fact_423_vwalk__arcs_Ocases,axiom,
    ! [X3: list_dtree_a_b] :
      ( ( X3 != nil_dtree_a_b )
     => ( ! [X2: dtree_a_b] :
            ( X3
           != ( cons_dtree_a_b @ X2 @ nil_dtree_a_b ) )
       => ~ ! [X2: dtree_a_b,Y3: dtree_a_b,Xs2: list_dtree_a_b] :
              ( X3
             != ( cons_dtree_a_b @ X2 @ ( cons_dtree_a_b @ Y3 @ Xs2 ) ) ) ) ) ).

% vwalk_arcs.cases
thf(fact_424_vwalk__arcs_Ocases,axiom,
    ! [X3: list_P5360711134766023690_a_b_b] :
      ( ( X3 != nil_Pr5403147374433350260_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b] :
            ( X3
           != ( cons_P2785074014425598660_a_b_b @ X2 @ nil_Pr5403147374433350260_a_b_b ) )
       => ~ ! [X2: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b] :
              ( X3
             != ( cons_P2785074014425598660_a_b_b @ X2 @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Xs2 ) ) ) ) ) ).

% vwalk_arcs.cases
thf(fact_425_vwalk__arcs_Ocases,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( X3 != nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b] :
            ( X3
           != ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) )
       => ~ ! [X2: product_prod_a_b,Y3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
              ( X3
             != ( cons_P7316939131009794654od_a_b @ X2 @ ( cons_P7316939131009794654od_a_b @ Y3 @ Xs2 ) ) ) ) ) ).

% vwalk_arcs.cases
thf(fact_426_vwalk__to__vpath_Ocases,axiom,
    ! [X3: list_l8778361445553822004od_a_b] :
      ( ( X3 != nil_li8635777946366267444od_a_b )
     => ~ ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
            ( X3
           != ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) ) ) ).

% vwalk_to_vpath.cases
thf(fact_427_vwalk__to__vpath_Ocases,axiom,
    ! [X3: list_P3463435030753280173od_a_b] :
      ( ( X3 != nil_Pr906174322249854893od_a_b )
     => ~ ! [X2: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b] :
            ( X3
           != ( cons_P8222935586017696605od_a_b @ X2 @ Xs2 ) ) ) ).

% vwalk_to_vpath.cases
thf(fact_428_vwalk__to__vpath_Ocases,axiom,
    ! [X3: list_dtree_a_b] :
      ( ( X3 != nil_dtree_a_b )
     => ~ ! [X2: dtree_a_b,Xs2: list_dtree_a_b] :
            ( X3
           != ( cons_dtree_a_b @ X2 @ Xs2 ) ) ) ).

% vwalk_to_vpath.cases
thf(fact_429_vwalk__to__vpath_Ocases,axiom,
    ! [X3: list_P5360711134766023690_a_b_b] :
      ( ( X3 != nil_Pr5403147374433350260_a_b_b )
     => ~ ! [X2: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( cons_P2785074014425598660_a_b_b @ X2 @ Xs2 ) ) ) ).

% vwalk_to_vpath.cases
thf(fact_430_vwalk__to__vpath_Ocases,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( X3 != nil_Product_prod_a_b )
     => ~ ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
            ( X3
           != ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) ) ) ).

% vwalk_to_vpath.cases
thf(fact_431_list__exhaust2,axiom,
    ! [Y: list_P1467974523212632366od_a_b,Ya: list_P1467974523212632366od_a_b] :
      ( ( ( Y = nil_Product_prod_a_b )
       => ( Ya != nil_Product_prod_a_b ) )
     => ( ( ( Y = nil_Product_prod_a_b )
         => ! [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
              ( Ya
             != ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                ( Y
                = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_Product_prod_a_b ) )
         => ~ ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                  ( Y
                  = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
             => ! [X21a: product_prod_a_b,X22a: list_P1467974523212632366od_a_b] :
                  ( Ya
                 != ( cons_P7316939131009794654od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_432_list__exhaust2,axiom,
    ! [Y: list_dtree_a_b,Ya: list_P1467974523212632366od_a_b] :
      ( ( ( Y = nil_dtree_a_b )
       => ( Ya != nil_Product_prod_a_b ) )
     => ( ( ( Y = nil_dtree_a_b )
         => ! [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
              ( Ya
             != ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                ( Y
                = ( cons_dtree_a_b @ X212 @ X223 ) )
           => ( Ya != nil_Product_prod_a_b ) )
         => ~ ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                  ( Y
                  = ( cons_dtree_a_b @ X212 @ X223 ) )
             => ! [X21a: product_prod_a_b,X22a: list_P1467974523212632366od_a_b] :
                  ( Ya
                 != ( cons_P7316939131009794654od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_433_list__exhaust2,axiom,
    ! [Y: list_P1467974523212632366od_a_b,Ya: list_dtree_a_b] :
      ( ( ( Y = nil_Product_prod_a_b )
       => ( Ya != nil_dtree_a_b ) )
     => ( ( ( Y = nil_Product_prod_a_b )
         => ! [X212: dtree_a_b,X223: list_dtree_a_b] :
              ( Ya
             != ( cons_dtree_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                ( Y
                = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_dtree_a_b ) )
         => ~ ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                  ( Y
                  = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
             => ! [X21a: dtree_a_b,X22a: list_dtree_a_b] :
                  ( Ya
                 != ( cons_dtree_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_434_list__exhaust2,axiom,
    ! [Y: list_dtree_a_b,Ya: list_dtree_a_b] :
      ( ( ( Y = nil_dtree_a_b )
       => ( Ya != nil_dtree_a_b ) )
     => ( ( ( Y = nil_dtree_a_b )
         => ! [X212: dtree_a_b,X223: list_dtree_a_b] :
              ( Ya
             != ( cons_dtree_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                ( Y
                = ( cons_dtree_a_b @ X212 @ X223 ) )
           => ( Ya != nil_dtree_a_b ) )
         => ~ ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                  ( Y
                  = ( cons_dtree_a_b @ X212 @ X223 ) )
             => ! [X21a: dtree_a_b,X22a: list_dtree_a_b] :
                  ( Ya
                 != ( cons_dtree_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_435_list__exhaust2,axiom,
    ! [Y: list_l8778361445553822004od_a_b,Ya: list_P1467974523212632366od_a_b] :
      ( ( ( Y = nil_li8635777946366267444od_a_b )
       => ( Ya != nil_Product_prod_a_b ) )
     => ( ( ( Y = nil_li8635777946366267444od_a_b )
         => ! [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
              ( Ya
             != ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                ( Y
                = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_Product_prod_a_b ) )
         => ~ ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                  ( Y
                  = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
             => ! [X21a: product_prod_a_b,X22a: list_P1467974523212632366od_a_b] :
                  ( Ya
                 != ( cons_P7316939131009794654od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_436_list__exhaust2,axiom,
    ! [Y: list_P1467974523212632366od_a_b,Ya: list_l8778361445553822004od_a_b] :
      ( ( ( Y = nil_Product_prod_a_b )
       => ( Ya != nil_li8635777946366267444od_a_b ) )
     => ( ( ( Y = nil_Product_prod_a_b )
         => ! [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
              ( Ya
             != ( cons_l907386227682280420od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                ( Y
                = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_li8635777946366267444od_a_b ) )
         => ~ ( ? [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
                  ( Y
                  = ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) )
             => ! [X21a: list_P1467974523212632366od_a_b,X22a: list_l8778361445553822004od_a_b] :
                  ( Ya
                 != ( cons_l907386227682280420od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_437_list__exhaust2,axiom,
    ! [Y: list_dtree_a_b,Ya: list_l8778361445553822004od_a_b] :
      ( ( ( Y = nil_dtree_a_b )
       => ( Ya != nil_li8635777946366267444od_a_b ) )
     => ( ( ( Y = nil_dtree_a_b )
         => ! [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
              ( Ya
             != ( cons_l907386227682280420od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                ( Y
                = ( cons_dtree_a_b @ X212 @ X223 ) )
           => ( Ya != nil_li8635777946366267444od_a_b ) )
         => ~ ( ? [X212: dtree_a_b,X223: list_dtree_a_b] :
                  ( Y
                  = ( cons_dtree_a_b @ X212 @ X223 ) )
             => ! [X21a: list_P1467974523212632366od_a_b,X22a: list_l8778361445553822004od_a_b] :
                  ( Ya
                 != ( cons_l907386227682280420od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_438_list__exhaust2,axiom,
    ! [Y: list_l8778361445553822004od_a_b,Ya: list_dtree_a_b] :
      ( ( ( Y = nil_li8635777946366267444od_a_b )
       => ( Ya != nil_dtree_a_b ) )
     => ( ( ( Y = nil_li8635777946366267444od_a_b )
         => ! [X212: dtree_a_b,X223: list_dtree_a_b] :
              ( Ya
             != ( cons_dtree_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                ( Y
                = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_dtree_a_b ) )
         => ~ ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                  ( Y
                  = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
             => ! [X21a: dtree_a_b,X22a: list_dtree_a_b] :
                  ( Ya
                 != ( cons_dtree_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_439_list__exhaust2,axiom,
    ! [Y: list_P5360711134766023690_a_b_b,Ya: list_P1467974523212632366od_a_b] :
      ( ( ( Y = nil_Pr5403147374433350260_a_b_b )
       => ( Ya != nil_Product_prod_a_b ) )
     => ( ( ( Y = nil_Pr5403147374433350260_a_b_b )
         => ! [X212: product_prod_a_b,X223: list_P1467974523212632366od_a_b] :
              ( Ya
             != ( cons_P7316939131009794654od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: produc4558475209616630778_a_b_b,X223: list_P5360711134766023690_a_b_b] :
                ( Y
                = ( cons_P2785074014425598660_a_b_b @ X212 @ X223 ) )
           => ( Ya != nil_Product_prod_a_b ) )
         => ~ ( ? [X212: produc4558475209616630778_a_b_b,X223: list_P5360711134766023690_a_b_b] :
                  ( Y
                  = ( cons_P2785074014425598660_a_b_b @ X212 @ X223 ) )
             => ! [X21a: product_prod_a_b,X22a: list_P1467974523212632366od_a_b] :
                  ( Ya
                 != ( cons_P7316939131009794654od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_440_list__exhaust2,axiom,
    ! [Y: list_l8778361445553822004od_a_b,Ya: list_l8778361445553822004od_a_b] :
      ( ( ( Y = nil_li8635777946366267444od_a_b )
       => ( Ya != nil_li8635777946366267444od_a_b ) )
     => ( ( ( Y = nil_li8635777946366267444od_a_b )
         => ! [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
              ( Ya
             != ( cons_l907386227682280420od_a_b @ X212 @ X223 ) ) )
       => ( ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                ( Y
                = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
           => ( Ya != nil_li8635777946366267444od_a_b ) )
         => ~ ( ? [X212: list_P1467974523212632366od_a_b,X223: list_l8778361445553822004od_a_b] :
                  ( Y
                  = ( cons_l907386227682280420od_a_b @ X212 @ X223 ) )
             => ! [X21a: list_P1467974523212632366od_a_b,X22a: list_l8778361445553822004od_a_b] :
                  ( Ya
                 != ( cons_l907386227682280420od_a_b @ X21a @ X22a ) ) ) ) ) ) ).

% list_exhaust2
thf(fact_441_bot__set__def,axiom,
    ( bot_bo3721250822024684356_a_b_b
    = ( collec1368399972772960719_a_b_b @ bot_bo7321339186913516097_b_b_o ) ) ).

% bot_set_def
thf(fact_442_bot__set__def,axiom,
    ( bot_bo8730652382759064772ee_a_b
    = ( collect_dtree_a_b @ bot_bot_dtree_a_b_o ) ) ).

% bot_set_def
thf(fact_443_bot__set__def,axiom,
    ( bot_bot_set_b
    = ( collect_b @ bot_bot_b_o ) ) ).

% bot_set_def
thf(fact_444_bot__set__def,axiom,
    ( bot_bot_set_a
    = ( collect_a @ bot_bot_a_o ) ) ).

% bot_set_def
thf(fact_445_ex__in__conv,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b] :
      ( ( ? [X4: produc5177672665255943253ee_a_b] : ( member2060280516343777534ee_a_b @ X4 @ A2 ) )
      = ( A2 != bot_bo6208222296400721441ee_a_b ) ) ).

% ex_in_conv
thf(fact_446_ex__in__conv,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b] :
      ( ( ? [X4: produc7397007428618769063od_a_b] : ( member3051990972100052432od_a_b @ X4 @ A2 ) )
      = ( A2 != bot_bo5083760590458426867od_a_b ) ) ).

% ex_in_conv
thf(fact_447_ex__in__conv,axiom,
    ! [A2: set_Product_prod_a_b] :
      ( ( ? [X4: product_prod_a_b] : ( member1426531481828664017od_a_b @ X4 @ A2 ) )
      = ( A2 != bot_bo3428410327501040244od_a_b ) ) ).

% ex_in_conv
thf(fact_448_ex__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ? [X4: b] : ( member_b @ X4 @ A2 ) )
      = ( A2 != bot_bot_set_b ) ) ).

% ex_in_conv
thf(fact_449_ex__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ? [X4: a] : ( member_a @ X4 @ A2 ) )
      = ( A2 != bot_bot_set_a ) ) ).

% ex_in_conv
thf(fact_450_ex__in__conv,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( ? [X4: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X4 @ A2 ) )
      = ( A2 != bot_bo3721250822024684356_a_b_b ) ) ).

% ex_in_conv
thf(fact_451_ex__in__conv,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( ? [X4: dtree_a_b] : ( member_dtree_a_b @ X4 @ A2 ) )
      = ( A2 != bot_bo8730652382759064772ee_a_b ) ) ).

% ex_in_conv
thf(fact_452_equals0I,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b] :
      ( ! [Y3: produc5177672665255943253ee_a_b] :
          ~ ( member2060280516343777534ee_a_b @ Y3 @ A2 )
     => ( A2 = bot_bo6208222296400721441ee_a_b ) ) ).

% equals0I
thf(fact_453_equals0I,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b] :
      ( ! [Y3: produc7397007428618769063od_a_b] :
          ~ ( member3051990972100052432od_a_b @ Y3 @ A2 )
     => ( A2 = bot_bo5083760590458426867od_a_b ) ) ).

% equals0I
thf(fact_454_equals0I,axiom,
    ! [A2: set_Product_prod_a_b] :
      ( ! [Y3: product_prod_a_b] :
          ~ ( member1426531481828664017od_a_b @ Y3 @ A2 )
     => ( A2 = bot_bo3428410327501040244od_a_b ) ) ).

% equals0I
thf(fact_455_equals0I,axiom,
    ! [A2: set_b] :
      ( ! [Y3: b] :
          ~ ( member_b @ Y3 @ A2 )
     => ( A2 = bot_bot_set_b ) ) ).

% equals0I
thf(fact_456_equals0I,axiom,
    ! [A2: set_a] :
      ( ! [Y3: a] :
          ~ ( member_a @ Y3 @ A2 )
     => ( A2 = bot_bot_set_a ) ) ).

% equals0I
thf(fact_457_equals0I,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ! [Y3: produc4558475209616630778_a_b_b] :
          ~ ( member4380921116106875537_a_b_b @ Y3 @ A2 )
     => ( A2 = bot_bo3721250822024684356_a_b_b ) ) ).

% equals0I
thf(fact_458_equals0I,axiom,
    ! [A2: set_dtree_a_b] :
      ( ! [Y3: dtree_a_b] :
          ~ ( member_dtree_a_b @ Y3 @ A2 )
     => ( A2 = bot_bo8730652382759064772ee_a_b ) ) ).

% equals0I
thf(fact_459_equals0D,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b,A: produc5177672665255943253ee_a_b] :
      ( ( A2 = bot_bo6208222296400721441ee_a_b )
     => ~ ( member2060280516343777534ee_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_460_equals0D,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b,A: produc7397007428618769063od_a_b] :
      ( ( A2 = bot_bo5083760590458426867od_a_b )
     => ~ ( member3051990972100052432od_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_461_equals0D,axiom,
    ! [A2: set_Product_prod_a_b,A: product_prod_a_b] :
      ( ( A2 = bot_bo3428410327501040244od_a_b )
     => ~ ( member1426531481828664017od_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_462_equals0D,axiom,
    ! [A2: set_b,A: b] :
      ( ( A2 = bot_bot_set_b )
     => ~ ( member_b @ A @ A2 ) ) ).

% equals0D
thf(fact_463_equals0D,axiom,
    ! [A2: set_a,A: a] :
      ( ( A2 = bot_bot_set_a )
     => ~ ( member_a @ A @ A2 ) ) ).

% equals0D
thf(fact_464_equals0D,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( A2 = bot_bo3721250822024684356_a_b_b )
     => ~ ( member4380921116106875537_a_b_b @ A @ A2 ) ) ).

% equals0D
thf(fact_465_equals0D,axiom,
    ! [A2: set_dtree_a_b,A: dtree_a_b] :
      ( ( A2 = bot_bo8730652382759064772ee_a_b )
     => ~ ( member_dtree_a_b @ A @ A2 ) ) ).

% equals0D
thf(fact_466_emptyE,axiom,
    ! [A: produc5177672665255943253ee_a_b] :
      ~ ( member2060280516343777534ee_a_b @ A @ bot_bo6208222296400721441ee_a_b ) ).

% emptyE
thf(fact_467_emptyE,axiom,
    ! [A: produc7397007428618769063od_a_b] :
      ~ ( member3051990972100052432od_a_b @ A @ bot_bo5083760590458426867od_a_b ) ).

% emptyE
thf(fact_468_emptyE,axiom,
    ! [A: product_prod_a_b] :
      ~ ( member1426531481828664017od_a_b @ A @ bot_bo3428410327501040244od_a_b ) ).

% emptyE
thf(fact_469_emptyE,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ) ).

% emptyE
thf(fact_470_emptyE,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ) ).

% emptyE
thf(fact_471_emptyE,axiom,
    ! [A: produc4558475209616630778_a_b_b] :
      ~ ( member4380921116106875537_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ).

% emptyE
thf(fact_472_emptyE,axiom,
    ! [A: dtree_a_b] :
      ~ ( member_dtree_a_b @ A @ bot_bo8730652382759064772ee_a_b ) ).

% emptyE
thf(fact_473_list__exhaust__NSC,axiom,
    ! [Xs: list_l8778361445553822004od_a_b] :
      ( ( Xs != nil_li8635777946366267444od_a_b )
     => ( ! [X2: list_P1467974523212632366od_a_b] :
            ( Xs
           != ( cons_l907386227682280420od_a_b @ X2 @ nil_li8635777946366267444od_a_b ) )
       => ~ ! [X2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Ys3: list_l8778361445553822004od_a_b] :
              ( Xs
             != ( cons_l907386227682280420od_a_b @ X2 @ ( cons_l907386227682280420od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% list_exhaust_NSC
thf(fact_474_list__exhaust__NSC,axiom,
    ! [Xs: list_P3463435030753280173od_a_b] :
      ( ( Xs != nil_Pr906174322249854893od_a_b )
     => ( ! [X2: produc2233330766403592615od_a_b] :
            ( Xs
           != ( cons_P8222935586017696605od_a_b @ X2 @ nil_Pr906174322249854893od_a_b ) )
       => ~ ! [X2: produc2233330766403592615od_a_b,Y3: produc2233330766403592615od_a_b,Ys3: list_P3463435030753280173od_a_b] :
              ( Xs
             != ( cons_P8222935586017696605od_a_b @ X2 @ ( cons_P8222935586017696605od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% list_exhaust_NSC
thf(fact_475_list__exhaust__NSC,axiom,
    ! [Xs: list_dtree_a_b] :
      ( ( Xs != nil_dtree_a_b )
     => ( ! [X2: dtree_a_b] :
            ( Xs
           != ( cons_dtree_a_b @ X2 @ nil_dtree_a_b ) )
       => ~ ! [X2: dtree_a_b,Y3: dtree_a_b,Ys3: list_dtree_a_b] :
              ( Xs
             != ( cons_dtree_a_b @ X2 @ ( cons_dtree_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% list_exhaust_NSC
thf(fact_476_list__exhaust__NSC,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b] :
      ( ( Xs != nil_Pr5403147374433350260_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b] :
            ( Xs
           != ( cons_P2785074014425598660_a_b_b @ X2 @ nil_Pr5403147374433350260_a_b_b ) )
       => ~ ! [X2: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,Ys3: list_P5360711134766023690_a_b_b] :
              ( Xs
             != ( cons_P2785074014425598660_a_b_b @ X2 @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Ys3 ) ) ) ) ) ).

% list_exhaust_NSC
thf(fact_477_list__exhaust__NSC,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b] :
            ( Xs
           != ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) )
       => ~ ! [X2: product_prod_a_b,Y3: product_prod_a_b,Ys3: list_P1467974523212632366od_a_b] :
              ( Xs
             != ( cons_P7316939131009794654od_a_b @ X2 @ ( cons_P7316939131009794654od_a_b @ Y3 @ Ys3 ) ) ) ) ) ).

% list_exhaust_NSC
thf(fact_478_subset__eq__mset__impl_Ocases,axiom,
    ! [X3: produc1688629678973589927od_a_b] :
      ( ! [Ys3: list_l8778361445553822004od_a_b] :
          ( X3
         != ( produc3466467997744452247od_a_b @ nil_li8635777946366267444od_a_b @ Ys3 ) )
     => ~ ! [X2: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b,Ys3: list_l8778361445553822004od_a_b] :
            ( X3
           != ( produc3466467997744452247od_a_b @ ( cons_l907386227682280420od_a_b @ X2 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_479_subset__eq__mset__impl_Ocases,axiom,
    ! [X3: produc1627906242116850535od_a_b] :
      ( ! [Ys3: list_P3463435030753280173od_a_b] :
          ( X3
         != ( produc3836617586516638167od_a_b @ nil_Pr906174322249854893od_a_b @ Ys3 ) )
     => ~ ! [X2: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b,Ys3: list_P3463435030753280173od_a_b] :
            ( X3
           != ( produc3836617586516638167od_a_b @ ( cons_P8222935586017696605od_a_b @ X2 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_480_subset__eq__mset__impl_Ocases,axiom,
    ! [X3: produc5339155667539881461ee_a_b] :
      ( ! [Ys3: list_dtree_a_b] :
          ( X3
         != ( produc6019849452775264557ee_a_b @ nil_dtree_a_b @ Ys3 ) )
     => ~ ! [X2: dtree_a_b,Xs2: list_dtree_a_b,Ys3: list_dtree_a_b] :
            ( X3
           != ( produc6019849452775264557ee_a_b @ ( cons_dtree_a_b @ X2 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_481_subset__eq__mset__impl_Ocases,axiom,
    ! [X3: produc6081131995383004661_a_b_b] :
      ( ! [Ys3: list_P5360711134766023690_a_b_b] :
          ( X3
         != ( produc4608802955787333421_a_b_b @ nil_Pr5403147374433350260_a_b_b @ Ys3 ) )
     => ~ ! [X2: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b,Ys3: list_P5360711134766023690_a_b_b] :
            ( X3
           != ( produc4608802955787333421_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X2 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_482_subset__eq__mset__impl_Ocases,axiom,
    ! [X3: produc7397007428618769063od_a_b] :
      ( ! [Ys3: list_P1467974523212632366od_a_b] :
          ( X3
         != ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Ys3 ) )
     => ~ ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b,Ys3: list_P1467974523212632366od_a_b] :
            ( X3
           != ( produc5288560138351607191od_a_b @ ( cons_P7316939131009794654od_a_b @ X2 @ Xs2 ) @ Ys3 ) ) ) ).

% subset_eq_mset_impl.cases
thf(fact_483_disjoint__dverts__if__wf__aux,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,T1: dtree_8690448868185853351ee_a_b,E1: dtree_a_b,T22: dtree_8690448868185853351ee_a_b,E22: dtree_a_b] :
      ( ( wf_dve8044060998984177273ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
     => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ T1 @ E1 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
       => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ T22 @ E22 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
         => ( ( ( produc8867760425442229946ee_a_b @ T1 @ E1 )
             != ( produc8867760425442229946ee_a_b @ T22 @ E22 ) )
           => ( ( inf_in6138156342456174402_a_b_b @ ( dverts2972317704043987696ee_a_b @ T1 ) @ ( dverts2972317704043987696ee_a_b @ T22 ) )
              = bot_bo3721250822024684356_a_b_b ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_484_disjoint__dverts__if__wf__aux,axiom,
    ! [R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,T1: dtree_6636540493345571111_a_b_b,E1: produc4558475209616630778_a_b_b,T22: dtree_6636540493345571111_a_b_b,E22: produc4558475209616630778_a_b_b] :
      ( ( wf_dve6839618634935551225_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
     => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ T1 @ E1 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
       => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ T22 @ E22 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
         => ( ( ( produc6281861845666676666_a_b_b @ T1 @ E1 )
             != ( produc6281861845666676666_a_b_b @ T22 @ E22 ) )
           => ( ( inf_in6138156342456174402_a_b_b @ ( dverts1640268204329280112_a_b_b @ T1 ) @ ( dverts1640268204329280112_a_b_b @ T22 ) )
              = bot_bo3721250822024684356_a_b_b ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_485_disjoint__dverts__if__wf__aux,axiom,
    ! [R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,T1: dtree_1861073144021109543ee_a_b,E1: dtree_a_b,T22: dtree_1861073144021109543ee_a_b,E22: dtree_a_b] :
      ( ( wf_dve9201916681887519993ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
     => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ T1 @ E1 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
       => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ T22 @ E22 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
         => ( ( ( produc2775200505768408122ee_a_b @ T1 @ E1 )
             != ( produc2775200505768408122ee_a_b @ T22 @ E22 ) )
           => ( ( inf_in5903708963019302594ee_a_b @ ( dverts2436977245124431984ee_a_b @ T1 ) @ ( dverts2436977245124431984ee_a_b @ T22 ) )
              = bot_bo8730652382759064772ee_a_b ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_486_disjoint__dverts__if__wf__aux,axiom,
    ! [R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,T1: dtree_8397784528784866983_a_b_b,E1: produc4558475209616630778_a_b_b,T22: dtree_8397784528784866983_a_b_b,E22: produc4558475209616630778_a_b_b] :
      ( ( wf_dve1338770620977398649_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
     => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ T1 @ E1 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
       => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ T22 @ E22 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
         => ( ( ( produc74755587182097722_a_b_b @ T1 @ E1 )
             != ( produc74755587182097722_a_b_b @ T22 @ E22 ) )
           => ( ( inf_in5903708963019302594ee_a_b @ ( dverts5490399362891984880_a_b_b @ T1 ) @ ( dverts5490399362891984880_a_b_b @ T22 ) )
              = bot_bo8730652382759064772ee_a_b ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_487_disjoint__dverts__if__wf__aux,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T22: dtree_a_b,E22: b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T22 @ E22 ) )
           => ( ( inf_inf_set_a @ ( dverts_a_b @ T1 ) @ ( dverts_a_b @ T22 ) )
              = bot_bot_set_a ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_488_product__lists_Osimps_I1_J,axiom,
    ( ( produc4369083959415664285od_a_b @ nil_li2802039260981550394od_a_b )
    = ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ nil_li2802039260981550394od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_489_product__lists_Osimps_I1_J,axiom,
    ( ( produc3864309093259441302od_a_b @ nil_li9150416971034547123od_a_b )
    = ( cons_l5043155473145997155od_a_b @ nil_Pr906174322249854893od_a_b @ nil_li9150416971034547123od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_490_product__lists_Osimps_I1_J,axiom,
    ( ( produc5544102775981650891ee_a_b @ nil_list_dtree_a_b )
    = ( cons_list_dtree_a_b @ nil_dtree_a_b @ nil_list_dtree_a_b ) ) ).

% product_lists.simps(1)
thf(fact_491_product__lists_Osimps_I1_J,axiom,
    ( ( produc8247723432148779083_a_b_b @ nil_li143336474603867524_a_b_b )
    = ( cons_l8517938233221414356_a_b_b @ nil_Pr5403147374433350260_a_b_b @ nil_li143336474603867524_a_b_b ) ) ).

% product_lists.simps(1)
thf(fact_492_product__lists_Osimps_I1_J,axiom,
    ( ( produc5891818806577749399od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% product_lists.simps(1)
thf(fact_493_single__subtree__child__root__dverts,axiom,
    ! [V22: dtree_a_b,T22: dtree_1861073144021109543ee_a_b,E22: dtree_a_b,T1: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ ( node_d7487230363575057332ee_a_b @ V22 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T22 @ E22 ) @ bot_bo5711572498106067156ee_a_b ) ) @ T1 )
     => ( member_dtree_a_b @ ( root_d1746759089207908692ee_a_b @ T22 ) @ ( dverts2436977245124431984ee_a_b @ T1 ) ) ) ).

% single_subtree_child_root_dverts
thf(fact_494_single__subtree__child__root__dverts,axiom,
    ! [V22: produc4558475209616630778_a_b_b,T22: dtree_8690448868185853351ee_a_b,E22: dtree_a_b,T1: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ ( node_P2753077162091514420ee_a_b @ V22 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T22 @ E22 ) @ bot_bo3079078458218859348ee_a_b ) ) @ T1 )
     => ( member4380921116106875537_a_b_b @ ( root_P5553465985260390356ee_a_b @ T22 ) @ ( dverts2972317704043987696ee_a_b @ T1 ) ) ) ).

% single_subtree_child_root_dverts
thf(fact_495_single__subtree__child__root__dverts,axiom,
    ! [V22: dtree_a_b,T22: dtree_8397784528784866983_a_b_b,E22: produc4558475209616630778_a_b_b,T1: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ ( node_d5271158820939511604_a_b_b @ V22 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T22 @ E22 ) @ bot_bo1493276529839087060_a_b_b ) ) @ T1 )
     => ( member_dtree_a_b @ ( root_d8071547644108387540_a_b_b @ T22 ) @ ( dverts5490399362891984880_a_b_b @ T1 ) ) ) ).

% single_subtree_child_root_dverts
thf(fact_496_single__subtree__child__root__dverts,axiom,
    ! [V22: produc4558475209616630778_a_b_b,T22: dtree_6636540493345571111_a_b_b,E22: produc4558475209616630778_a_b_b,T1: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ ( node_P961815112480277940_a_b_b @ V22 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T22 @ E22 ) @ bot_bo6312180378851360852_a_b_b ) ) @ T1 )
     => ( member4380921116106875537_a_b_b @ ( root_P204151722342556500_a_b_b @ T22 ) @ ( dverts1640268204329280112_a_b_b @ T1 ) ) ) ).

% single_subtree_child_root_dverts
thf(fact_497_single__subtree__child__root__dverts,axiom,
    ! [V22: a,T22: dtree_a_b,E22: b,T1: dtree_a_b] :
      ( ( is_subtree_a_b @ ( node_a_b @ V22 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ bot_bo2895716411488905534_a_b_b ) ) @ T1 )
     => ( member_a @ ( root_a_b @ T22 ) @ ( dverts_a_b @ T1 ) ) ) ).

% single_subtree_child_root_dverts
thf(fact_498_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_2253494508914376569od_a_b,Y: list_P3463435030753280173od_a_b] :
      ( ( ( dtree_983605638134528549od_a_b @ X3 )
        = Y )
     => ( ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ X3 )
       => ( ! [R2: product_prod_a_b,T2: dtree_2253494508914376569od_a_b,E2: product_prod_a_b] :
              ( ( X3
                = ( node_P1936840572307073598od_a_b @ R2 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T2 @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) )
             => ( ( Y
                  = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T2 ) @ E2 ) @ ( dtree_983605638134528549od_a_b @ T2 ) ) )
               => ~ ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R2 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T2 @ E2 ) @ bot_bo7856883933444951080od_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P6924693328471822228od_a_b,R2: product_prod_a_b] :
                ( ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc2878020351943352036od_a_b] :
                      ( Xs2
                     != ( finser5347476252697843100od_a_b @ X @ bot_bo7856883933444951080od_a_b ) )
                 => ( ( X3
                      = ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) )
                   => ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P6924693328471822228od_a_b] :
                  ( ! [X: produc2878020351943352036od_a_b] :
                      ( Xs2
                     != ( finser5347476252697843100od_a_b @ X @ bot_bo7856883933444951080od_a_b ) )
                 => ! [R2: product_prod_a_b] :
                      ( ( X3
                        = ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr906174322249854893od_a_b )
                       => ~ ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_499_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_1861073144021109543ee_a_b,Y: list_P7294506862534405595ee_a_b] :
      ( ( ( dtree_5459410236902894363ee_a_b @ X3 )
        = Y )
     => ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ X3 )
       => ( ! [R2: dtree_a_b,T2: dtree_1861073144021109543ee_a_b,E2: dtree_a_b] :
              ( ( X3
                = ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) )
             => ( ( Y
                  = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T2 ) @ E2 ) @ ( dtree_5459410236902894363ee_a_b @ T2 ) ) )
               => ~ ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P5991447722532490344ee_a_b,R2: dtree_a_b] :
                ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc6260003399586931330ee_a_b] :
                      ( Xs2
                     != ( finser8516331313445392842ee_a_b @ X @ bot_bo5711572498106067156ee_a_b ) )
                 => ( ( X3
                      = ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) )
                   => ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P5991447722532490344ee_a_b] :
                  ( ! [X: produc6260003399586931330ee_a_b] :
                      ( Xs2
                     != ( finser8516331313445392842ee_a_b @ X @ bot_bo5711572498106067156ee_a_b ) )
                 => ! [R2: dtree_a_b] :
                      ( ( X3
                        = ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr558572586965427547ee_a_b )
                       => ~ ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_500_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_8690448868185853351ee_a_b,Y: list_P3724575226198589275ee_a_b] :
      ( ( ( dtree_9187971570250218139ee_a_b @ X3 )
        = Y )
     => ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ X3 )
       => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_8690448868185853351ee_a_b,E2: dtree_a_b] :
              ( ( X3
                = ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) )
             => ( ( Y
                  = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T2 ) @ E2 ) @ ( dtree_9187971570250218139ee_a_b @ T2 ) ) )
               => ~ ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P1087233464713034472ee_a_b,R2: produc4558475209616630778_a_b_b] :
                ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc1961764714219340802ee_a_b] :
                      ( Xs2
                     != ( finser7847761039489690442ee_a_b @ X @ bot_bo3079078458218859348ee_a_b ) )
                 => ( ( X3
                      = ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) )
                   => ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P1087233464713034472ee_a_b] :
                  ( ! [X: produc1961764714219340802ee_a_b] :
                      ( Xs2
                     != ( finser7847761039489690442ee_a_b @ X @ bot_bo3079078458218859348ee_a_b ) )
                 => ! [R2: produc4558475209616630778_a_b_b] :
                      ( ( X3
                        = ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr148742403700823003ee_a_b )
                       => ~ ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_501_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_8397784528784866983_a_b_b,Y: list_P7142016109841313883_a_b_b] :
      ( ( ( dtree_2482681192243439515_a_b_b @ X3 )
        = Y )
     => ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ X3 )
       => ( ! [R2: dtree_a_b,T2: dtree_8397784528784866983_a_b_b,E2: produc4558475209616630778_a_b_b] :
              ( ( X3
                = ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) )
             => ( ( Y
                  = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T2 ) @ E2 ) @ ( dtree_2482681192243439515_a_b_b @ T2 ) ) )
               => ~ ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) ) ) )
         => ( ! [Xs2: fset_P8532786667068971368_a_b_b,R2: dtree_a_b] :
                ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) )
               => ( ! [X: produc4081214457754080642_a_b_b] :
                      ( Xs2
                     != ( finser5778094437704840394_a_b_b @ X @ bot_bo1493276529839087060_a_b_b ) )
                 => ( ( X3
                      = ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) )
                   => ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P8532786667068971368_a_b_b] :
                  ( ! [X: produc4081214457754080642_a_b_b] :
                      ( Xs2
                     != ( finser5778094437704840394_a_b_b @ X @ bot_bo1493276529839087060_a_b_b ) )
                 => ! [R2: dtree_a_b] :
                      ( ( X3
                        = ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr9079450101154612443_a_b_b )
                       => ~ ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_502_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_6636540493345571111_a_b_b,Y: list_P7924273279524553179_a_b_b] :
      ( ( ( dtree_1768895223656068891_a_b_b @ X3 )
        = Y )
     => ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ X3 )
       => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_6636540493345571111_a_b_b,E2: produc4558475209616630778_a_b_b] :
              ( ( X3
                = ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) )
             => ( ( Y
                  = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T2 ) @ E2 ) @ ( dtree_1768895223656068891_a_b_b @ T2 ) ) )
               => ~ ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) ) ) )
         => ( ! [Xs2: fset_P271555816861255656_a_b_b,R2: produc4558475209616630778_a_b_b] :
                ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) )
               => ( ! [X: produc8137180380982048514_a_b_b] :
                      ( Xs2
                     != ( finser3407669804807474762_a_b_b @ X @ bot_bo6312180378851360852_a_b_b ) )
                 => ( ( X3
                      = ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) )
                   => ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P271555816861255656_a_b_b] :
                  ( ! [X: produc8137180380982048514_a_b_b] :
                      ( Xs2
                     != ( finser3407669804807474762_a_b_b @ X @ bot_bo6312180378851360852_a_b_b ) )
                 => ! [R2: produc4558475209616630778_a_b_b] :
                      ( ( X3
                        = ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr5872703755862520667_a_b_b )
                       => ~ ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_503_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_dtree_a_b_b,Y: list_P5360711134766023690_a_b_b] :
      ( ( ( dtree_29943561566189470_a_b_b @ X3 )
        = Y )
     => ( ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ X3 )
       => ( ! [R2: dtree_a_b,T2: dtree_dtree_a_b_b,E2: b] :
              ( ( X3
                = ( node_dtree_a_b_b @ R2 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T2 @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) )
             => ( ( Y
                  = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T2 ) @ E2 ) @ ( dtree_29943561566189470_a_b_b @ T2 ) ) )
               => ~ ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R2 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T2 @ E2 ) @ bot_bo4737202254184417232_b_b_b ) ) ) ) )
         => ( ! [Xs2: fset_P3031279327735363940_b_b_b,R2: dtree_a_b] :
                ( ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R2 @ Xs2 ) )
               => ( ! [X: produc5284372313782567166_b_b_b] :
                      ( Xs2
                     != ( finser6734551996811508806_b_b_b @ X @ bot_bo4737202254184417232_b_b_b ) )
                 => ( ( X3
                      = ( node_dtree_a_b_b @ R2 @ Xs2 ) )
                   => ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P3031279327735363940_b_b_b] :
                  ( ! [X: produc5284372313782567166_b_b_b] :
                      ( Xs2
                     != ( finser6734551996811508806_b_b_b @ X @ bot_bo4737202254184417232_b_b_b ) )
                 => ! [R2: dtree_a_b] :
                      ( ( X3
                        = ( node_dtree_a_b_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr5403147374433350260_a_b_b )
                       => ~ ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_504_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_5519289247442030201od_a_b,Y: list_P8601282865932132013od_a_b] :
      ( ( ( dtree_5213960014362835749od_a_b @ X3 )
        = Y )
     => ( ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ X3 )
       => ( ! [R2: list_P1467974523212632366od_a_b,T2: dtree_5519289247442030201od_a_b,E2: list_P1467974523212632366od_a_b] :
              ( ( X3
                = ( node_l1136085673055119934od_a_b @ R2 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T2 @ E2 ) @ bot_bo2863178955461725870od_a_b ) ) )
             => ( ( Y
                  = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T2 ) @ E2 ) @ ( dtree_5213960014362835749od_a_b @ T2 ) ) )
               => ~ ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ ( node_l1136085673055119934od_a_b @ R2 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T2 @ E2 ) @ bot_bo2863178955461725870od_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P5910908224067821594od_a_b,R2: list_P1467974523212632366od_a_b] :
                ( ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc4044292680377378282od_a_b] :
                      ( Xs2
                     != ( finser4916530145793648802od_a_b @ X @ bot_bo2863178955461725870od_a_b ) )
                 => ( ( X3
                      = ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) )
                   => ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P5910908224067821594od_a_b] :
                  ( ! [X: produc4044292680377378282od_a_b] :
                      ( Xs2
                     != ( finser4916530145793648802od_a_b @ X @ bot_bo2863178955461725870od_a_b ) )
                 => ! [R2: list_P1467974523212632366od_a_b] :
                      ( ( X3
                        = ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr2412700377486846637od_a_b )
                       => ~ ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ ( node_l1136085673055119934od_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_505_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_8339642294131873593od_a_b,Y: list_P8094385941167427565od_a_b] :
      ( ( ( dtree_2881821214123584869od_a_b @ X3 )
        = Y )
     => ( ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ X3 )
       => ( ! [R2: product_prod_a_b > product_prod_a_b > $o,T2: dtree_8339642294131873593od_a_b,E2: list_P1467974523212632366od_a_b] :
              ( ( X3
                = ( node_P5897935084763704574od_a_b @ R2 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T2 @ E2 ) @ bot_bo137739038786217454od_a_b ) ) )
             => ( ( Y
                  = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T2 ) @ E2 ) @ ( dtree_2881821214123584869od_a_b @ T2 ) ) )
               => ~ ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ ( node_P5897935084763704574od_a_b @ R2 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T2 @ E2 ) @ bot_bo137739038786217454od_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P9180166578942778714od_a_b,R2: product_prod_a_b > product_prod_a_b > $o] :
                ( ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc6844405789190802602od_a_b] :
                      ( Xs2
                     != ( finser4631589853810920290od_a_b @ X @ bot_bo137739038786217454od_a_b ) )
                 => ( ( X3
                      = ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) )
                   => ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P9180166578942778714od_a_b] :
                  ( ! [X: produc6844405789190802602od_a_b] :
                      ( Xs2
                     != ( finser4631589853810920290od_a_b @ X @ bot_bo137739038786217454od_a_b ) )
                 => ! [R2: product_prod_a_b > product_prod_a_b > $o] :
                      ( ( X3
                        = ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr7311172237979606381od_a_b )
                       => ~ ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ ( node_P5897935084763704574od_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_506_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_8545934391348768041od_a_b,Y: list_P5700792096213675741od_a_b] :
      ( ( ( dtree_4297255050927138389od_a_b @ X3 )
        = Y )
     => ( ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ X3 )
       => ( ! [R2: a,T2: dtree_8545934391348768041od_a_b,E2: list_P1467974523212632366od_a_b] :
              ( ( X3
                = ( node_a6325075177599301358od_a_b @ R2 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T2 @ E2 ) @ bot_bo577854266114829310od_a_b ) ) )
             => ( ( Y
                  = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T2 ) @ E2 ) @ ( dtree_4297255050927138389od_a_b @ T2 ) ) )
               => ~ ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ ( node_a6325075177599301358od_a_b @ R2 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T2 @ E2 ) @ bot_bo577854266114829310od_a_b ) ) ) ) )
         => ( ! [Xs2: fset_P8869035697996476266od_a_b,R2: a] :
                ( ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc229868702982719930od_a_b] :
                      ( Xs2
                     != ( finser2699324603737210994od_a_b @ X @ bot_bo577854266114829310od_a_b ) )
                 => ( ( X3
                      = ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) )
                   => ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P8869035697996476266od_a_b] :
                  ( ! [X: produc229868702982719930od_a_b] :
                      ( Xs2
                     != ( finser2699324603737210994od_a_b @ X @ bot_bo577854266114829310od_a_b ) )
                 => ! [R2: a] :
                      ( ( X3
                        = ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Pr7243433834293086045od_a_b )
                       => ~ ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ ( node_a6325075177599301358od_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_507_dtree__to__list_Opelims,axiom,
    ! [X3: dtree_a_b,Y: list_P1467974523212632366od_a_b] :
      ( ( ( dtree_to_list_a_b @ X3 )
        = Y )
     => ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ X3 )
       => ( ! [R2: a,T2: dtree_a_b,E2: b] :
              ( ( X3
                = ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) )
             => ( ( Y
                  = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T2 ) @ E2 ) @ ( dtree_to_list_a_b @ T2 ) ) )
               => ~ ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) )
         => ( ! [Xs2: fset_P5281107635120001194_a_b_b,R2: a] :
                ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ Xs2 ) )
               => ( ! [X: produc4558475209616630778_a_b_b] :
                      ( Xs2
                     != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) )
                 => ( ( X3
                      = ( node_a_b @ R2 @ Xs2 ) )
                   => ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ Xs2 ) ) ) ) )
           => ~ ! [Xs2: fset_P5281107635120001194_a_b_b] :
                  ( ! [X: produc4558475209616630778_a_b_b] :
                      ( Xs2
                     != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) )
                 => ! [R2: a] :
                      ( ( X3
                        = ( node_a_b @ R2 @ Xs2 ) )
                     => ( ( Y = nil_Product_prod_a_b )
                       => ~ ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ Xs2 ) ) ) ) ) ) ) ) ) ).

% dtree_to_list.pelims
thf(fact_508_subseqs_Osimps_I1_J,axiom,
    ( ( subseq465733082264987907od_a_b @ nil_li8635777946366267444od_a_b )
    = ( cons_l4798275018037426410od_a_b @ nil_li8635777946366267444od_a_b @ nil_li2802039260981550394od_a_b ) ) ).

% subseqs.simps(1)
thf(fact_509_subseqs_Osimps_I1_J,axiom,
    ( ( subseq3833396900492357116od_a_b @ nil_Pr906174322249854893od_a_b )
    = ( cons_l5043155473145997155od_a_b @ nil_Pr906174322249854893od_a_b @ nil_li9150416971034547123od_a_b ) ) ).

% subseqs.simps(1)
thf(fact_510_subseqs_Osimps_I1_J,axiom,
    ( ( subseqs_dtree_a_b @ nil_dtree_a_b )
    = ( cons_list_dtree_a_b @ nil_dtree_a_b @ nil_list_dtree_a_b ) ) ).

% subseqs.simps(1)
thf(fact_511_subseqs_Osimps_I1_J,axiom,
    ( ( subseq5611861847932087141_a_b_b @ nil_Pr5403147374433350260_a_b_b )
    = ( cons_l8517938233221414356_a_b_b @ nil_Pr5403147374433350260_a_b_b @ nil_li143336474603867524_a_b_b ) ) ).

% subseqs.simps(1)
thf(fact_512_subseqs_Osimps_I1_J,axiom,
    ( ( subseq3159716953272533757od_a_b @ nil_Product_prod_a_b )
    = ( cons_l907386227682280420od_a_b @ nil_Product_prod_a_b @ nil_li8635777946366267444od_a_b ) ) ).

% subseqs.simps(1)
thf(fact_513_vwalk__arcs_Oelims,axiom,
    ! [X3: list_P3463435030753280173od_a_b,Y: list_P5357134975691234797od_a_b] :
      ( ( ( vertex6365343018446862111od_a_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_Pr906174322249854893od_a_b )
         => ( Y != nil_Pr1799676319544484077od_a_b ) )
       => ( ( ? [X2: produc2233330766403592615od_a_b] :
                ( X3
                = ( cons_P8222935586017696605od_a_b @ X2 @ nil_Pr906174322249854893od_a_b ) )
           => ( Y != nil_Pr1799676319544484077od_a_b ) )
         => ~ ! [X2: produc2233330766403592615od_a_b,Y3: produc2233330766403592615od_a_b,Xs2: list_P3463435030753280173od_a_b] :
                ( ( X3
                  = ( cons_P8222935586017696605od_a_b @ X2 @ ( cons_P8222935586017696605od_a_b @ Y3 @ Xs2 ) ) )
               => ( Y
                 != ( cons_P5303771978918612125od_a_b @ ( produc8133154353881416535od_a_b @ X2 @ Y3 ) @ ( vertex6365343018446862111od_a_b @ ( cons_P8222935586017696605od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).

% vwalk_arcs.elims
thf(fact_514_vwalk__arcs_Oelims,axiom,
    ! [X3: list_l8778361445553822004od_a_b,Y: list_P8601282865932132013od_a_b] :
      ( ( ( vertex1682407011257858726od_a_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_li8635777946366267444od_a_b )
         => ( Y != nil_Pr2412700377486846637od_a_b ) )
       => ( ( ? [X2: list_P1467974523212632366od_a_b] :
                ( X3
                = ( cons_l907386227682280420od_a_b @ X2 @ nil_li8635777946366267444od_a_b ) )
           => ( Y != nil_Pr2412700377486846637od_a_b ) )
         => ~ ! [X2: list_P1467974523212632366od_a_b,Y3: list_P1467974523212632366od_a_b,Xs2: list_l8778361445553822004od_a_b] :
                ( ( X3
                  = ( cons_l907386227682280420od_a_b @ X2 @ ( cons_l907386227682280420od_a_b @ Y3 @ Xs2 ) ) )
               => ( Y
                 != ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ X2 @ Y3 ) @ ( vertex1682407011257858726od_a_b @ ( cons_l907386227682280420od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).

% vwalk_arcs.elims
thf(fact_515_vwalk__arcs_Oelims,axiom,
    ! [X3: list_dtree_a_b,Y: list_P7294506862534405595ee_a_b] :
      ( ( ( vertex6757798842484198146ee_a_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_dtree_a_b )
         => ( Y != nil_Pr558572586965427547ee_a_b ) )
       => ( ( ? [X2: dtree_a_b] :
                ( X3
                = ( cons_dtree_a_b @ X2 @ nil_dtree_a_b ) )
           => ( Y != nil_Pr558572586965427547ee_a_b ) )
         => ~ ! [X2: dtree_a_b,Y3: dtree_a_b,Xs2: list_dtree_a_b] :
                ( ( X3
                  = ( cons_dtree_a_b @ X2 @ ( cons_dtree_a_b @ Y3 @ Xs2 ) ) )
               => ( Y
                 != ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ X2 @ Y3 ) @ ( vertex6757798842484198146ee_a_b @ ( cons_dtree_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).

% vwalk_arcs.elims
thf(fact_516_vwalk__arcs_Oelims,axiom,
    ! [X3: list_P5360711134766023690_a_b_b,Y: list_P7924273279524553179_a_b_b] :
      ( ( ( vertex6010537929073084546_a_b_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_Pr5403147374433350260_a_b_b )
         => ( Y != nil_Pr5872703755862520667_a_b_b ) )
       => ( ( ? [X2: produc4558475209616630778_a_b_b] :
                ( X3
                = ( cons_P2785074014425598660_a_b_b @ X2 @ nil_Pr5403147374433350260_a_b_b ) )
           => ( Y != nil_Pr5872703755862520667_a_b_b ) )
         => ~ ! [X2: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,Xs2: list_P5360711134766023690_a_b_b] :
                ( ( X3
                  = ( cons_P2785074014425598660_a_b_b @ X2 @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Xs2 ) ) )
               => ( Y
                 != ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ X2 @ Y3 ) @ ( vertex6010537929073084546_a_b_b @ ( cons_P2785074014425598660_a_b_b @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).

% vwalk_arcs.elims
thf(fact_517_vwalk__arcs_Oelims,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y: list_P3463435030753280173od_a_b] :
      ( ( ( vertex3879532237292798496od_a_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_Product_prod_a_b )
         => ( Y != nil_Pr906174322249854893od_a_b ) )
       => ( ( ? [X2: product_prod_a_b] :
                ( X3
                = ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) )
           => ( Y != nil_Pr906174322249854893od_a_b ) )
         => ~ ! [X2: product_prod_a_b,Y3: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
                ( ( X3
                  = ( cons_P7316939131009794654od_a_b @ X2 @ ( cons_P7316939131009794654od_a_b @ Y3 @ Xs2 ) ) )
               => ( Y
                 != ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ X2 @ Y3 ) @ ( vertex3879532237292798496od_a_b @ ( cons_P7316939131009794654od_a_b @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).

% vwalk_arcs.elims
thf(fact_518_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: product_prod_a_b,T: dtree_2253494508914376569od_a_b,E: product_prod_a_b] :
      ( ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T @ E ) @ bot_bo7856883933444951080od_a_b ) ) )
     => ( ( dtree_983605638134528549od_a_b @ ( node_P1936840572307073598od_a_b @ R @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T @ E ) @ bot_bo7856883933444951080od_a_b ) ) )
        = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T ) @ E ) @ ( dtree_983605638134528549od_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_519_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_1861073144021109543ee_a_b,E: dtree_a_b] :
      ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) ) )
     => ( ( dtree_5459410236902894363ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T @ E ) @ bot_bo5711572498106067156ee_a_b ) ) )
        = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T ) @ E ) @ ( dtree_5459410236902894363ee_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_520_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b,E: dtree_a_b] :
      ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) ) )
     => ( ( dtree_9187971570250218139ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T @ E ) @ bot_bo3079078458218859348ee_a_b ) ) )
        = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T ) @ E ) @ ( dtree_9187971570250218139ee_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_521_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) ) )
     => ( ( dtree_2482681192243439515_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T @ E ) @ bot_bo1493276529839087060_a_b_b ) ) )
        = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T ) @ E ) @ ( dtree_2482681192243439515_a_b_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_522_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) ) )
     => ( ( dtree_1768895223656068891_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T @ E ) @ bot_bo6312180378851360852_a_b_b ) ) )
        = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T ) @ E ) @ ( dtree_1768895223656068891_a_b_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_523_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: dtree_a_b,T: dtree_dtree_a_b_b,E: b] :
      ( ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T @ E ) @ bot_bo4737202254184417232_b_b_b ) ) )
     => ( ( dtree_29943561566189470_a_b_b @ ( node_dtree_a_b_b @ R @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T @ E ) @ bot_bo4737202254184417232_b_b_b ) ) )
        = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T ) @ E ) @ ( dtree_29943561566189470_a_b_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_524_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: list_P1467974523212632366od_a_b,T: dtree_5519289247442030201od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( accp_d8312782500435053104od_a_b @ dtree_1941884435189367316od_a_b @ ( node_l1136085673055119934od_a_b @ R @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T @ E ) @ bot_bo2863178955461725870od_a_b ) ) )
     => ( ( dtree_5213960014362835749od_a_b @ ( node_l1136085673055119934od_a_b @ R @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T @ E ) @ bot_bo2863178955461725870od_a_b ) ) )
        = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T ) @ E ) @ ( dtree_5213960014362835749od_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_525_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: product_prod_a_b > product_prod_a_b > $o,T: dtree_8339642294131873593od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( accp_d5529011194741156464od_a_b @ dtree_4748084400063416276od_a_b @ ( node_P5897935084763704574od_a_b @ R @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T @ E ) @ bot_bo137739038786217454od_a_b ) ) )
     => ( ( dtree_2881821214123584869od_a_b @ ( node_P5897935084763704574od_a_b @ R @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T @ E ) @ bot_bo137739038786217454od_a_b ) ) )
        = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T ) @ E ) @ ( dtree_2881821214123584869od_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_526_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: a,T: dtree_8545934391348768041od_a_b,E: list_P1467974523212632366od_a_b] :
      ( ( accp_d2542079058444124000od_a_b @ dtree_8751924142339798980od_a_b @ ( node_a6325075177599301358od_a_b @ R @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T @ E ) @ bot_bo577854266114829310od_a_b ) ) )
     => ( ( dtree_4297255050927138389od_a_b @ ( node_a6325075177599301358od_a_b @ R @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T @ E ) @ bot_bo577854266114829310od_a_b ) ) )
        = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T ) @ E ) @ ( dtree_4297255050927138389od_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_527_dtree__to__list_Opsimps_I1_J,axiom,
    ! [R: a,T: dtree_a_b,E: b] :
      ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) )
     => ( ( dtree_to_list_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) )
        = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T ) @ E ) @ ( dtree_to_list_a_b @ T ) ) ) ) ).

% dtree_to_list.psimps(1)
thf(fact_528_single__subtree__root__dverts,axiom,
    ! [V22: dtree_a_b,T22: dtree_1861073144021109543ee_a_b,E22: dtree_a_b,T1: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ ( node_d7487230363575057332ee_a_b @ V22 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T22 @ E22 ) @ bot_bo5711572498106067156ee_a_b ) ) @ T1 )
     => ( member_dtree_a_b @ V22 @ ( dverts2436977245124431984ee_a_b @ T1 ) ) ) ).

% single_subtree_root_dverts
thf(fact_529_single__subtree__root__dverts,axiom,
    ! [V22: produc4558475209616630778_a_b_b,T22: dtree_8690448868185853351ee_a_b,E22: dtree_a_b,T1: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ ( node_P2753077162091514420ee_a_b @ V22 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T22 @ E22 ) @ bot_bo3079078458218859348ee_a_b ) ) @ T1 )
     => ( member4380921116106875537_a_b_b @ V22 @ ( dverts2972317704043987696ee_a_b @ T1 ) ) ) ).

% single_subtree_root_dverts
thf(fact_530_single__subtree__root__dverts,axiom,
    ! [V22: dtree_a_b,T22: dtree_8397784528784866983_a_b_b,E22: produc4558475209616630778_a_b_b,T1: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ ( node_d5271158820939511604_a_b_b @ V22 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T22 @ E22 ) @ bot_bo1493276529839087060_a_b_b ) ) @ T1 )
     => ( member_dtree_a_b @ V22 @ ( dverts5490399362891984880_a_b_b @ T1 ) ) ) ).

% single_subtree_root_dverts
thf(fact_531_single__subtree__root__dverts,axiom,
    ! [V22: produc4558475209616630778_a_b_b,T22: dtree_6636540493345571111_a_b_b,E22: produc4558475209616630778_a_b_b,T1: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ ( node_P961815112480277940_a_b_b @ V22 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T22 @ E22 ) @ bot_bo6312180378851360852_a_b_b ) ) @ T1 )
     => ( member4380921116106875537_a_b_b @ V22 @ ( dverts1640268204329280112_a_b_b @ T1 ) ) ) ).

% single_subtree_root_dverts
thf(fact_532_single__subtree__root__dverts,axiom,
    ! [V22: a,T22: dtree_a_b,E22: b,T1: dtree_a_b] :
      ( ( is_subtree_a_b @ ( node_a_b @ V22 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ bot_bo2895716411488905534_a_b_b ) ) @ T1 )
     => ( member_a @ V22 @ ( dverts_a_b @ T1 ) ) ) ).

% single_subtree_root_dverts
thf(fact_533_Int__iff,axiom,
    ! [C: produc5177672665255943253ee_a_b,A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ C @ ( inf_in8710443480170685603ee_a_b @ A2 @ B4 ) )
      = ( ( member2060280516343777534ee_a_b @ C @ A2 )
        & ( member2060280516343777534ee_a_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_534_Int__iff,axiom,
    ! [C: produc7397007428618769063od_a_b,A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( member3051990972100052432od_a_b @ C @ ( inf_in1590458884271868277od_a_b @ A2 @ B4 ) )
      = ( ( member3051990972100052432od_a_b @ C @ A2 )
        & ( member3051990972100052432od_a_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_535_Int__iff,axiom,
    ! [C: product_prod_a_b,A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ C @ ( inf_in8976041639890736118od_a_b @ A2 @ B4 ) )
      = ( ( member1426531481828664017od_a_b @ C @ A2 )
        & ( member1426531481828664017od_a_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_536_Int__iff,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
      = ( ( member_a @ C @ A2 )
        & ( member_a @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_537_Int__iff,axiom,
    ! [C: b,A2: set_b,B4: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A2 @ B4 ) )
      = ( ( member_b @ C @ A2 )
        & ( member_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_538_Int__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A2 )
        & ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_539_Int__iff,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) )
      = ( ( member_dtree_a_b @ C @ A2 )
        & ( member_dtree_a_b @ C @ B4 ) ) ) ).

% Int_iff
thf(fact_540_IntI,axiom,
    ! [C: produc5177672665255943253ee_a_b,A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ C @ A2 )
     => ( ( member2060280516343777534ee_a_b @ C @ B4 )
       => ( member2060280516343777534ee_a_b @ C @ ( inf_in8710443480170685603ee_a_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_541_IntI,axiom,
    ! [C: produc7397007428618769063od_a_b,A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( member3051990972100052432od_a_b @ C @ A2 )
     => ( ( member3051990972100052432od_a_b @ C @ B4 )
       => ( member3051990972100052432od_a_b @ C @ ( inf_in1590458884271868277od_a_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_542_IntI,axiom,
    ! [C: product_prod_a_b,A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ C @ A2 )
     => ( ( member1426531481828664017od_a_b @ C @ B4 )
       => ( member1426531481828664017od_a_b @ C @ ( inf_in8976041639890736118od_a_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_543_IntI,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ A2 )
     => ( ( member_a @ C @ B4 )
       => ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_544_IntI,axiom,
    ! [C: b,A2: set_b,B4: set_b] :
      ( ( member_b @ C @ A2 )
     => ( ( member_b @ C @ B4 )
       => ( member_b @ C @ ( inf_inf_set_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_545_IntI,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A2 )
     => ( ( member4380921116106875537_a_b_b @ C @ B4 )
       => ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_546_IntI,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ A2 )
     => ( ( member_dtree_a_b @ C @ B4 )
       => ( member_dtree_a_b @ C @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ) ).

% IntI
thf(fact_547_Int__left__commute,axiom,
    ! [A2: set_a,B4: set_a,C2: set_a] :
      ( ( inf_inf_set_a @ A2 @ ( inf_inf_set_a @ B4 @ C2 ) )
      = ( inf_inf_set_a @ B4 @ ( inf_inf_set_a @ A2 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_548_Int__left__commute,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,C2: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) )
      = ( inf_in5903708963019302594ee_a_b @ B4 @ ( inf_in5903708963019302594ee_a_b @ A2 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_549_Int__left__commute,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,C2: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) )
      = ( inf_in6138156342456174402_a_b_b @ B4 @ ( inf_in6138156342456174402_a_b_b @ A2 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_550_Int__left__commute,axiom,
    ! [A2: set_b,B4: set_b,C2: set_b] :
      ( ( inf_inf_set_b @ A2 @ ( inf_inf_set_b @ B4 @ C2 ) )
      = ( inf_inf_set_b @ B4 @ ( inf_inf_set_b @ A2 @ C2 ) ) ) ).

% Int_left_commute
thf(fact_551_Int__left__absorb,axiom,
    ! [A2: set_a,B4: set_a] :
      ( ( inf_inf_set_a @ A2 @ ( inf_inf_set_a @ A2 @ B4 ) )
      = ( inf_inf_set_a @ A2 @ B4 ) ) ).

% Int_left_absorb
thf(fact_552_Int__left__absorb,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) )
      = ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ).

% Int_left_absorb
thf(fact_553_Int__left__absorb,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) )
      = ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ).

% Int_left_absorb
thf(fact_554_Int__left__absorb,axiom,
    ! [A2: set_b,B4: set_b] :
      ( ( inf_inf_set_b @ A2 @ ( inf_inf_set_b @ A2 @ B4 ) )
      = ( inf_inf_set_b @ A2 @ B4 ) ) ).

% Int_left_absorb
thf(fact_555_Int__commute,axiom,
    ( inf_inf_set_a
    = ( ^ [A5: set_a,B5: set_a] : ( inf_inf_set_a @ B5 @ A5 ) ) ) ).

% Int_commute
thf(fact_556_Int__commute,axiom,
    ( inf_in5903708963019302594ee_a_b
    = ( ^ [A5: set_dtree_a_b,B5: set_dtree_a_b] : ( inf_in5903708963019302594ee_a_b @ B5 @ A5 ) ) ) ).

% Int_commute
thf(fact_557_Int__commute,axiom,
    ( inf_in6138156342456174402_a_b_b
    = ( ^ [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] : ( inf_in6138156342456174402_a_b_b @ B5 @ A5 ) ) ) ).

% Int_commute
thf(fact_558_Int__commute,axiom,
    ( inf_inf_set_b
    = ( ^ [A5: set_b,B5: set_b] : ( inf_inf_set_b @ B5 @ A5 ) ) ) ).

% Int_commute
thf(fact_559_Int__absorb,axiom,
    ! [A2: set_a] :
      ( ( inf_inf_set_a @ A2 @ A2 )
      = A2 ) ).

% Int_absorb
thf(fact_560_Int__absorb,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A2 @ A2 )
      = A2 ) ).

% Int_absorb
thf(fact_561_Int__absorb,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A2 @ A2 )
      = A2 ) ).

% Int_absorb
thf(fact_562_Int__absorb,axiom,
    ! [A2: set_b] :
      ( ( inf_inf_set_b @ A2 @ A2 )
      = A2 ) ).

% Int_absorb
thf(fact_563_Int__assoc,axiom,
    ! [A2: set_a,B4: set_a,C2: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A2 @ B4 ) @ C2 )
      = ( inf_inf_set_a @ A2 @ ( inf_inf_set_a @ B4 @ C2 ) ) ) ).

% Int_assoc
thf(fact_564_Int__assoc,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,C2: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) @ C2 )
      = ( inf_in5903708963019302594ee_a_b @ A2 @ ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) ) ) ).

% Int_assoc
thf(fact_565_Int__assoc,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,C2: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) @ C2 )
      = ( inf_in6138156342456174402_a_b_b @ A2 @ ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) ) ) ).

% Int_assoc
thf(fact_566_Int__assoc,axiom,
    ! [A2: set_b,B4: set_b,C2: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A2 @ B4 ) @ C2 )
      = ( inf_inf_set_b @ A2 @ ( inf_inf_set_b @ B4 @ C2 ) ) ) ).

% Int_assoc
thf(fact_567_IntD2,axiom,
    ! [C: produc5177672665255943253ee_a_b,A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ C @ ( inf_in8710443480170685603ee_a_b @ A2 @ B4 ) )
     => ( member2060280516343777534ee_a_b @ C @ B4 ) ) ).

% IntD2
thf(fact_568_IntD2,axiom,
    ! [C: produc7397007428618769063od_a_b,A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( member3051990972100052432od_a_b @ C @ ( inf_in1590458884271868277od_a_b @ A2 @ B4 ) )
     => ( member3051990972100052432od_a_b @ C @ B4 ) ) ).

% IntD2
thf(fact_569_IntD2,axiom,
    ! [C: product_prod_a_b,A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ C @ ( inf_in8976041639890736118od_a_b @ A2 @ B4 ) )
     => ( member1426531481828664017od_a_b @ C @ B4 ) ) ).

% IntD2
thf(fact_570_IntD2,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ( member_a @ C @ B4 ) ) ).

% IntD2
thf(fact_571_IntD2,axiom,
    ! [C: b,A2: set_b,B4: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A2 @ B4 ) )
     => ( member_b @ C @ B4 ) ) ).

% IntD2
thf(fact_572_IntD2,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) )
     => ( member4380921116106875537_a_b_b @ C @ B4 ) ) ).

% IntD2
thf(fact_573_IntD2,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) )
     => ( member_dtree_a_b @ C @ B4 ) ) ).

% IntD2
thf(fact_574_IntD1,axiom,
    ! [C: produc5177672665255943253ee_a_b,A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ C @ ( inf_in8710443480170685603ee_a_b @ A2 @ B4 ) )
     => ( member2060280516343777534ee_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_575_IntD1,axiom,
    ! [C: produc7397007428618769063od_a_b,A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( member3051990972100052432od_a_b @ C @ ( inf_in1590458884271868277od_a_b @ A2 @ B4 ) )
     => ( member3051990972100052432od_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_576_IntD1,axiom,
    ! [C: product_prod_a_b,A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ C @ ( inf_in8976041639890736118od_a_b @ A2 @ B4 ) )
     => ( member1426531481828664017od_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_577_IntD1,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ( member_a @ C @ A2 ) ) ).

% IntD1
thf(fact_578_IntD1,axiom,
    ! [C: b,A2: set_b,B4: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A2 @ B4 ) )
     => ( member_b @ C @ A2 ) ) ).

% IntD1
thf(fact_579_IntD1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) )
     => ( member4380921116106875537_a_b_b @ C @ A2 ) ) ).

% IntD1
thf(fact_580_IntD1,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) )
     => ( member_dtree_a_b @ C @ A2 ) ) ).

% IntD1
thf(fact_581_IntE,axiom,
    ! [C: produc5177672665255943253ee_a_b,A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ C @ ( inf_in8710443480170685603ee_a_b @ A2 @ B4 ) )
     => ~ ( ( member2060280516343777534ee_a_b @ C @ A2 )
         => ~ ( member2060280516343777534ee_a_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_582_IntE,axiom,
    ! [C: produc7397007428618769063od_a_b,A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( member3051990972100052432od_a_b @ C @ ( inf_in1590458884271868277od_a_b @ A2 @ B4 ) )
     => ~ ( ( member3051990972100052432od_a_b @ C @ A2 )
         => ~ ( member3051990972100052432od_a_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_583_IntE,axiom,
    ! [C: product_prod_a_b,A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( member1426531481828664017od_a_b @ C @ ( inf_in8976041639890736118od_a_b @ A2 @ B4 ) )
     => ~ ( ( member1426531481828664017od_a_b @ C @ A2 )
         => ~ ( member1426531481828664017od_a_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_584_IntE,axiom,
    ! [C: a,A2: set_a,B4: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A2 @ B4 ) )
     => ~ ( ( member_a @ C @ A2 )
         => ~ ( member_a @ C @ B4 ) ) ) ).

% IntE
thf(fact_585_IntE,axiom,
    ! [C: b,A2: set_b,B4: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A2 @ B4 ) )
     => ~ ( ( member_b @ C @ A2 )
         => ~ ( member_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_586_IntE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) )
     => ~ ( ( member4380921116106875537_a_b_b @ C @ A2 )
         => ~ ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_587_IntE,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) )
     => ~ ( ( member_dtree_a_b @ C @ A2 )
         => ~ ( member_dtree_a_b @ C @ B4 ) ) ) ).

% IntE
thf(fact_588_self__subtree,axiom,
    ! [T: dtree_a_b] : ( is_subtree_a_b @ T @ T ) ).

% self_subtree
thf(fact_589_self__subtree,axiom,
    ! [T: dtree_1861073144021109543ee_a_b] : ( is_sub7866859304860047124ee_a_b @ T @ T ) ).

% self_subtree
thf(fact_590_self__subtree,axiom,
    ! [T: dtree_8690448868185853351ee_a_b] : ( is_sub791308131889186196ee_a_b @ T @ T ) ).

% self_subtree
thf(fact_591_self__subtree,axiom,
    ! [T: dtree_8397784528784866983_a_b_b] : ( is_sub3309389790737183380_a_b_b @ T @ T ) ).

% self_subtree
thf(fact_592_self__subtree,axiom,
    ! [T: dtree_6636540493345571111_a_b_b] : ( is_sub6703628162287821076_a_b_b @ T @ T ) ).

% self_subtree
thf(fact_593_subtree__trans,axiom,
    ! [X3: dtree_a_b,Y: dtree_a_b,Z: dtree_a_b] :
      ( ( is_subtree_a_b @ X3 @ Y )
     => ( ( is_subtree_a_b @ Y @ Z )
       => ( is_subtree_a_b @ X3 @ Z ) ) ) ).

% subtree_trans
thf(fact_594_subtree__trans,axiom,
    ! [X3: dtree_1861073144021109543ee_a_b,Y: dtree_1861073144021109543ee_a_b,Z: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ X3 @ Y )
     => ( ( is_sub7866859304860047124ee_a_b @ Y @ Z )
       => ( is_sub7866859304860047124ee_a_b @ X3 @ Z ) ) ) ).

% subtree_trans
thf(fact_595_subtree__trans,axiom,
    ! [X3: dtree_8690448868185853351ee_a_b,Y: dtree_8690448868185853351ee_a_b,Z: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ X3 @ Y )
     => ( ( is_sub791308131889186196ee_a_b @ Y @ Z )
       => ( is_sub791308131889186196ee_a_b @ X3 @ Z ) ) ) ).

% subtree_trans
thf(fact_596_subtree__trans,axiom,
    ! [X3: dtree_8397784528784866983_a_b_b,Y: dtree_8397784528784866983_a_b_b,Z: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ X3 @ Y )
     => ( ( is_sub3309389790737183380_a_b_b @ Y @ Z )
       => ( is_sub3309389790737183380_a_b_b @ X3 @ Z ) ) ) ).

% subtree_trans
thf(fact_597_subtree__trans,axiom,
    ! [X3: dtree_6636540493345571111_a_b_b,Y: dtree_6636540493345571111_a_b_b,Z: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ X3 @ Y )
     => ( ( is_sub6703628162287821076_a_b_b @ Y @ Z )
       => ( is_sub6703628162287821076_a_b_b @ X3 @ Z ) ) ) ).

% subtree_trans
thf(fact_598_subtree__antisym,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b] :
      ( ( is_subtree_a_b @ T1 @ T22 )
     => ( ( is_subtree_a_b @ T22 @ T1 )
       => ( T1 = T22 ) ) ) ).

% subtree_antisym
thf(fact_599_subtree__antisym,axiom,
    ! [T1: dtree_1861073144021109543ee_a_b,T22: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ T1 @ T22 )
     => ( ( is_sub7866859304860047124ee_a_b @ T22 @ T1 )
       => ( T1 = T22 ) ) ) ).

% subtree_antisym
thf(fact_600_subtree__antisym,axiom,
    ! [T1: dtree_8690448868185853351ee_a_b,T22: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ T1 @ T22 )
     => ( ( is_sub791308131889186196ee_a_b @ T22 @ T1 )
       => ( T1 = T22 ) ) ) ).

% subtree_antisym
thf(fact_601_subtree__antisym,axiom,
    ! [T1: dtree_8397784528784866983_a_b_b,T22: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ T1 @ T22 )
     => ( ( is_sub3309389790737183380_a_b_b @ T22 @ T1 )
       => ( T1 = T22 ) ) ) ).

% subtree_antisym
thf(fact_602_subtree__antisym,axiom,
    ! [T1: dtree_6636540493345571111_a_b_b,T22: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ T1 @ T22 )
     => ( ( is_sub6703628162287821076_a_b_b @ T22 @ T1 )
       => ( T1 = T22 ) ) ) ).

% subtree_antisym
thf(fact_603_subtree__eq__if__trans__eq1,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b,T3: dtree_a_b] :
      ( ( is_subtree_a_b @ T1 @ T22 )
     => ( ( is_subtree_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T1 = T22 ) ) ) ) ).

% subtree_eq_if_trans_eq1
thf(fact_604_subtree__eq__if__trans__eq1,axiom,
    ! [T1: dtree_1861073144021109543ee_a_b,T22: dtree_1861073144021109543ee_a_b,T3: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ T1 @ T22 )
     => ( ( is_sub7866859304860047124ee_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T1 = T22 ) ) ) ) ).

% subtree_eq_if_trans_eq1
thf(fact_605_subtree__eq__if__trans__eq1,axiom,
    ! [T1: dtree_8690448868185853351ee_a_b,T22: dtree_8690448868185853351ee_a_b,T3: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ T1 @ T22 )
     => ( ( is_sub791308131889186196ee_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T1 = T22 ) ) ) ) ).

% subtree_eq_if_trans_eq1
thf(fact_606_subtree__eq__if__trans__eq1,axiom,
    ! [T1: dtree_8397784528784866983_a_b_b,T22: dtree_8397784528784866983_a_b_b,T3: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ T1 @ T22 )
     => ( ( is_sub3309389790737183380_a_b_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T1 = T22 ) ) ) ) ).

% subtree_eq_if_trans_eq1
thf(fact_607_subtree__eq__if__trans__eq1,axiom,
    ! [T1: dtree_6636540493345571111_a_b_b,T22: dtree_6636540493345571111_a_b_b,T3: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ T1 @ T22 )
     => ( ( is_sub6703628162287821076_a_b_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T1 = T22 ) ) ) ) ).

% subtree_eq_if_trans_eq1
thf(fact_608_subtree__eq__if__trans__eq2,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b,T3: dtree_a_b] :
      ( ( is_subtree_a_b @ T1 @ T22 )
     => ( ( is_subtree_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T22 = T3 ) ) ) ) ).

% subtree_eq_if_trans_eq2
thf(fact_609_subtree__eq__if__trans__eq2,axiom,
    ! [T1: dtree_1861073144021109543ee_a_b,T22: dtree_1861073144021109543ee_a_b,T3: dtree_1861073144021109543ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ T1 @ T22 )
     => ( ( is_sub7866859304860047124ee_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T22 = T3 ) ) ) ) ).

% subtree_eq_if_trans_eq2
thf(fact_610_subtree__eq__if__trans__eq2,axiom,
    ! [T1: dtree_8690448868185853351ee_a_b,T22: dtree_8690448868185853351ee_a_b,T3: dtree_8690448868185853351ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ T1 @ T22 )
     => ( ( is_sub791308131889186196ee_a_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T22 = T3 ) ) ) ) ).

% subtree_eq_if_trans_eq2
thf(fact_611_subtree__eq__if__trans__eq2,axiom,
    ! [T1: dtree_8397784528784866983_a_b_b,T22: dtree_8397784528784866983_a_b_b,T3: dtree_8397784528784866983_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ T1 @ T22 )
     => ( ( is_sub3309389790737183380_a_b_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T22 = T3 ) ) ) ) ).

% subtree_eq_if_trans_eq2
thf(fact_612_subtree__eq__if__trans__eq2,axiom,
    ! [T1: dtree_6636540493345571111_a_b_b,T22: dtree_6636540493345571111_a_b_b,T3: dtree_6636540493345571111_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ T1 @ T22 )
     => ( ( is_sub6703628162287821076_a_b_b @ T22 @ T3 )
       => ( ( T1 = T3 )
         => ( T22 = T3 ) ) ) ) ).

% subtree_eq_if_trans_eq2
thf(fact_613_Int__emptyI,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ! [X2: produc5177672665255943253ee_a_b] :
          ( ( member2060280516343777534ee_a_b @ X2 @ A2 )
         => ~ ( member2060280516343777534ee_a_b @ X2 @ B4 ) )
     => ( ( inf_in8710443480170685603ee_a_b @ A2 @ B4 )
        = bot_bo6208222296400721441ee_a_b ) ) ).

% Int_emptyI
thf(fact_614_Int__emptyI,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ! [X2: produc7397007428618769063od_a_b] :
          ( ( member3051990972100052432od_a_b @ X2 @ A2 )
         => ~ ( member3051990972100052432od_a_b @ X2 @ B4 ) )
     => ( ( inf_in1590458884271868277od_a_b @ A2 @ B4 )
        = bot_bo5083760590458426867od_a_b ) ) ).

% Int_emptyI
thf(fact_615_Int__emptyI,axiom,
    ! [A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ! [X2: product_prod_a_b] :
          ( ( member1426531481828664017od_a_b @ X2 @ A2 )
         => ~ ( member1426531481828664017od_a_b @ X2 @ B4 ) )
     => ( ( inf_in8976041639890736118od_a_b @ A2 @ B4 )
        = bot_bo3428410327501040244od_a_b ) ) ).

% Int_emptyI
thf(fact_616_Int__emptyI,axiom,
    ! [A2: set_b,B4: set_b] :
      ( ! [X2: b] :
          ( ( member_b @ X2 @ A2 )
         => ~ ( member_b @ X2 @ B4 ) )
     => ( ( inf_inf_set_b @ A2 @ B4 )
        = bot_bot_set_b ) ) ).

% Int_emptyI
thf(fact_617_Int__emptyI,axiom,
    ! [A2: set_a,B4: set_a] :
      ( ! [X2: a] :
          ( ( member_a @ X2 @ A2 )
         => ~ ( member_a @ X2 @ B4 ) )
     => ( ( inf_inf_set_a @ A2 @ B4 )
        = bot_bot_set_a ) ) ).

% Int_emptyI
thf(fact_618_Int__emptyI,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
         => ~ ( member4380921116106875537_a_b_b @ X2 @ B4 ) )
     => ( ( inf_in6138156342456174402_a_b_b @ A2 @ B4 )
        = bot_bo3721250822024684356_a_b_b ) ) ).

% Int_emptyI
thf(fact_619_Int__emptyI,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ! [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ A2 )
         => ~ ( member_dtree_a_b @ X2 @ B4 ) )
     => ( ( inf_in5903708963019302594ee_a_b @ A2 @ B4 )
        = bot_bo8730652382759064772ee_a_b ) ) ).

% Int_emptyI
thf(fact_620_disjoint__iff,axiom,
    ! [A2: set_Pr8736279663640031669ee_a_b,B4: set_Pr8736279663640031669ee_a_b] :
      ( ( ( inf_in8710443480170685603ee_a_b @ A2 @ B4 )
        = bot_bo6208222296400721441ee_a_b )
      = ( ! [X4: produc5177672665255943253ee_a_b] :
            ( ( member2060280516343777534ee_a_b @ X4 @ A2 )
           => ~ ( member2060280516343777534ee_a_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_621_disjoint__iff,axiom,
    ! [A2: set_Pr3015088788472578951od_a_b,B4: set_Pr3015088788472578951od_a_b] :
      ( ( ( inf_in1590458884271868277od_a_b @ A2 @ B4 )
        = bot_bo5083760590458426867od_a_b )
      = ( ! [X4: produc7397007428618769063od_a_b] :
            ( ( member3051990972100052432od_a_b @ X4 @ A2 )
           => ~ ( member3051990972100052432od_a_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_622_disjoint__iff,axiom,
    ! [A2: set_Product_prod_a_b,B4: set_Product_prod_a_b] :
      ( ( ( inf_in8976041639890736118od_a_b @ A2 @ B4 )
        = bot_bo3428410327501040244od_a_b )
      = ( ! [X4: product_prod_a_b] :
            ( ( member1426531481828664017od_a_b @ X4 @ A2 )
           => ~ ( member1426531481828664017od_a_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_623_disjoint__iff,axiom,
    ! [A2: set_b,B4: set_b] :
      ( ( ( inf_inf_set_b @ A2 @ B4 )
        = bot_bot_set_b )
      = ( ! [X4: b] :
            ( ( member_b @ X4 @ A2 )
           => ~ ( member_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_624_disjoint__iff,axiom,
    ! [A2: set_a,B4: set_a] :
      ( ( ( inf_inf_set_a @ A2 @ B4 )
        = bot_bot_set_a )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ A2 )
           => ~ ( member_a @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_625_disjoint__iff,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ A2 @ B4 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X4: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X4 @ A2 )
           => ~ ( member4380921116106875537_a_b_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_626_disjoint__iff,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ( inf_in5903708963019302594ee_a_b @ A2 @ B4 )
        = bot_bo8730652382759064772ee_a_b )
      = ( ! [X4: dtree_a_b] :
            ( ( member_dtree_a_b @ X4 @ A2 )
           => ~ ( member_dtree_a_b @ X4 @ B4 ) ) ) ) ).

% disjoint_iff
thf(fact_627_Int__empty__left,axiom,
    ! [B4: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ bot_bo3721250822024684356_a_b_b @ B4 )
      = bot_bo3721250822024684356_a_b_b ) ).

% Int_empty_left
thf(fact_628_Int__empty__left,axiom,
    ! [B4: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ bot_bo8730652382759064772ee_a_b @ B4 )
      = bot_bo8730652382759064772ee_a_b ) ).

% Int_empty_left
thf(fact_629_Int__empty__left,axiom,
    ! [B4: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ B4 )
      = bot_bot_set_b ) ).

% Int_empty_left
thf(fact_630_Int__empty__left,axiom,
    ! [B4: set_a] :
      ( ( inf_inf_set_a @ bot_bot_set_a @ B4 )
      = bot_bot_set_a ) ).

% Int_empty_left
thf(fact_631_Int__empty__right,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A2 @ bot_bo3721250822024684356_a_b_b )
      = bot_bo3721250822024684356_a_b_b ) ).

% Int_empty_right
thf(fact_632_Int__empty__right,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A2 @ bot_bo8730652382759064772ee_a_b )
      = bot_bo8730652382759064772ee_a_b ) ).

% Int_empty_right
thf(fact_633_Int__empty__right,axiom,
    ! [A2: set_b] :
      ( ( inf_inf_set_b @ A2 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% Int_empty_right
thf(fact_634_Int__empty__right,axiom,
    ! [A2: set_a] :
      ( ( inf_inf_set_a @ A2 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% Int_empty_right
thf(fact_635_disjoint__iff__not__equal,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ A2 @ B4 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X4: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X4 @ A2 )
           => ! [Y4: produc4558475209616630778_a_b_b] :
                ( ( member4380921116106875537_a_b_b @ Y4 @ B4 )
               => ( X4 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_636_disjoint__iff__not__equal,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ( inf_in5903708963019302594ee_a_b @ A2 @ B4 )
        = bot_bo8730652382759064772ee_a_b )
      = ( ! [X4: dtree_a_b] :
            ( ( member_dtree_a_b @ X4 @ A2 )
           => ! [Y4: dtree_a_b] :
                ( ( member_dtree_a_b @ Y4 @ B4 )
               => ( X4 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_637_disjoint__iff__not__equal,axiom,
    ! [A2: set_b,B4: set_b] :
      ( ( ( inf_inf_set_b @ A2 @ B4 )
        = bot_bot_set_b )
      = ( ! [X4: b] :
            ( ( member_b @ X4 @ A2 )
           => ! [Y4: b] :
                ( ( member_b @ Y4 @ B4 )
               => ( X4 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_638_disjoint__iff__not__equal,axiom,
    ! [A2: set_a,B4: set_a] :
      ( ( ( inf_inf_set_a @ A2 @ B4 )
        = bot_bot_set_a )
      = ( ! [X4: a] :
            ( ( member_a @ X4 @ A2 )
           => ! [Y4: a] :
                ( ( member_a @ Y4 @ B4 )
               => ( X4 != Y4 ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_639_subtree__root__if__dverts,axiom,
    ! [X3: dtree_a_b,T: dtree_1861073144021109543ee_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( dverts2436977245124431984ee_a_b @ T ) )
     => ? [Xs2: fset_P5991447722532490344ee_a_b] : ( is_sub7866859304860047124ee_a_b @ ( node_d7487230363575057332ee_a_b @ X3 @ Xs2 ) @ T ) ) ).

% subtree_root_if_dverts
thf(fact_640_subtree__root__if__dverts,axiom,
    ! [X3: produc4558475209616630778_a_b_b,T: dtree_8690448868185853351ee_a_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( dverts2972317704043987696ee_a_b @ T ) )
     => ? [Xs2: fset_P1087233464713034472ee_a_b] : ( is_sub791308131889186196ee_a_b @ ( node_P2753077162091514420ee_a_b @ X3 @ Xs2 ) @ T ) ) ).

% subtree_root_if_dverts
thf(fact_641_subtree__root__if__dverts,axiom,
    ! [X3: dtree_a_b,T: dtree_8397784528784866983_a_b_b] :
      ( ( member_dtree_a_b @ X3 @ ( dverts5490399362891984880_a_b_b @ T ) )
     => ? [Xs2: fset_P8532786667068971368_a_b_b] : ( is_sub3309389790737183380_a_b_b @ ( node_d5271158820939511604_a_b_b @ X3 @ Xs2 ) @ T ) ) ).

% subtree_root_if_dverts
thf(fact_642_subtree__root__if__dverts,axiom,
    ! [X3: produc4558475209616630778_a_b_b,T: dtree_6636540493345571111_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( dverts1640268204329280112_a_b_b @ T ) )
     => ? [Xs2: fset_P271555816861255656_a_b_b] : ( is_sub6703628162287821076_a_b_b @ ( node_P961815112480277940_a_b_b @ X3 @ Xs2 ) @ T ) ) ).

% subtree_root_if_dverts
thf(fact_643_subtree__root__if__dverts,axiom,
    ! [X3: a,T: dtree_a_b] :
      ( ( member_a @ X3 @ ( dverts_a_b @ T ) )
     => ? [Xs2: fset_P5281107635120001194_a_b_b] : ( is_subtree_a_b @ ( node_a_b @ X3 @ Xs2 ) @ T ) ) ).

% subtree_root_if_dverts
thf(fact_644_vwalk__arcs_Osimps_I1_J,axiom,
    ( ( vertex1682407011257858726od_a_b @ nil_li8635777946366267444od_a_b )
    = nil_Pr2412700377486846637od_a_b ) ).

% vwalk_arcs.simps(1)
thf(fact_645_vwalk__arcs_Osimps_I1_J,axiom,
    ( ( vertex6365343018446862111od_a_b @ nil_Pr906174322249854893od_a_b )
    = nil_Pr1799676319544484077od_a_b ) ).

% vwalk_arcs.simps(1)
thf(fact_646_vwalk__arcs_Osimps_I1_J,axiom,
    ( ( vertex6757798842484198146ee_a_b @ nil_dtree_a_b )
    = nil_Pr558572586965427547ee_a_b ) ).

% vwalk_arcs.simps(1)
thf(fact_647_vwalk__arcs_Osimps_I1_J,axiom,
    ( ( vertex6010537929073084546_a_b_b @ nil_Pr5403147374433350260_a_b_b )
    = nil_Pr5872703755862520667_a_b_b ) ).

% vwalk_arcs.simps(1)
thf(fact_648_vwalk__arcs_Osimps_I1_J,axiom,
    ( ( vertex3879532237292798496od_a_b @ nil_Product_prod_a_b )
    = nil_Pr906174322249854893od_a_b ) ).

% vwalk_arcs.simps(1)
thf(fact_649_dtree__to__list_Opinduct,axiom,
    ! [A0: dtree_1861073144021109543ee_a_b,P: dtree_1861073144021109543ee_a_b > $o] :
      ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ A0 )
     => ( ! [R2: dtree_a_b,T2: dtree_1861073144021109543ee_a_b,E2: dtree_a_b] :
            ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) )
           => ( ( P @ T2 )
             => ( P @ ( node_d7487230363575057332ee_a_b @ R2 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T2 @ E2 ) @ bot_bo5711572498106067156ee_a_b ) ) ) ) )
       => ( ! [Xs2: fset_P5991447722532490344ee_a_b,R2: dtree_a_b] :
              ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) )
             => ( ! [X: produc6260003399586931330ee_a_b] :
                    ( Xs2
                   != ( finser8516331313445392842ee_a_b @ X @ bot_bo5711572498106067156ee_a_b ) )
               => ( P @ ( node_d7487230363575057332ee_a_b @ R2 @ Xs2 ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% dtree_to_list.pinduct
thf(fact_650_dtree__to__list_Opinduct,axiom,
    ! [A0: dtree_8690448868185853351ee_a_b,P: dtree_8690448868185853351ee_a_b > $o] :
      ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ A0 )
     => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_8690448868185853351ee_a_b,E2: dtree_a_b] :
            ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) )
           => ( ( P @ T2 )
             => ( P @ ( node_P2753077162091514420ee_a_b @ R2 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T2 @ E2 ) @ bot_bo3079078458218859348ee_a_b ) ) ) ) )
       => ( ! [Xs2: fset_P1087233464713034472ee_a_b,R2: produc4558475209616630778_a_b_b] :
              ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) )
             => ( ! [X: produc1961764714219340802ee_a_b] :
                    ( Xs2
                   != ( finser7847761039489690442ee_a_b @ X @ bot_bo3079078458218859348ee_a_b ) )
               => ( P @ ( node_P2753077162091514420ee_a_b @ R2 @ Xs2 ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% dtree_to_list.pinduct
thf(fact_651_dtree__to__list_Opinduct,axiom,
    ! [A0: dtree_8397784528784866983_a_b_b,P: dtree_8397784528784866983_a_b_b > $o] :
      ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ A0 )
     => ( ! [R2: dtree_a_b,T2: dtree_8397784528784866983_a_b_b,E2: produc4558475209616630778_a_b_b] :
            ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) )
           => ( ( P @ T2 )
             => ( P @ ( node_d5271158820939511604_a_b_b @ R2 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T2 @ E2 ) @ bot_bo1493276529839087060_a_b_b ) ) ) ) )
       => ( ! [Xs2: fset_P8532786667068971368_a_b_b,R2: dtree_a_b] :
              ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) )
             => ( ! [X: produc4081214457754080642_a_b_b] :
                    ( Xs2
                   != ( finser5778094437704840394_a_b_b @ X @ bot_bo1493276529839087060_a_b_b ) )
               => ( P @ ( node_d5271158820939511604_a_b_b @ R2 @ Xs2 ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% dtree_to_list.pinduct
thf(fact_652_dtree__to__list_Opinduct,axiom,
    ! [A0: dtree_6636540493345571111_a_b_b,P: dtree_6636540493345571111_a_b_b > $o] :
      ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ A0 )
     => ( ! [R2: produc4558475209616630778_a_b_b,T2: dtree_6636540493345571111_a_b_b,E2: produc4558475209616630778_a_b_b] :
            ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) )
           => ( ( P @ T2 )
             => ( P @ ( node_P961815112480277940_a_b_b @ R2 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T2 @ E2 ) @ bot_bo6312180378851360852_a_b_b ) ) ) ) )
       => ( ! [Xs2: fset_P271555816861255656_a_b_b,R2: produc4558475209616630778_a_b_b] :
              ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) )
             => ( ! [X: produc8137180380982048514_a_b_b] :
                    ( Xs2
                   != ( finser3407669804807474762_a_b_b @ X @ bot_bo6312180378851360852_a_b_b ) )
               => ( P @ ( node_P961815112480277940_a_b_b @ R2 @ Xs2 ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% dtree_to_list.pinduct
thf(fact_653_dtree__to__list_Opinduct,axiom,
    ! [A0: dtree_a_b,P: dtree_a_b > $o] :
      ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ A0 )
     => ( ! [R2: a,T2: dtree_a_b,E2: b] :
            ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) )
           => ( ( P @ T2 )
             => ( P @ ( node_a_b @ R2 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) )
       => ( ! [Xs2: fset_P5281107635120001194_a_b_b,R2: a] :
              ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R2 @ Xs2 ) )
             => ( ! [X: produc4558475209616630778_a_b_b] :
                    ( Xs2
                   != ( finser8437519239679886002_a_b_b @ X @ bot_bo2895716411488905534_a_b_b ) )
               => ( P @ ( node_a_b @ R2 @ Xs2 ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% dtree_to_list.pinduct
thf(fact_654_vwalk__arcs_Osimps_I3_J,axiom,
    ! [X3: produc2233330766403592615od_a_b,Y: produc2233330766403592615od_a_b,Xs: list_P3463435030753280173od_a_b] :
      ( ( vertex6365343018446862111od_a_b @ ( cons_P8222935586017696605od_a_b @ X3 @ ( cons_P8222935586017696605od_a_b @ Y @ Xs ) ) )
      = ( cons_P5303771978918612125od_a_b @ ( produc8133154353881416535od_a_b @ X3 @ Y ) @ ( vertex6365343018446862111od_a_b @ ( cons_P8222935586017696605od_a_b @ Y @ Xs ) ) ) ) ).

% vwalk_arcs.simps(3)
thf(fact_655_vwalk__arcs_Osimps_I3_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y: list_P1467974523212632366od_a_b,Xs: list_l8778361445553822004od_a_b] :
      ( ( vertex1682407011257858726od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ ( cons_l907386227682280420od_a_b @ Y @ Xs ) ) )
      = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ X3 @ Y ) @ ( vertex1682407011257858726od_a_b @ ( cons_l907386227682280420od_a_b @ Y @ Xs ) ) ) ) ).

% vwalk_arcs.simps(3)
thf(fact_656_vwalk__arcs_Osimps_I3_J,axiom,
    ! [X3: product_prod_a_b,Y: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( vertex3879532237292798496od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ ( cons_P7316939131009794654od_a_b @ Y @ Xs ) ) )
      = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ X3 @ Y ) @ ( vertex3879532237292798496od_a_b @ ( cons_P7316939131009794654od_a_b @ Y @ Xs ) ) ) ) ).

% vwalk_arcs.simps(3)
thf(fact_657_vwalk__arcs_Osimps_I3_J,axiom,
    ! [X3: dtree_a_b,Y: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( vertex6757798842484198146ee_a_b @ ( cons_dtree_a_b @ X3 @ ( cons_dtree_a_b @ Y @ Xs ) ) )
      = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ X3 @ Y ) @ ( vertex6757798842484198146ee_a_b @ ( cons_dtree_a_b @ Y @ Xs ) ) ) ) ).

% vwalk_arcs.simps(3)
thf(fact_658_vwalk__arcs_Osimps_I3_J,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( vertex6010537929073084546_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X3 @ ( cons_P2785074014425598660_a_b_b @ Y @ Xs ) ) )
      = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y ) @ ( vertex6010537929073084546_a_b_b @ ( cons_P2785074014425598660_a_b_b @ Y @ Xs ) ) ) ) ).

% vwalk_arcs.simps(3)
thf(fact_659_vwalk__arcs_Osimps_I2_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( vertex1682407011257858726od_a_b @ ( cons_l907386227682280420od_a_b @ X3 @ nil_li8635777946366267444od_a_b ) )
      = nil_Pr2412700377486846637od_a_b ) ).

% vwalk_arcs.simps(2)
thf(fact_660_vwalk__arcs_Osimps_I2_J,axiom,
    ! [X3: produc2233330766403592615od_a_b] :
      ( ( vertex6365343018446862111od_a_b @ ( cons_P8222935586017696605od_a_b @ X3 @ nil_Pr906174322249854893od_a_b ) )
      = nil_Pr1799676319544484077od_a_b ) ).

% vwalk_arcs.simps(2)
thf(fact_661_vwalk__arcs_Osimps_I2_J,axiom,
    ! [X3: dtree_a_b] :
      ( ( vertex6757798842484198146ee_a_b @ ( cons_dtree_a_b @ X3 @ nil_dtree_a_b ) )
      = nil_Pr558572586965427547ee_a_b ) ).

% vwalk_arcs.simps(2)
thf(fact_662_vwalk__arcs_Osimps_I2_J,axiom,
    ! [X3: produc4558475209616630778_a_b_b] :
      ( ( vertex6010537929073084546_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X3 @ nil_Pr5403147374433350260_a_b_b ) )
      = nil_Pr5872703755862520667_a_b_b ) ).

% vwalk_arcs.simps(2)
thf(fact_663_vwalk__arcs_Osimps_I2_J,axiom,
    ! [X3: product_prod_a_b] :
      ( ( vertex3879532237292798496od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) )
      = nil_Pr906174322249854893od_a_b ) ).

% vwalk_arcs.simps(2)
thf(fact_664_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P6924693328471822228od_a_b,R: product_prod_a_b] :
      ( ! [X2: produc2878020351943352036od_a_b] :
          ( Xs
         != ( finser5347476252697843100od_a_b @ X2 @ bot_bo7856883933444951080od_a_b ) )
     => ( ( accp_d5695662582940224048od_a_b @ dtree_5602071207833618452od_a_b @ ( node_P1936840572307073598od_a_b @ R @ Xs ) )
       => ( ( dtree_983605638134528549od_a_b @ ( node_P1936840572307073598od_a_b @ R @ Xs ) )
          = nil_Pr906174322249854893od_a_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_665_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P3031279327735363940_b_b_b,R: dtree_a_b] :
      ( ! [X2: produc5284372313782567166_b_b_b] :
          ( Xs
         != ( finser6734551996811508806_b_b_b @ X2 @ bot_bo4737202254184417232_b_b_b ) )
     => ( ( accp_d7585430846279353905_a_b_b @ dtree_7148473427102603503_a_b_b @ ( node_dtree_a_b_b @ R @ Xs ) )
       => ( ( dtree_29943561566189470_a_b_b @ ( node_dtree_a_b_b @ R @ Xs ) )
          = nil_Pr5403147374433350260_a_b_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_666_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P5991447722532490344ee_a_b,R: dtree_a_b] :
      ( ! [X2: produc6260003399586931330ee_a_b] :
          ( Xs
         != ( finser8516331313445392842ee_a_b @ X2 @ bot_bo5711572498106067156ee_a_b ) )
     => ( ( accp_d5080589847971241310ee_a_b @ dtree_690707291460779146ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
       => ( ( dtree_5459410236902894363ee_a_b @ ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
          = nil_Pr558572586965427547ee_a_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_667_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P1087233464713034472ee_a_b,R: produc4558475209616630778_a_b_b] :
      ( ! [X2: produc1961764714219340802ee_a_b] :
          ( Xs
         != ( finser7847761039489690442ee_a_b @ X2 @ bot_bo3079078458218859348ee_a_b ) )
     => ( ( accp_d8696696969779859678ee_a_b @ dtree_3333118632715683082ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
       => ( ( dtree_9187971570250218139ee_a_b @ ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
          = nil_Pr148742403700823003ee_a_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_668_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P8532786667068971368_a_b_b,R: dtree_a_b] :
      ( ! [X2: produc4081214457754080642_a_b_b] :
          ( Xs
         != ( finser5778094437704840394_a_b_b @ X2 @ bot_bo1493276529839087060_a_b_b ) )
     => ( ( accp_d8404032630378873310_a_b_b @ dtree_5851200291563680266_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
       => ( ( dtree_2482681192243439515_a_b_b @ ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
          = nil_Pr9079450101154612443_a_b_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_669_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P271555816861255656_a_b_b,R: produc4558475209616630778_a_b_b] :
      ( ! [X2: produc8137180380982048514_a_b_b] :
          ( Xs
         != ( finser3407669804807474762_a_b_b @ X2 @ bot_bo6312180378851360852_a_b_b ) )
     => ( ( accp_d2303357675354748254_a_b_b @ dtree_5584907631894100618_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
       => ( ( dtree_1768895223656068891_a_b_b @ ( node_P961815112480277940_a_b_b @ R @ Xs ) )
          = nil_Pr5872703755862520667_a_b_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_670_dtree__to__list_Opsimps_I2_J,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( Xs
         != ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) )
     => ( ( accp_dtree_a_b @ dtree_9180682678494368405el_a_b @ ( node_a_b @ R @ Xs ) )
       => ( ( dtree_to_list_a_b @ ( node_a_b @ R @ Xs ) )
          = nil_Product_prod_a_b ) ) ) ).

% dtree_to_list.psimps(2)
thf(fact_671_inf__bot__left,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ bot_bo3721250822024684356_a_b_b @ X3 )
      = bot_bo3721250822024684356_a_b_b ) ).

% inf_bot_left
thf(fact_672_inf__bot__left,axiom,
    ! [X3: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ bot_bo8730652382759064772ee_a_b @ X3 )
      = bot_bo8730652382759064772ee_a_b ) ).

% inf_bot_left
thf(fact_673_inf__bot__left,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ X3 )
      = bot_bot_set_b ) ).

% inf_bot_left
thf(fact_674_inf__bot__left,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ bot_bot_set_a @ X3 )
      = bot_bot_set_a ) ).

% inf_bot_left
thf(fact_675_inf__bot__left,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ bot_bo7321339186913516097_b_b_o @ X3 )
      = bot_bo7321339186913516097_b_b_o ) ).

% inf_bot_left
thf(fact_676_inf__bot__left,axiom,
    ! [X3: dtree_a_b > $o] :
      ( ( inf_inf_dtree_a_b_o @ bot_bot_dtree_a_b_o @ X3 )
      = bot_bot_dtree_a_b_o ) ).

% inf_bot_left
thf(fact_677_inf__bot__left,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ bot_bo2895716411488905534_a_b_b @ X3 )
      = bot_bo2895716411488905534_a_b_b ) ).

% inf_bot_left
thf(fact_678_inf__bot__right,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b )
      = bot_bo3721250822024684356_a_b_b ) ).

% inf_bot_right
thf(fact_679_inf__bot__right,axiom,
    ! [X3: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ X3 @ bot_bo8730652382759064772ee_a_b )
      = bot_bo8730652382759064772ee_a_b ) ).

% inf_bot_right
thf(fact_680_inf__bot__right,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ X3 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% inf_bot_right
thf(fact_681_inf__bot__right,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ X3 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% inf_bot_right
thf(fact_682_inf__bot__right,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ X3 @ bot_bo7321339186913516097_b_b_o )
      = bot_bo7321339186913516097_b_b_o ) ).

% inf_bot_right
thf(fact_683_inf__bot__right,axiom,
    ! [X3: dtree_a_b > $o] :
      ( ( inf_inf_dtree_a_b_o @ X3 @ bot_bot_dtree_a_b_o )
      = bot_bot_dtree_a_b_o ) ).

% inf_bot_right
thf(fact_684_inf__bot__right,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b )
      = bot_bo2895716411488905534_a_b_b ) ).

% inf_bot_right
thf(fact_685_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ bot_bo3721250822024684356_a_b_b @ X3 )
      = bot_bo3721250822024684356_a_b_b ) ).

% boolean_algebra.conj_zero_left
thf(fact_686_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ bot_bo8730652382759064772ee_a_b @ X3 )
      = bot_bo8730652382759064772ee_a_b ) ).

% boolean_algebra.conj_zero_left
thf(fact_687_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ X3 )
      = bot_bot_set_b ) ).

% boolean_algebra.conj_zero_left
thf(fact_688_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ bot_bot_set_a @ X3 )
      = bot_bot_set_a ) ).

% boolean_algebra.conj_zero_left
thf(fact_689_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ bot_bo7321339186913516097_b_b_o @ X3 )
      = bot_bo7321339186913516097_b_b_o ) ).

% boolean_algebra.conj_zero_left
thf(fact_690_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: dtree_a_b > $o] :
      ( ( inf_inf_dtree_a_b_o @ bot_bot_dtree_a_b_o @ X3 )
      = bot_bot_dtree_a_b_o ) ).

% boolean_algebra.conj_zero_left
thf(fact_691_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b )
      = bot_bo3721250822024684356_a_b_b ) ).

% boolean_algebra.conj_zero_right
thf(fact_692_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ X3 @ bot_bo8730652382759064772ee_a_b )
      = bot_bo8730652382759064772ee_a_b ) ).

% boolean_algebra.conj_zero_right
thf(fact_693_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ X3 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% boolean_algebra.conj_zero_right
thf(fact_694_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ X3 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% boolean_algebra.conj_zero_right
thf(fact_695_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ X3 @ bot_bo7321339186913516097_b_b_o )
      = bot_bo7321339186913516097_b_b_o ) ).

% boolean_algebra.conj_zero_right
thf(fact_696_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: dtree_a_b > $o] :
      ( ( inf_inf_dtree_a_b_o @ X3 @ bot_bot_dtree_a_b_o )
      = bot_bot_dtree_a_b_o ) ).

% boolean_algebra.conj_zero_right
thf(fact_697_dtree__from__list__sequence,axiom,
    ! [R0: product_prod_a_b,T0: dtree_2253494508914376569od_a_b,E0: product_prod_a_b,V1: product_prod_a_b,Ys: list_P3463435030753280173od_a_b,E1: product_prod_a_b] :
      ( ( is_sub6933245819845350814od_a_b @ ( node_P1936840572307073598od_a_b @ R0 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T0 @ E0 ) @ bot_bo7856883933444951080od_a_b ) ) @ ( dtree_1864022081312108148od_a_b @ V1 @ Ys ) )
     => ? [E2: product_prod_a_b,As: list_P3463435030753280173od_a_b,Bs: list_P3463435030753280173od_a_b] :
          ( ( append3447563168971123522od_a_b @ As @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ R0 @ E2 ) @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_698_dtree__from__list__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_1861073144021109543ee_a_b,E0: dtree_a_b,V1: dtree_a_b,Ys: list_P7294506862534405595ee_a_b,E1: dtree_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ ( node_d7487230363575057332ee_a_b @ R0 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T0 @ E0 ) @ bot_bo5711572498106067156ee_a_b ) ) @ ( dtree_7424119665891431146ee_a_b @ V1 @ Ys ) )
     => ? [E2: dtree_a_b,As: list_P7294506862534405595ee_a_b,Bs: list_P7294506862534405595ee_a_b] :
          ( ( append5407404413692997488ee_a_b @ As @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ R0 @ E2 ) @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_699_dtree__from__list__sequence,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_8690448868185853351ee_a_b,E0: dtree_a_b,V1: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b,E1: dtree_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ ( node_P2753077162091514420ee_a_b @ R0 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T0 @ E0 ) @ bot_bo3079078458218859348ee_a_b ) ) @ ( dtree_7850083854586231658ee_a_b @ V1 @ Ys ) )
     => ? [E2: dtree_a_b,As: list_P3724575226198589275ee_a_b,Bs: list_P3724575226198589275ee_a_b] :
          ( ( append301462268945678576ee_a_b @ As @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ R0 @ E2 ) @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_700_dtree__from__list__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_8397784528784866983_a_b_b,E0: produc4558475209616630778_a_b_b,V1: dtree_a_b,Ys: list_P7142016109841313883_a_b_b,E1: produc4558475209616630778_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ ( node_d5271158820939511604_a_b_b @ R0 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T0 @ E0 ) @ bot_bo1493276529839087060_a_b_b ) ) @ ( dtree_1144793476579453034_a_b_b @ V1 @ Ys ) )
     => ? [E2: produc4558475209616630778_a_b_b,As: list_P7142016109841313883_a_b_b,Bs: list_P7142016109841313883_a_b_b] :
          ( ( append8797929544692208_a_b_b @ As @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ R0 @ E2 ) @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_701_dtree__from__list__sequence,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_6636540493345571111_a_b_b,E0: produc4558475209616630778_a_b_b,V1: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b,E1: produc4558475209616630778_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ ( node_P961815112480277940_a_b_b @ R0 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T0 @ E0 ) @ bot_bo6312180378851360852_a_b_b ) ) @ ( dtree_450453658713739498_a_b_b @ V1 @ Ys ) )
     => ? [E2: produc4558475209616630778_a_b_b,As: list_P7924273279524553179_a_b_b,Bs: list_P7924273279524553179_a_b_b] :
          ( ( append7918683371861672816_a_b_b @ As @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ R0 @ E2 ) @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_702_dtree__from__list__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_dtree_a_b_b,E0: b,V1: dtree_a_b,Ys: list_P5360711134766023690_a_b_b,E1: b] :
      ( ( is_sub2776994699154135781_a_b_b @ ( node_dtree_a_b_b @ R0 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T0 @ E0 ) @ bot_bo4737202254184417232_b_b_b ) ) @ ( dtree_5255521609252960911_a_b_b @ V1 @ Ys ) )
     => ? [E2: b,As: list_P5360711134766023690_a_b_b,Bs: list_P5360711134766023690_a_b_b] :
          ( ( append86853766581025439_a_b_b @ As @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ R0 @ E2 ) @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_703_dtree__from__list__sequence,axiom,
    ! [R0: list_P1467974523212632366od_a_b,T0: dtree_5519289247442030201od_a_b,E0: list_P1467974523212632366od_a_b,V1: list_P1467974523212632366od_a_b,Ys: list_P8601282865932132013od_a_b,E1: list_P1467974523212632366od_a_b] :
      ( ( is_sub3969663741311890846od_a_b @ ( node_l1136085673055119934od_a_b @ R0 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T0 @ E0 ) @ bot_bo2863178955461725870od_a_b ) ) @ ( dtree_6507962483783174260od_a_b @ V1 @ Ys ) )
     => ? [E2: list_P1467974523212632366od_a_b,As: list_P8601282865932132013od_a_b,Bs: list_P8601282865932132013od_a_b] :
          ( ( append5385366555182926146od_a_b @ As @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ R0 @ E2 ) @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_704_dtree__from__list__sequence,axiom,
    ! [R0: product_prod_a_b > product_prod_a_b > $o,T0: dtree_8339642294131873593od_a_b,E0: list_P1467974523212632366od_a_b,V1: product_prod_a_b > product_prod_a_b > $o,Ys: list_P8094385941167427565od_a_b,E1: list_P1467974523212632366od_a_b] :
      ( ( is_sub9145550046624671838od_a_b @ ( node_P5897935084763704574od_a_b @ R0 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T0 @ E0 ) @ bot_bo137739038786217454od_a_b ) ) @ ( dtree_4383916385682046516od_a_b @ V1 @ Ys ) )
     => ? [E2: list_P1467974523212632366od_a_b,As: list_P8094385941167427565od_a_b,Bs: list_P8094385941167427565od_a_b] :
          ( ( append2461588412122937986od_a_b @ As @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ R0 @ E2 ) @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_705_dtree__from__list__sequence,axiom,
    ! [R0: a,T0: dtree_8545934391348768041od_a_b,E0: list_P1467974523212632366od_a_b,V1: a,Ys: list_P5700792096213675741od_a_b,E1: list_P1467974523212632366od_a_b] :
      ( ( is_sub6704704118884291150od_a_b @ ( node_a6325075177599301358od_a_b @ R0 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T0 @ E0 ) @ bot_bo577854266114829310od_a_b ) ) @ ( dtree_6261964479915675172od_a_b @ V1 @ Ys ) )
     => ? [E2: list_P1467974523212632366od_a_b,As: list_P5700792096213675741od_a_b,Bs: list_P5700792096213675741od_a_b] :
          ( ( append2868893624165880178od_a_b @ As @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ R0 @ E2 ) @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_706_dtree__from__list__sequence,axiom,
    ! [R0: a,T0: dtree_a_b,E0: b,V1: a,Ys: list_P1467974523212632366od_a_b,E1: b] :
      ( ( is_subtree_a_b @ ( node_a_b @ R0 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T0 @ E0 ) @ bot_bo2895716411488905534_a_b_b ) ) @ ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ? [E2: b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
          ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ R0 @ E2 ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T0 ) @ E0 ) @ Bs ) ) )
          = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V1 @ E1 ) @ Ys ) ) ) ).

% dtree_from_list_sequence
thf(fact_707_dtree__from__list__uneq__sequence,axiom,
    ! [R0: product_prod_a_b,T0: dtree_2253494508914376569od_a_b,E0: product_prod_a_b,V1: product_prod_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( is_sub6933245819845350814od_a_b @ ( node_P1936840572307073598od_a_b @ R0 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T0 @ E0 ) @ bot_bo7856883933444951080od_a_b ) ) @ ( dtree_1864022081312108148od_a_b @ V1 @ Ys ) )
     => ( ( ( node_P1936840572307073598od_a_b @ R0 @ ( finser5347476252697843100od_a_b @ ( produc8904365110017546518od_a_b @ T0 @ E0 ) @ bot_bo7856883933444951080od_a_b ) )
         != ( dtree_1864022081312108148od_a_b @ V1 @ Ys ) )
       => ? [E2: product_prod_a_b,As: list_P3463435030753280173od_a_b,Bs: list_P3463435030753280173od_a_b] :
            ( ( append3447563168971123522od_a_b @ As @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ R0 @ E2 ) @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( root_P6595957619955152862od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_708_dtree__from__list__uneq__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_1861073144021109543ee_a_b,E0: dtree_a_b,V1: dtree_a_b,Ys: list_P7294506862534405595ee_a_b] :
      ( ( is_sub7866859304860047124ee_a_b @ ( node_d7487230363575057332ee_a_b @ R0 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T0 @ E0 ) @ bot_bo5711572498106067156ee_a_b ) ) @ ( dtree_7424119665891431146ee_a_b @ V1 @ Ys ) )
     => ( ( ( node_d7487230363575057332ee_a_b @ R0 @ ( finser8516331313445392842ee_a_b @ ( produc2775200505768408122ee_a_b @ T0 @ E0 ) @ bot_bo5711572498106067156ee_a_b ) )
         != ( dtree_7424119665891431146ee_a_b @ V1 @ Ys ) )
       => ? [E2: dtree_a_b,As: list_P7294506862534405595ee_a_b,Bs: list_P7294506862534405595ee_a_b] :
            ( ( append5407404413692997488ee_a_b @ As @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ R0 @ E2 ) @ ( cons_P1798951315401763083ee_a_b @ ( produc7805419539522982029ee_a_b @ ( root_d1746759089207908692ee_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_709_dtree__from__list__uneq__sequence,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_8690448868185853351ee_a_b,E0: dtree_a_b,V1: produc4558475209616630778_a_b_b,Ys: list_P3724575226198589275ee_a_b] :
      ( ( is_sub791308131889186196ee_a_b @ ( node_P2753077162091514420ee_a_b @ R0 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T0 @ E0 ) @ bot_bo3079078458218859348ee_a_b ) ) @ ( dtree_7850083854586231658ee_a_b @ V1 @ Ys ) )
     => ( ( ( node_P2753077162091514420ee_a_b @ R0 @ ( finser7847761039489690442ee_a_b @ ( produc8867760425442229946ee_a_b @ T0 @ E0 ) @ bot_bo3079078458218859348ee_a_b ) )
         != ( dtree_7850083854586231658ee_a_b @ V1 @ Ys ) )
       => ? [E2: dtree_a_b,As: list_P3724575226198589275ee_a_b,Bs: list_P3724575226198589275ee_a_b] :
            ( ( append301462268945678576ee_a_b @ As @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ R0 @ E2 ) @ ( cons_P5264852942667048843ee_a_b @ ( produc2660662345621397005ee_a_b @ ( root_P5553465985260390356ee_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_710_dtree__from__list__uneq__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_8397784528784866983_a_b_b,E0: produc4558475209616630778_a_b_b,V1: dtree_a_b,Ys: list_P7142016109841313883_a_b_b] :
      ( ( is_sub3309389790737183380_a_b_b @ ( node_d5271158820939511604_a_b_b @ R0 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T0 @ E0 ) @ bot_bo1493276529839087060_a_b_b ) ) @ ( dtree_1144793476579453034_a_b_b @ V1 @ Ys ) )
     => ( ( ( node_d5271158820939511604_a_b_b @ R0 @ ( finser5778094437704840394_a_b_b @ ( produc74755587182097722_a_b_b @ T0 @ E0 ) @ bot_bo1493276529839087060_a_b_b ) )
         != ( dtree_1144793476579453034_a_b_b @ V1 @ Ys ) )
       => ? [E2: produc4558475209616630778_a_b_b,As: list_P7142016109841313883_a_b_b,Bs: list_P7142016109841313883_a_b_b] :
            ( ( append8797929544692208_a_b_b @ As @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ R0 @ E2 ) @ ( cons_P4972188603266062475_a_b_b @ ( produc5178744004469394189_a_b_b @ ( root_d8071547644108387540_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_711_dtree__from__list__uneq__sequence,axiom,
    ! [R0: produc4558475209616630778_a_b_b,T0: dtree_6636540493345571111_a_b_b,E0: produc4558475209616630778_a_b_b,V1: produc4558475209616630778_a_b_b,Ys: list_P7924273279524553179_a_b_b] :
      ( ( is_sub6703628162287821076_a_b_b @ ( node_P961815112480277940_a_b_b @ R0 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T0 @ E0 ) @ bot_bo6312180378851360852_a_b_b ) ) @ ( dtree_450453658713739498_a_b_b @ V1 @ Ys ) )
     => ( ( ( node_P961815112480277940_a_b_b @ R0 @ ( finser3407669804807474762_a_b_b @ ( produc6281861845666676666_a_b_b @ T0 @ E0 ) @ bot_bo6312180378851360852_a_b_b ) )
         != ( dtree_450453658713739498_a_b_b @ V1 @ Ys ) )
       => ? [E2: produc4558475209616630778_a_b_b,As: list_P7924273279524553179_a_b_b,Bs: list_P7924273279524553179_a_b_b] :
            ( ( append7918683371861672816_a_b_b @ As @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ R0 @ E2 ) @ ( cons_P9068067167194404619_a_b_b @ ( produc6533307410877503629_a_b_b @ ( root_P204151722342556500_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_712_dtree__from__list__uneq__sequence,axiom,
    ! [R0: dtree_a_b,T0: dtree_dtree_a_b_b,E0: b,V1: dtree_a_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( is_sub2776994699154135781_a_b_b @ ( node_dtree_a_b_b @ R0 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T0 @ E0 ) @ bot_bo4737202254184417232_b_b_b ) ) @ ( dtree_5255521609252960911_a_b_b @ V1 @ Ys ) )
     => ( ( ( node_dtree_a_b_b @ R0 @ ( finser6734551996811508806_b_b_b @ ( produc3612315917713105134_b_b_b @ T0 @ E0 ) @ bot_bo4737202254184417232_b_b_b ) )
         != ( dtree_5255521609252960911_a_b_b @ V1 @ Ys ) )
       => ? [E2: b,As: list_P5360711134766023690_a_b_b,Bs: list_P5360711134766023690_a_b_b] :
            ( ( append86853766581025439_a_b_b @ As @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ R0 @ E2 ) @ ( cons_P2785074014425598660_a_b_b @ ( produc331601717337510060_a_b_b @ ( root_dtree_a_b_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_713_dtree__from__list__uneq__sequence,axiom,
    ! [R0: list_P1467974523212632366od_a_b,T0: dtree_5519289247442030201od_a_b,E0: list_P1467974523212632366od_a_b,V1: list_P1467974523212632366od_a_b,Ys: list_P8601282865932132013od_a_b] :
      ( ( is_sub3969663741311890846od_a_b @ ( node_l1136085673055119934od_a_b @ R0 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T0 @ E0 ) @ bot_bo2863178955461725870od_a_b ) ) @ ( dtree_6507962483783174260od_a_b @ V1 @ Ys ) )
     => ( ( ( node_l1136085673055119934od_a_b @ R0 @ ( finser4916530145793648802od_a_b @ ( produc101167938378516380od_a_b @ T0 @ E0 ) @ bot_bo2863178955461725870od_a_b ) )
         != ( dtree_6507962483783174260od_a_b @ V1 @ Ys ) )
       => ? [E2: list_P1467974523212632366od_a_b,As: list_P8601282865932132013od_a_b,Bs: list_P8601282865932132013od_a_b] :
            ( ( append5385366555182926146od_a_b @ As @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ R0 @ E2 ) @ ( cons_P1529385591390545501od_a_b @ ( produc5288560138351607191od_a_b @ ( root_l2497086882398443486od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_714_dtree__from__list__uneq__sequence,axiom,
    ! [R0: product_prod_a_b > product_prod_a_b > $o,T0: dtree_8339642294131873593od_a_b,E0: list_P1467974523212632366od_a_b,V1: product_prod_a_b > product_prod_a_b > $o,Ys: list_P8094385941167427565od_a_b] :
      ( ( is_sub9145550046624671838od_a_b @ ( node_P5897935084763704574od_a_b @ R0 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T0 @ E0 ) @ bot_bo137739038786217454od_a_b ) ) @ ( dtree_4383916385682046516od_a_b @ V1 @ Ys ) )
     => ( ( ( node_P5897935084763704574od_a_b @ R0 @ ( finser4631589853810920290od_a_b @ ( produc3171423612928471772od_a_b @ T0 @ E0 ) @ bot_bo137739038786217454od_a_b ) )
         != ( dtree_4383916385682046516od_a_b @ V1 @ Ys ) )
       => ? [E2: list_P1467974523212632366od_a_b,As: list_P8094385941167427565od_a_b,Bs: list_P8094385941167427565od_a_b] :
            ( ( append2461588412122937986od_a_b @ As @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ R0 @ E2 ) @ ( cons_P3561991119763190045od_a_b @ ( produc7704224619955794135od_a_b @ ( root_P7917853640449190558od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_715_dtree__from__list__uneq__sequence,axiom,
    ! [R0: a,T0: dtree_8545934391348768041od_a_b,E0: list_P1467974523212632366od_a_b,V1: a,Ys: list_P5700792096213675741od_a_b] :
      ( ( is_sub6704704118884291150od_a_b @ ( node_a6325075177599301358od_a_b @ R0 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T0 @ E0 ) @ bot_bo577854266114829310od_a_b ) ) @ ( dtree_6261964479915675172od_a_b @ V1 @ Ys ) )
     => ( ( ( node_a6325075177599301358od_a_b @ R0 @ ( finser2699324603737210994od_a_b @ ( produc8281931372741142764od_a_b @ T0 @ E0 ) @ bot_bo577854266114829310od_a_b ) )
         != ( dtree_6261964479915675172od_a_b @ V1 @ Ys ) )
       => ? [E2: list_P1467974523212632366od_a_b,As: list_P5700792096213675741od_a_b,Bs: list_P5700792096213675741od_a_b] :
            ( ( append2868893624165880178od_a_b @ As @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ R0 @ E2 ) @ ( cons_P8483812562729421581od_a_b @ ( produc6643264353547226055od_a_b @ ( root_a584603903232152718od_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_716_dtree__from__list__uneq__sequence,axiom,
    ! [R0: a,T0: dtree_a_b,E0: b,V1: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( is_subtree_a_b @ ( node_a_b @ R0 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T0 @ E0 ) @ bot_bo2895716411488905534_a_b_b ) ) @ ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ( ( ( node_a_b @ R0 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T0 @ E0 ) @ bot_bo2895716411488905534_a_b_b ) )
         != ( dtree_from_list_a_b @ V1 @ Ys ) )
       => ? [E2: b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
            ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ R0 @ E2 ) @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ ( root_a_b @ T0 ) @ E0 ) @ Bs ) ) )
            = Ys ) ) ) ).

% dtree_from_list_uneq_sequence
thf(fact_717_inf_Oidem,axiom,
    ! [A: set_a] :
      ( ( inf_inf_set_a @ A @ A )
      = A ) ).

% inf.idem
thf(fact_718_inf_Oidem,axiom,
    ! [A: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A @ A )
      = A ) ).

% inf.idem
thf(fact_719_inf_Oidem,axiom,
    ! [A: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A @ A )
      = A ) ).

% inf.idem
thf(fact_720_inf_Oidem,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ A @ A )
      = A ) ).

% inf.idem
thf(fact_721_inf_Oidem,axiom,
    ! [A: set_b] :
      ( ( inf_inf_set_b @ A @ A )
      = A ) ).

% inf.idem
thf(fact_722_inf__idem,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_723_inf__idem,axiom,
    ! [X3: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_724_inf__idem,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_725_inf__idem,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_726_inf__idem,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ X3 @ X3 )
      = X3 ) ).

% inf_idem
thf(fact_727_inf_Oleft__idem,axiom,
    ! [A: set_a,B: set_a] :
      ( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
      = ( inf_inf_set_a @ A @ B ) ) ).

% inf.left_idem
thf(fact_728_inf_Oleft__idem,axiom,
    ! [A: set_dtree_a_b,B: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ A @ ( inf_in5903708963019302594ee_a_b @ A @ B ) )
      = ( inf_in5903708963019302594ee_a_b @ A @ B ) ) ).

% inf.left_idem
thf(fact_729_inf_Oleft__idem,axiom,
    ! [A: set_Pr3012420139608375472_a_b_b,B: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ A @ B ) )
      = ( inf_in6138156342456174402_a_b_b @ A @ B ) ) ).

% inf.left_idem
thf(fact_730_inf_Oleft__idem,axiom,
    ! [A: fset_P5281107635120001194_a_b_b,B: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ A @ B ) )
      = ( inf_in7138637532943773244_a_b_b @ A @ B ) ) ).

% inf.left_idem
thf(fact_731_inf_Oleft__idem,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
      = ( inf_inf_set_b @ A @ B ) ) ).

% inf.left_idem
thf(fact_732_inf__right__idem,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ X3 @ Y ) @ Y )
      = ( inf_inf_set_a @ X3 @ Y ) ) ).

% inf_right_idem
thf(fact_733_inf__right__idem,axiom,
    ! [X3: set_dtree_a_b,Y: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ ( inf_in5903708963019302594ee_a_b @ X3 @ Y ) @ Y )
      = ( inf_in5903708963019302594ee_a_b @ X3 @ Y ) ) ).

% inf_right_idem
thf(fact_734_inf__right__idem,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b,Y: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ ( inf_in6138156342456174402_a_b_b @ X3 @ Y ) @ Y )
      = ( inf_in6138156342456174402_a_b_b @ X3 @ Y ) ) ).

% inf_right_idem
thf(fact_735_inf__right__idem,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ ( inf_in7138637532943773244_a_b_b @ X3 @ Y ) @ Y )
      = ( inf_in7138637532943773244_a_b_b @ X3 @ Y ) ) ).

% inf_right_idem
thf(fact_736_inf__right__idem,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ X3 @ Y ) @ Y )
      = ( inf_inf_set_b @ X3 @ Y ) ) ).

% inf_right_idem
thf(fact_737_inf_Oright__idem,axiom,
    ! [A: set_a,B: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
      = ( inf_inf_set_a @ A @ B ) ) ).

% inf.right_idem
thf(fact_738_inf_Oright__idem,axiom,
    ! [A: set_dtree_a_b,B: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ ( inf_in5903708963019302594ee_a_b @ A @ B ) @ B )
      = ( inf_in5903708963019302594ee_a_b @ A @ B ) ) ).

% inf.right_idem
thf(fact_739_inf_Oright__idem,axiom,
    ! [A: set_Pr3012420139608375472_a_b_b,B: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ ( inf_in6138156342456174402_a_b_b @ A @ B ) @ B )
      = ( inf_in6138156342456174402_a_b_b @ A @ B ) ) ).

% inf.right_idem
thf(fact_740_inf_Oright__idem,axiom,
    ! [A: fset_P5281107635120001194_a_b_b,B: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ ( inf_in7138637532943773244_a_b_b @ A @ B ) @ B )
      = ( inf_in7138637532943773244_a_b_b @ A @ B ) ) ).

% inf.right_idem
thf(fact_741_inf_Oright__idem,axiom,
    ! [A: set_b,B: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
      = ( inf_inf_set_b @ A @ B ) ) ).

% inf.right_idem
thf(fact_742_inf__left__idem,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( inf_inf_set_a @ X3 @ ( inf_inf_set_a @ X3 @ Y ) )
      = ( inf_inf_set_a @ X3 @ Y ) ) ).

% inf_left_idem
thf(fact_743_inf__left__idem,axiom,
    ! [X3: set_dtree_a_b,Y: set_dtree_a_b] :
      ( ( inf_in5903708963019302594ee_a_b @ X3 @ ( inf_in5903708963019302594ee_a_b @ X3 @ Y ) )
      = ( inf_in5903708963019302594ee_a_b @ X3 @ Y ) ) ).

% inf_left_idem
thf(fact_744_inf__left__idem,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b,Y: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ X3 @ ( inf_in6138156342456174402_a_b_b @ X3 @ Y ) )
      = ( inf_in6138156342456174402_a_b_b @ X3 @ Y ) ) ).

% inf_left_idem
thf(fact_745_inf__left__idem,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ X3 @ ( inf_in7138637532943773244_a_b_b @ X3 @ Y ) )
      = ( inf_in7138637532943773244_a_b_b @ X3 @ Y ) ) ).

% inf_left_idem
thf(fact_746_inf__left__idem,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( inf_inf_set_b @ X3 @ ( inf_inf_set_b @ X3 @ Y ) )
      = ( inf_inf_set_b @ X3 @ Y ) ) ).

% inf_left_idem
thf(fact_747_append_Oassoc,axiom,
    ! [A: list_P1467974523212632366od_a_b,B: list_P1467974523212632366od_a_b,C: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ ( append5335208823350062147od_a_b @ A @ B ) @ C )
      = ( append5335208823350062147od_a_b @ A @ ( append5335208823350062147od_a_b @ B @ C ) ) ) ).

% append.assoc
thf(fact_748_append_Oassoc,axiom,
    ! [A: list_P3463435030753280173od_a_b,B: list_P3463435030753280173od_a_b,C: list_P3463435030753280173od_a_b] :
      ( ( append3447563168971123522od_a_b @ ( append3447563168971123522od_a_b @ A @ B ) @ C )
      = ( append3447563168971123522od_a_b @ A @ ( append3447563168971123522od_a_b @ B @ C ) ) ) ).

% append.assoc
thf(fact_749_append_Oassoc,axiom,
    ! [A: list_dtree_a_b,B: list_dtree_a_b,C: list_dtree_a_b] :
      ( ( append_dtree_a_b @ ( append_dtree_a_b @ A @ B ) @ C )
      = ( append_dtree_a_b @ A @ ( append_dtree_a_b @ B @ C ) ) ) ).

% append.assoc
thf(fact_750_append_Oassoc,axiom,
    ! [A: list_P5360711134766023690_a_b_b,B: list_P5360711134766023690_a_b_b,C: list_P5360711134766023690_a_b_b] :
      ( ( append86853766581025439_a_b_b @ ( append86853766581025439_a_b_b @ A @ B ) @ C )
      = ( append86853766581025439_a_b_b @ A @ ( append86853766581025439_a_b_b @ B @ C ) ) ) ).

% append.assoc
thf(fact_751_append__assoc,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) @ Zs )
      = ( append5335208823350062147od_a_b @ Xs @ ( append5335208823350062147od_a_b @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_752_append__assoc,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b,Zs: list_P3463435030753280173od_a_b] :
      ( ( append3447563168971123522od_a_b @ ( append3447563168971123522od_a_b @ Xs @ Ys ) @ Zs )
      = ( append3447563168971123522od_a_b @ Xs @ ( append3447563168971123522od_a_b @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_753_append__assoc,axiom,
    ! [Xs: list_dtree_a_b,Ys: list_dtree_a_b,Zs: list_dtree_a_b] :
      ( ( append_dtree_a_b @ ( append_dtree_a_b @ Xs @ Ys ) @ Zs )
      = ( append_dtree_a_b @ Xs @ ( append_dtree_a_b @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_754_append__assoc,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b,Zs: list_P5360711134766023690_a_b_b] :
      ( ( append86853766581025439_a_b_b @ ( append86853766581025439_a_b_b @ Xs @ Ys ) @ Zs )
      = ( append86853766581025439_a_b_b @ Xs @ ( append86853766581025439_a_b_b @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_755_append__same__eq,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Ys @ Xs )
        = ( append5335208823350062147od_a_b @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_756_append__same__eq,axiom,
    ! [Ys: list_P3463435030753280173od_a_b,Xs: list_P3463435030753280173od_a_b,Zs: list_P3463435030753280173od_a_b] :
      ( ( ( append3447563168971123522od_a_b @ Ys @ Xs )
        = ( append3447563168971123522od_a_b @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_757_append__same__eq,axiom,
    ! [Ys: list_dtree_a_b,Xs: list_dtree_a_b,Zs: list_dtree_a_b] :
      ( ( ( append_dtree_a_b @ Ys @ Xs )
        = ( append_dtree_a_b @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_758_append__same__eq,axiom,
    ! [Ys: list_P5360711134766023690_a_b_b,Xs: list_P5360711134766023690_a_b_b,Zs: list_P5360711134766023690_a_b_b] :
      ( ( ( append86853766581025439_a_b_b @ Ys @ Xs )
        = ( append86853766581025439_a_b_b @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_759_same__append__eq,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ Ys )
        = ( append5335208823350062147od_a_b @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_760_same__append__eq,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b,Zs: list_P3463435030753280173od_a_b] :
      ( ( ( append3447563168971123522od_a_b @ Xs @ Ys )
        = ( append3447563168971123522od_a_b @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_761_same__append__eq,axiom,
    ! [Xs: list_dtree_a_b,Ys: list_dtree_a_b,Zs: list_dtree_a_b] :
      ( ( ( append_dtree_a_b @ Xs @ Ys )
        = ( append_dtree_a_b @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_762_same__append__eq,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b,Zs: list_P5360711134766023690_a_b_b] :
      ( ( ( append86853766581025439_a_b_b @ Xs @ Ys )
        = ( append86853766581025439_a_b_b @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_763_finsert__inter__finsert,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ A2 ) @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
      = ( finser8437519239679886002_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ A2 @ B4 ) ) ) ).

% finsert_inter_finsert
thf(fact_764_append__is__Nil__conv,axiom,
    ! [Xs: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( ( append7557446516274476873od_a_b @ Xs @ Ys )
        = nil_li8635777946366267444od_a_b )
      = ( ( Xs = nil_li8635777946366267444od_a_b )
        & ( Ys = nil_li8635777946366267444od_a_b ) ) ) ).

% append_is_Nil_conv
thf(fact_765_append__is__Nil__conv,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( ( append3447563168971123522od_a_b @ Xs @ Ys )
        = nil_Pr906174322249854893od_a_b )
      = ( ( Xs = nil_Pr906174322249854893od_a_b )
        & ( Ys = nil_Pr906174322249854893od_a_b ) ) ) ).

% append_is_Nil_conv
thf(fact_766_append__is__Nil__conv,axiom,
    ! [Xs: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( ( append_dtree_a_b @ Xs @ Ys )
        = nil_dtree_a_b )
      = ( ( Xs = nil_dtree_a_b )
        & ( Ys = nil_dtree_a_b ) ) ) ).

% append_is_Nil_conv
thf(fact_767_append__is__Nil__conv,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( append86853766581025439_a_b_b @ Xs @ Ys )
        = nil_Pr5403147374433350260_a_b_b )
      = ( ( Xs = nil_Pr5403147374433350260_a_b_b )
        & ( Ys = nil_Pr5403147374433350260_a_b_b ) ) ) ).

% append_is_Nil_conv
thf(fact_768_append__is__Nil__conv,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ Ys )
        = nil_Product_prod_a_b )
      = ( ( Xs = nil_Product_prod_a_b )
        & ( Ys = nil_Product_prod_a_b ) ) ) ).

% append_is_Nil_conv
thf(fact_769_Nil__is__append__conv,axiom,
    ! [Xs: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( nil_li8635777946366267444od_a_b
        = ( append7557446516274476873od_a_b @ Xs @ Ys ) )
      = ( ( Xs = nil_li8635777946366267444od_a_b )
        & ( Ys = nil_li8635777946366267444od_a_b ) ) ) ).

% Nil_is_append_conv
thf(fact_770_Nil__is__append__conv,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( nil_Pr906174322249854893od_a_b
        = ( append3447563168971123522od_a_b @ Xs @ Ys ) )
      = ( ( Xs = nil_Pr906174322249854893od_a_b )
        & ( Ys = nil_Pr906174322249854893od_a_b ) ) ) ).

% Nil_is_append_conv
thf(fact_771_Nil__is__append__conv,axiom,
    ! [Xs: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( nil_dtree_a_b
        = ( append_dtree_a_b @ Xs @ Ys ) )
      = ( ( Xs = nil_dtree_a_b )
        & ( Ys = nil_dtree_a_b ) ) ) ).

% Nil_is_append_conv
thf(fact_772_Nil__is__append__conv,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( nil_Pr5403147374433350260_a_b_b
        = ( append86853766581025439_a_b_b @ Xs @ Ys ) )
      = ( ( Xs = nil_Pr5403147374433350260_a_b_b )
        & ( Ys = nil_Pr5403147374433350260_a_b_b ) ) ) ).

% Nil_is_append_conv
thf(fact_773_Nil__is__append__conv,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( nil_Product_prod_a_b
        = ( append5335208823350062147od_a_b @ Xs @ Ys ) )
      = ( ( Xs = nil_Product_prod_a_b )
        & ( Ys = nil_Product_prod_a_b ) ) ) ).

% Nil_is_append_conv
thf(fact_774_self__append__conv2,axiom,
    ! [Y: list_l8778361445553822004od_a_b,Xs: list_l8778361445553822004od_a_b] :
      ( ( Y
        = ( append7557446516274476873od_a_b @ Xs @ Y ) )
      = ( Xs = nil_li8635777946366267444od_a_b ) ) ).

% self_append_conv2
thf(fact_775_self__append__conv2,axiom,
    ! [Y: list_P3463435030753280173od_a_b,Xs: list_P3463435030753280173od_a_b] :
      ( ( Y
        = ( append3447563168971123522od_a_b @ Xs @ Y ) )
      = ( Xs = nil_Pr906174322249854893od_a_b ) ) ).

% self_append_conv2
thf(fact_776_self__append__conv2,axiom,
    ! [Y: list_dtree_a_b,Xs: list_dtree_a_b] :
      ( ( Y
        = ( append_dtree_a_b @ Xs @ Y ) )
      = ( Xs = nil_dtree_a_b ) ) ).

% self_append_conv2
thf(fact_777_self__append__conv2,axiom,
    ! [Y: list_P5360711134766023690_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( Y
        = ( append86853766581025439_a_b_b @ Xs @ Y ) )
      = ( Xs = nil_Pr5403147374433350260_a_b_b ) ) ).

% self_append_conv2
thf(fact_778_self__append__conv2,axiom,
    ! [Y: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( Y
        = ( append5335208823350062147od_a_b @ Xs @ Y ) )
      = ( Xs = nil_Product_prod_a_b ) ) ).

% self_append_conv2
thf(fact_779_append__self__conv2,axiom,
    ! [Xs: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( ( append7557446516274476873od_a_b @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_li8635777946366267444od_a_b ) ) ).

% append_self_conv2
thf(fact_780_append__self__conv2,axiom,
    ! [Xs: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( ( append3447563168971123522od_a_b @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_Pr906174322249854893od_a_b ) ) ).

% append_self_conv2
thf(fact_781_append__self__conv2,axiom,
    ! [Xs: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( ( append_dtree_a_b @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_dtree_a_b ) ) ).

% append_self_conv2
thf(fact_782_append__self__conv2,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( append86853766581025439_a_b_b @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_Pr5403147374433350260_a_b_b ) ) ).

% append_self_conv2
thf(fact_783_append__self__conv2,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_Product_prod_a_b ) ) ).

% append_self_conv2
thf(fact_784_self__append__conv,axiom,
    ! [Y: list_l8778361445553822004od_a_b,Ys: list_l8778361445553822004od_a_b] :
      ( ( Y
        = ( append7557446516274476873od_a_b @ Y @ Ys ) )
      = ( Ys = nil_li8635777946366267444od_a_b ) ) ).

% self_append_conv
thf(fact_785_self__append__conv,axiom,
    ! [Y: list_P3463435030753280173od_a_b,Ys: list_P3463435030753280173od_a_b] :
      ( ( Y
        = ( append3447563168971123522od_a_b @ Y @ Ys ) )
      = ( Ys = nil_Pr906174322249854893od_a_b ) ) ).

% self_append_conv
thf(fact_786_self__append__conv,axiom,
    ! [Y: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( Y
        = ( append_dtree_a_b @ Y @ Ys ) )
      = ( Ys = nil_dtree_a_b ) ) ).

% self_append_conv
thf(fact_787_self__append__conv,axiom,
    ! [Y: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( Y
        = ( append86853766581025439_a_b_b @ Y @ Ys ) )
      = ( Ys = nil_Pr5403147374433350260_a_b_b ) ) ).

% self_append_conv
thf(fact_788_self__append__conv,axiom,
    ! [Y: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( Y
        = ( append5335208823350062147od_a_b @ Y @ Ys ) )
      = ( Ys = nil_Product_prod_a_b ) ) ).

% self_append_conv
thf(fact_789_append__self__conv,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( append86853766581025439_a_b_b @ Xs @ Ys )
        = Xs )
      = ( Ys = nil_Pr5403147374433350260_a_b_b ) ) ).

% append_self_conv
thf(fact_790_append__self__conv,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ Ys )
        = Xs )
      = ( Ys = nil_Product_prod_a_b ) ) ).

% append_self_conv
thf(fact_791_append__Nil2,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ Xs @ nil_Product_prod_a_b )
      = Xs ) ).

% append_Nil2
thf(fact_792_append_Oright__neutral,axiom,
    ! [A: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ A @ nil_Product_prod_a_b )
      = A ) ).

% append.right_neutral
thf(fact_793_inter__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( inf_in7138637532943773244_a_b_b @ X3 @ Xa ) )
      = ( inf_in6138156342456174402_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa ) ) ) ).

% inter_fset
thf(fact_794_append1__eq__conv,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b,Ys: list_P1467974523212632366od_a_b,Y: product_prod_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) )
        = ( append5335208823350062147od_a_b @ Ys @ ( cons_P7316939131009794654od_a_b @ Y @ nil_Product_prod_a_b ) ) )
      = ( ( Xs = Ys )
        & ( X3 = Y ) ) ) ).

% append1_eq_conv
thf(fact_795_eq__Nil__appendI,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( Xs = Ys )
     => ( Xs
        = ( append5335208823350062147od_a_b @ nil_Product_prod_a_b @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_796_append_Oleft__neutral,axiom,
    ! [A: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ nil_Product_prod_a_b @ A )
      = A ) ).

% append.left_neutral
thf(fact_797_append__Nil,axiom,
    ! [Ys: list_P1467974523212632366od_a_b] :
      ( ( append5335208823350062147od_a_b @ nil_Product_prod_a_b @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_798_finter__fempty__right,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ A2 @ bot_bo2895716411488905534_a_b_b )
      = bot_bo2895716411488905534_a_b_b ) ).

% finter_fempty_right
thf(fact_799_finter__fempty__left,axiom,
    ! [B4: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ bot_bo2895716411488905534_a_b_b @ B4 )
      = bot_bo2895716411488905534_a_b_b ) ).

% finter_fempty_left
thf(fact_800_rev__induct,axiom,
    ! [P: list_P1467974523212632366od_a_b > $o,Xs: list_P1467974523212632366od_a_b] :
      ( ( P @ nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
            ( ( P @ Xs2 )
           => ( P @ ( append5335208823350062147od_a_b @ Xs2 @ ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_801_rev__exhaust,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ~ ! [Ys3: list_P1467974523212632366od_a_b,Y3: product_prod_a_b] :
            ( Xs
           != ( append5335208823350062147od_a_b @ Ys3 @ ( cons_P7316939131009794654od_a_b @ Y3 @ nil_Product_prod_a_b ) ) ) ) ).

% rev_exhaust
thf(fact_802_Cons__eq__append__conv,axiom,
    ! [X3: product_prod_a_b,Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b] :
      ( ( ( cons_P7316939131009794654od_a_b @ X3 @ Xs )
        = ( append5335208823350062147od_a_b @ Ys @ Zs ) )
      = ( ( ( Ys = nil_Product_prod_a_b )
          & ( ( cons_P7316939131009794654od_a_b @ X3 @ Xs )
            = Zs ) )
        | ? [Ys4: list_P1467974523212632366od_a_b] :
            ( ( ( cons_P7316939131009794654od_a_b @ X3 @ Ys4 )
              = Ys )
            & ( Xs
              = ( append5335208823350062147od_a_b @ Ys4 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_803_append__eq__Cons__conv,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Zs: list_P1467974523212632366od_a_b,X3: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Ys @ Zs )
        = ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
      = ( ( ( Ys = nil_Product_prod_a_b )
          & ( Zs
            = ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) ) )
        | ? [Ys4: list_P1467974523212632366od_a_b] :
            ( ( Ys
              = ( cons_P7316939131009794654od_a_b @ X3 @ Ys4 ) )
            & ( ( append5335208823350062147od_a_b @ Ys4 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_804_rev__nonempty__induct,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,P: list_P1467974523212632366od_a_b > $o] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ! [X2: product_prod_a_b] : ( P @ ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) )
       => ( ! [X2: product_prod_a_b,Xs2: list_P1467974523212632366od_a_b] :
              ( ( Xs2 != nil_Product_prod_a_b )
             => ( ( P @ Xs2 )
               => ( P @ ( append5335208823350062147od_a_b @ Xs2 @ ( cons_P7316939131009794654od_a_b @ X2 @ nil_Product_prod_a_b ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_805_dtree__from__list__sequence__xs,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V1: a,Ys: list_P1467974523212632366od_a_b,E1: b] :
      ( ( is_subtree_a_b @ ( node_a_b @ R @ Xs ) @ ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ? [E2: b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
          ( ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ R @ E2 ) @ Bs ) )
            = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V1 @ E1 ) @ Ys ) )
          & ( ( node_a_b @ R @ Xs )
            = ( dtree_from_list_a_b @ R @ Bs ) ) ) ) ).

% dtree_from_list_sequence_xs
thf(fact_806_dtree__from__list__uneq__sequence__xs,axiom,
    ! [R0: a,Xs0: fset_P5281107635120001194_a_b_b,V1: a,Ys: list_P1467974523212632366od_a_b] :
      ( ( strict_subtree_a_b @ ( node_a_b @ R0 @ Xs0 ) @ ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ? [E2: b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
          ( ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ R0 @ E2 ) @ Bs ) )
            = Ys )
          & ( ( node_a_b @ R0 @ Xs0 )
            = ( dtree_from_list_a_b @ R0 @ Bs ) ) ) ) ).

% dtree_from_list_uneq_sequence_xs
thf(fact_807_bot__empty__eq,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X4: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X4 @ bot_bo3721250822024684356_a_b_b ) ) ) ).

% bot_empty_eq
thf(fact_808_bot__empty__eq,axiom,
    ( bot_bot_dtree_a_b_o
    = ( ^ [X4: dtree_a_b] : ( member_dtree_a_b @ X4 @ bot_bo8730652382759064772ee_a_b ) ) ) ).

% bot_empty_eq
thf(fact_809_disjoint__darcs__if__wf__aux2,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T22: dtree_a_b,E22: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T22 @ E22 ) )
           => ( ( inf_inf_set_b @ ( darcs_a_b @ T1 ) @ ( darcs_a_b @ T22 ) )
              = bot_bot_set_b ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux2
thf(fact_810_vwalk__arcs__Cons,axiom,
    ! [P2: list_P1467974523212632366od_a_b,U2: product_prod_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( vertex3879532237292798496od_a_b @ ( cons_P7316939131009794654od_a_b @ U2 @ P2 ) )
        = ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ U2 @ ( hd_Product_prod_a_b @ P2 ) ) @ ( vertex3879532237292798496od_a_b @ P2 ) ) ) ) ).

% vwalk_arcs_Cons
thf(fact_811_bind__simps_I1_J,axiom,
    ! [F2: product_prod_a_b > list_P1467974523212632366od_a_b] :
      ( ( bind_P7003926910255595655od_a_b @ nil_Product_prod_a_b @ F2 )
      = nil_Product_prod_a_b ) ).

% bind_simps(1)
thf(fact_812_hd__append2,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ( hd_Product_prod_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
        = ( hd_Product_prod_a_b @ Xs ) ) ) ).

% hd_append2
thf(fact_813_longest__common__prefix,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
    ? [Ps: list_P1467974523212632366od_a_b,Xs3: list_P1467974523212632366od_a_b,Ys5: list_P1467974523212632366od_a_b] :
      ( ( Xs
        = ( append5335208823350062147od_a_b @ Ps @ Xs3 ) )
      & ( Ys
        = ( append5335208823350062147od_a_b @ Ps @ Ys5 ) )
      & ( ( Xs3 = nil_Product_prod_a_b )
        | ( Ys5 = nil_Product_prod_a_b )
        | ( ( hd_Product_prod_a_b @ Xs3 )
         != ( hd_Product_prod_a_b @ Ys5 ) ) ) ) ).

% longest_common_prefix
thf(fact_814_hd__append,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( Xs = nil_Product_prod_a_b )
       => ( ( hd_Product_prod_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( hd_Product_prod_a_b @ Ys ) ) )
      & ( ( Xs != nil_Product_prod_a_b )
       => ( ( hd_Product_prod_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( hd_Product_prod_a_b @ Xs ) ) ) ) ).

% hd_append
thf(fact_815_dtree_Oset__intros_I3_J,axiom,
    ! [Ye: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Yf: dtree_a_b,Yh: b,X1: a] :
      ( ( member4380921116106875537_a_b_b @ Ye @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_dtree_a_b @ Yf @ ( basic_7578771248400840636_a_b_b @ Ye ) )
       => ( ( member_b @ Yh @ ( darcs_a_b @ Yf ) )
         => ( member_b @ Yh @ ( darcs_a_b @ ( node_a_b @ X1 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(3)
thf(fact_816_dtree_Oset__sel_I3_J,axiom,
    ! [Xe: produc4558475209616630778_a_b_b,A: dtree_a_b,Xf: dtree_a_b,Xh: b] :
      ( ( member4380921116106875537_a_b_b @ Xe @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_dtree_a_b @ Xf @ ( basic_7578771248400840636_a_b_b @ Xe ) )
       => ( ( member_b @ Xh @ ( darcs_a_b @ Xf ) )
         => ( member_b @ Xh @ ( darcs_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(3)
thf(fact_817_disjoint__darcs__if__wf__aux1,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ~ ( member_b @ E1 @ ( darcs_a_b @ T1 ) ) ) ) ).

% disjoint_darcs_if_wf_aux1
thf(fact_818_disjoint__darcs__if__wf__aux3,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T22: dtree_a_b,E22: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ~ ( member_b @ E22 @ ( darcs_a_b @ T1 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux3
thf(fact_819_vwalk__arcs__append,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( Q2 != nil_Product_prod_a_b )
       => ( ( vertex3879532237292798496od_a_b @ ( append5335208823350062147od_a_b @ P2 @ Q2 ) )
          = ( append3447563168971123522od_a_b @ ( vertex3879532237292798496od_a_b @ P2 ) @ ( cons_P8222935586017696605od_a_b @ ( produc6550459592057863831od_a_b @ ( last_P8790725272581694279od_a_b @ P2 ) @ ( hd_Product_prod_a_b @ Q2 ) ) @ ( vertex3879532237292798496od_a_b @ Q2 ) ) ) ) ) ) ).

% vwalk_arcs_append
thf(fact_820_dtree_Oset__cases_I2_J,axiom,
    ! [E: b,A: dtree_a_b] :
      ( ( member_b @ E @ ( darcs_a_b @ A ) )
     => ( ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
            ( ( A
              = ( node_a_b @ Z1 @ Z2 ) )
           => ! [X2: produc4558475209616630778_a_b_b] :
                ( ( member4380921116106875537_a_b_b @ X2 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
               => ! [Xa2: dtree_a_b] :
                    ( ( member_dtree_a_b @ Xa2 @ ( basic_7578771248400840636_a_b_b @ X2 ) )
                   => ~ ( member_b @ E @ ( darcs_a_b @ Xa2 ) ) ) ) )
       => ~ ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
              ( ( A
                = ( node_a_b @ Z1 @ Z2 ) )
             => ! [X2: produc4558475209616630778_a_b_b] :
                  ( ( member4380921116106875537_a_b_b @ X2 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
                 => ~ ( member_b @ E @ ( basic_1877077703026942_a_b_b @ X2 ) ) ) ) ) ) ).

% dtree.set_cases(2)
thf(fact_821_snoc__listrel1__snoc__iff,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b,Ys: list_P1467974523212632366od_a_b,Y: product_prod_a_b,R: set_Pr5493900063595384711od_a_b] :
      ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ ( append5335208823350062147od_a_b @ Xs @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) @ ( append5335208823350062147od_a_b @ Ys @ ( cons_P7316939131009794654od_a_b @ Y @ nil_Product_prod_a_b ) ) ) @ ( listre2955263632500257159od_a_b @ R ) )
      = ( ( ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Xs @ Ys ) @ ( listre2955263632500257159od_a_b @ R ) )
          & ( X3 = Y ) )
        | ( ( Xs = Ys )
          & ( member5065438833300252112od_a_b @ ( produc6550459592057863831od_a_b @ X3 @ Y ) @ R ) ) ) ) ).

% snoc_listrel1_snoc_iff
thf(fact_822_last__appendL,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( Ys = nil_Product_prod_a_b )
     => ( ( last_P8790725272581694279od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
        = ( last_P8790725272581694279od_a_b @ Xs ) ) ) ).

% last_appendL
thf(fact_823_last__appendR,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( Ys != nil_Product_prod_a_b )
     => ( ( last_P8790725272581694279od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
        = ( last_P8790725272581694279od_a_b @ Ys ) ) ) ).

% last_appendR
thf(fact_824_last__snoc,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( last_P8790725272581694279od_a_b @ ( append5335208823350062147od_a_b @ Xs @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) )
      = X3 ) ).

% last_snoc
thf(fact_825_bot_Onot__eq__extremum,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( A != bot_bo2895716411488905534_a_b_b )
      = ( ord_le7001451600920047870_a_b_b @ bot_bo2895716411488905534_a_b_b @ A ) ) ).

% bot.not_eq_extremum
thf(fact_826_bot_Oextremum__strict,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ~ ( ord_le7001451600920047870_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ).

% bot.extremum_strict
thf(fact_827_last_Osimps,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( ( Xs = nil_Product_prod_a_b )
       => ( ( last_P8790725272581694279od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
          = X3 ) )
      & ( ( Xs != nil_Product_prod_a_b )
       => ( ( last_P8790725272581694279od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
          = ( last_P8790725272581694279od_a_b @ Xs ) ) ) ) ).

% last.simps
thf(fact_828_last__ConsL,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( Xs = nil_Product_prod_a_b )
     => ( ( last_P8790725272581694279od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
        = X3 ) ) ).

% last_ConsL
thf(fact_829_last__ConsR,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ( last_P8790725272581694279od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
        = ( last_P8790725272581694279od_a_b @ Xs ) ) ) ).

% last_ConsR
thf(fact_830_last__append,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( ( Ys = nil_Product_prod_a_b )
       => ( ( last_P8790725272581694279od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( last_P8790725272581694279od_a_b @ Xs ) ) )
      & ( ( Ys != nil_Product_prod_a_b )
       => ( ( last_P8790725272581694279od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( last_P8790725272581694279od_a_b @ Ys ) ) ) ) ).

% last_append
thf(fact_831_longest__common__suffix,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
    ? [Ss: list_P1467974523212632366od_a_b,Xs3: list_P1467974523212632366od_a_b,Ys5: list_P1467974523212632366od_a_b] :
      ( ( Xs
        = ( append5335208823350062147od_a_b @ Xs3 @ Ss ) )
      & ( Ys
        = ( append5335208823350062147od_a_b @ Ys5 @ Ss ) )
      & ( ( Xs3 = nil_Product_prod_a_b )
        | ( Ys5 = nil_Product_prod_a_b )
        | ( ( last_P8790725272581694279od_a_b @ Xs3 )
         != ( last_P8790725272581694279od_a_b @ Ys5 ) ) ) ) ).

% longest_common_suffix
thf(fact_832_hd__Nil__eq__last,axiom,
    ( ( hd_Product_prod_a_b @ nil_Product_prod_a_b )
    = ( last_P8790725272581694279od_a_b @ nil_Product_prod_a_b ) ) ).

% hd_Nil_eq_last
thf(fact_833_not__Nil__listrel1,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,R: set_Pr5493900063595384711od_a_b] :
      ~ ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ Xs ) @ ( listre2955263632500257159od_a_b @ R ) ) ).

% not_Nil_listrel1
thf(fact_834_not__listrel1__Nil,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,R: set_Pr5493900063595384711od_a_b] :
      ~ ( member3051990972100052432od_a_b @ ( produc5288560138351607191od_a_b @ Xs @ nil_Product_prod_a_b ) @ ( listre2955263632500257159od_a_b @ R ) ) ).

% not_listrel1_Nil
thf(fact_835_dtree_Oset__intros_I4_J,axiom,
    ! [Ye: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Yi: b,X1: a] :
      ( ( member4380921116106875537_a_b_b @ Ye @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_b @ Yi @ ( basic_1877077703026942_a_b_b @ Ye ) )
       => ( member_b @ Yi @ ( darcs_a_b @ ( node_a_b @ X1 @ X22 ) ) ) ) ) ).

% dtree.set_intros(4)
thf(fact_836_dtree_Oset__sel_I4_J,axiom,
    ! [Xe: produc4558475209616630778_a_b_b,A: dtree_a_b,Xi: b] :
      ( ( member4380921116106875537_a_b_b @ Xe @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_b @ Xi @ ( basic_1877077703026942_a_b_b @ Xe ) )
       => ( member_b @ Xi @ ( darcs_a_b @ A ) ) ) ) ).

% dtree.set_sel(4)
thf(fact_837_dtree__size__decr__aux,axiom,
    ! [X3: dtree_a_b,Y: b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
     => ( ord_less_nat @ ( size_size_dtree_a_b @ X3 ) @ ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% dtree_size_decr_aux
thf(fact_838_split__last__eq,axiom,
    ! [As2: list_P1467974523212632366od_a_b,Y: product_prod_a_b,Bs2: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ As2 @ ( cons_P7316939131009794654od_a_b @ Y @ Bs2 ) )
        = Xs )
     => ( ( Bs2 != nil_Product_prod_a_b )
       => ( ( last_P8790725272581694279od_a_b @ Bs2 )
          = ( last_P8790725272581694279od_a_b @ Xs ) ) ) ) ).

% split_last_eq
thf(fact_839_in__set__vwalk__arcs__append2,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b,X3: produc2233330766403592615od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( Q2 != nil_Product_prod_a_b )
       => ( ( ( member5065438833300252112od_a_b @ X3 @ ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ P2 ) ) )
            | ( X3
              = ( produc6550459592057863831od_a_b @ ( last_P8790725272581694279od_a_b @ P2 ) @ ( hd_Product_prod_a_b @ Q2 ) ) )
            | ( member5065438833300252112od_a_b @ X3 @ ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ Q2 ) ) ) )
         => ( member5065438833300252112od_a_b @ X3 @ ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ ( append5335208823350062147od_a_b @ P2 @ Q2 ) ) ) ) ) ) ) ).

% in_set_vwalk_arcs_append2
thf(fact_840_append__butlast__last__id,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ( append5335208823350062147od_a_b @ ( butlas8142365734376493050od_a_b @ Xs ) @ ( cons_P7316939131009794654od_a_b @ ( last_P8790725272581694279od_a_b @ Xs ) @ nil_Product_prod_a_b ) )
        = Xs ) ) ).

% append_butlast_last_id
thf(fact_841_distinct__adj__append__iff,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( distin2562679511629466758od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
      = ( ( distin2562679511629466758od_a_b @ Xs )
        & ( distin2562679511629466758od_a_b @ Ys )
        & ( ( Xs = nil_Product_prod_a_b )
          | ( Ys = nil_Product_prod_a_b )
          | ( ( last_P8790725272581694279od_a_b @ Xs )
           != ( hd_Product_prod_a_b @ Ys ) ) ) ) ) ).

% distinct_adj_append_iff
thf(fact_842_joinableI,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( ( last_P8790725272581694279od_a_b @ P2 )
        = ( hd_Product_prod_a_b @ Q2 ) )
     => ( ( P2 != nil_Product_prod_a_b )
       => ( ( Q2 != nil_Product_prod_a_b )
         => ( vertex7469968122360900522od_a_b @ P2 @ Q2 ) ) ) ) ).

% joinableI
thf(fact_843_joinable__Nil__l__iff,axiom,
    ! [P2: list_P1467974523212632366od_a_b] :
      ~ ( vertex7469968122360900522od_a_b @ nil_Product_prod_a_b @ P2 ) ).

% joinable_Nil_l_iff
thf(fact_844_joinable__Nil__r__iff,axiom,
    ! [Q2: list_P1467974523212632366od_a_b] :
      ~ ( vertex7469968122360900522od_a_b @ Q2 @ nil_Product_prod_a_b ) ).

% joinable_Nil_r_iff
thf(fact_845_set__empty2,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( bot_bo3428410327501040244od_a_b
        = ( set_Product_prod_a_b2 @ Xs ) )
      = ( Xs = nil_Product_prod_a_b ) ) ).

% set_empty2
thf(fact_846_set__empty,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( ( set_Product_prod_a_b2 @ Xs )
        = bot_bo3428410327501040244od_a_b )
      = ( Xs = nil_Product_prod_a_b ) ) ).

% set_empty
thf(fact_847_joinable__Cons__l__iff,axiom,
    ! [P2: list_P1467974523212632366od_a_b,V: product_prod_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( vertex7469968122360900522od_a_b @ ( cons_P7316939131009794654od_a_b @ V @ P2 ) @ Q2 )
        = ( vertex7469968122360900522od_a_b @ P2 @ Q2 ) ) ) ).

% joinable_Cons_l_iff
thf(fact_848_butlast__snoc,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( butlas8142365734376493050od_a_b @ ( append5335208823350062147od_a_b @ Xs @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) )
      = Xs ) ).

% butlast_snoc
thf(fact_849_joinable__Snoc__r__iff,axiom,
    ! [Q2: list_P1467974523212632366od_a_b,P2: list_P1467974523212632366od_a_b,V: product_prod_a_b] :
      ( ( Q2 != nil_Product_prod_a_b )
     => ( ( vertex7469968122360900522od_a_b @ P2 @ ( append5335208823350062147od_a_b @ Q2 @ ( cons_P7316939131009794654od_a_b @ V @ nil_Product_prod_a_b ) ) )
        = ( vertex7469968122360900522od_a_b @ P2 @ Q2 ) ) ) ).

% joinable_Snoc_r_iff
thf(fact_850_in__set__butlastD,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ ( butlas7288446807591328296_a_b_b @ Xs ) ) )
     => ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) ) ) ).

% in_set_butlastD
thf(fact_851_in__set__butlastD,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ ( butlast_dtree_a_b @ Xs ) ) )
     => ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) ) ) ).

% in_set_butlastD
thf(fact_852_in__set__butlast__appendI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ ( butlas7288446807591328296_a_b_b @ Xs ) ) )
        | ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ ( butlas7288446807591328296_a_b_b @ Ys ) ) ) )
     => ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ ( butlas7288446807591328296_a_b_b @ ( append86853766581025439_a_b_b @ Xs @ Ys ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_853_in__set__butlast__appendI,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b,Ys: list_dtree_a_b] :
      ( ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ ( butlast_dtree_a_b @ Xs ) ) )
        | ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ ( butlast_dtree_a_b @ Ys ) ) ) )
     => ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ ( butlast_dtree_a_b @ ( append_dtree_a_b @ Xs @ Ys ) ) ) ) ) ).

% in_set_butlast_appendI
thf(fact_854_in__set__vwalk__arcsE,axiom,
    ! [U2: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,P2: list_P5360711134766023690_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ U2 @ V ) @ ( set_Pr1544013579528541546_a_b_b @ ( vertex6010537929073084546_a_b_b @ P2 ) ) )
     => ~ ( ( member4380921116106875537_a_b_b @ U2 @ ( set_Pr8239206241032387877_a_b_b @ P2 ) )
         => ~ ( member4380921116106875537_a_b_b @ V @ ( set_Pr8239206241032387877_a_b_b @ P2 ) ) ) ) ).

% in_set_vwalk_arcsE
thf(fact_855_in__set__vwalk__arcsE,axiom,
    ! [U2: dtree_a_b,V: dtree_a_b,P2: list_dtree_a_b] :
      ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ U2 @ V ) @ ( set_Pr2725521476954953066ee_a_b @ ( vertex6757798842484198146ee_a_b @ P2 ) ) )
     => ~ ( ( member_dtree_a_b @ U2 @ ( set_dtree_a_b2 @ P2 ) )
         => ~ ( member_dtree_a_b @ V @ ( set_dtree_a_b2 @ P2 ) ) ) ) ).

% in_set_vwalk_arcsE
thf(fact_856_list_Oset__intros_I2_J,axiom,
    ! [Y: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b,X21: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ X222 ) )
     => ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X21 @ X222 ) ) ) ) ).

% list.set_intros(2)
thf(fact_857_list_Oset__intros_I2_J,axiom,
    ! [Y: dtree_a_b,X222: list_dtree_a_b,X21: dtree_a_b] :
      ( ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ X222 ) )
     => ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ ( cons_dtree_a_b @ X21 @ X222 ) ) ) ) ).

% list.set_intros(2)
thf(fact_858_list_Oset__intros_I1_J,axiom,
    ! [X21: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b] : ( member4380921116106875537_a_b_b @ X21 @ ( set_Pr8239206241032387877_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X21 @ X222 ) ) ) ).

% list.set_intros(1)
thf(fact_859_list_Oset__intros_I1_J,axiom,
    ! [X21: dtree_a_b,X222: list_dtree_a_b] : ( member_dtree_a_b @ X21 @ ( set_dtree_a_b2 @ ( cons_dtree_a_b @ X21 @ X222 ) ) ) ).

% list.set_intros(1)
thf(fact_860_list_Oset__cases,axiom,
    ! [E: produc4558475209616630778_a_b_b,A: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ E @ ( set_Pr8239206241032387877_a_b_b @ A ) )
     => ( ! [Z2: list_P5360711134766023690_a_b_b] :
            ( A
           != ( cons_P2785074014425598660_a_b_b @ E @ Z2 ) )
       => ~ ! [Z1: produc4558475209616630778_a_b_b,Z2: list_P5360711134766023690_a_b_b] :
              ( ( A
                = ( cons_P2785074014425598660_a_b_b @ Z1 @ Z2 ) )
             => ~ ( member4380921116106875537_a_b_b @ E @ ( set_Pr8239206241032387877_a_b_b @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_861_list_Oset__cases,axiom,
    ! [E: dtree_a_b,A: list_dtree_a_b] :
      ( ( member_dtree_a_b @ E @ ( set_dtree_a_b2 @ A ) )
     => ( ! [Z2: list_dtree_a_b] :
            ( A
           != ( cons_dtree_a_b @ E @ Z2 ) )
       => ~ ! [Z1: dtree_a_b,Z2: list_dtree_a_b] :
              ( ( A
                = ( cons_dtree_a_b @ Z1 @ Z2 ) )
             => ~ ( member_dtree_a_b @ E @ ( set_dtree_a_b2 @ Z2 ) ) ) ) ) ).

% list.set_cases
thf(fact_862_set__ConsD,axiom,
    ! [Y: produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X3 @ Xs ) ) )
     => ( ( Y = X3 )
        | ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_863_set__ConsD,axiom,
    ! [Y: dtree_a_b,X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ ( cons_dtree_a_b @ X3 @ Xs ) ) )
     => ( ( Y = X3 )
        | ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_864_not__pfsubset__fempty,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ~ ( ord_le7001451600920047870_a_b_b @ A2 @ bot_bo2895716411488905534_a_b_b ) ).

% not_pfsubset_fempty
thf(fact_865_butlast_Osimps_I1_J,axiom,
    ( ( butlas8142365734376493050od_a_b @ nil_Product_prod_a_b )
    = nil_Product_prod_a_b ) ).

% butlast.simps(1)
thf(fact_866_joinable__non__Nil_I2_J,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( vertex7469968122360900522od_a_b @ P2 @ Q2 )
     => ( Q2 != nil_Product_prod_a_b ) ) ).

% joinable_non_Nil(2)
thf(fact_867_joinable__non__Nil_I1_J,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( vertex7469968122360900522od_a_b @ P2 @ Q2 )
     => ( P2 != nil_Product_prod_a_b ) ) ).

% joinable_non_Nil(1)
thf(fact_868_distinct__adj__Nil,axiom,
    distin2562679511629466758od_a_b @ nil_Product_prod_a_b ).

% distinct_adj_Nil
thf(fact_869_empty__set,axiom,
    ( bot_bo3428410327501040244od_a_b
    = ( set_Product_prod_a_b2 @ nil_Product_prod_a_b ) ) ).

% empty_set
thf(fact_870_in__set__conv__decomp__first,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
      = ( ? [Ys2: list_P5360711134766023690_a_b_b,Zs2: list_P5360711134766023690_a_b_b] :
            ( ( Xs
              = ( append86853766581025439_a_b_b @ Ys2 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs2 ) ) )
            & ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Ys2 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_871_in__set__conv__decomp__first,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
      = ( ? [Ys2: list_dtree_a_b,Zs2: list_dtree_a_b] :
            ( ( Xs
              = ( append_dtree_a_b @ Ys2 @ ( cons_dtree_a_b @ X3 @ Zs2 ) ) )
            & ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Ys2 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_872_in__set__conv__decomp__last,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
      = ( ? [Ys2: list_P5360711134766023690_a_b_b,Zs2: list_P5360711134766023690_a_b_b] :
            ( ( Xs
              = ( append86853766581025439_a_b_b @ Ys2 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs2 ) ) )
            & ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_873_in__set__conv__decomp__last,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
      = ( ? [Ys2: list_dtree_a_b,Zs2: list_dtree_a_b] :
            ( ( Xs
              = ( append_dtree_a_b @ Ys2 @ ( cons_dtree_a_b @ X3 @ Zs2 ) ) )
            & ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_874_in__set__conv__decomp,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
      = ( ? [Ys2: list_P5360711134766023690_a_b_b,Zs2: list_P5360711134766023690_a_b_b] :
            ( Xs
            = ( append86853766581025439_a_b_b @ Ys2 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_875_in__set__conv__decomp,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
      = ( ? [Ys2: list_dtree_a_b,Zs2: list_dtree_a_b] :
            ( Xs
            = ( append_dtree_a_b @ Ys2 @ ( cons_dtree_a_b @ X3 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_876_append__Cons__eq__iff,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b,Ys: list_P5360711134766023690_a_b_b,Xs4: list_P5360711134766023690_a_b_b,Ys6: list_P5360711134766023690_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ( ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Ys ) )
       => ( ( ( append86853766581025439_a_b_b @ Xs @ ( cons_P2785074014425598660_a_b_b @ X3 @ Ys ) )
            = ( append86853766581025439_a_b_b @ Xs4 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_877_append__Cons__eq__iff,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b,Ys: list_dtree_a_b,Xs4: list_dtree_a_b,Ys6: list_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
     => ( ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Ys ) )
       => ( ( ( append_dtree_a_b @ Xs @ ( cons_dtree_a_b @ X3 @ Ys ) )
            = ( append_dtree_a_b @ Xs4 @ ( cons_dtree_a_b @ X3 @ Ys6 ) ) )
          = ( ( Xs = Xs4 )
            & ( Ys = Ys6 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_878_split__list__first,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ? [Ys3: list_P5360711134766023690_a_b_b,Zs3: list_P5360711134766023690_a_b_b] :
          ( ( Xs
            = ( append86853766581025439_a_b_b @ Ys3 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs3 ) ) )
          & ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_879_split__list__first,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
     => ? [Ys3: list_dtree_a_b,Zs3: list_dtree_a_b] :
          ( ( Xs
            = ( append_dtree_a_b @ Ys3 @ ( cons_dtree_a_b @ X3 @ Zs3 ) ) )
          & ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Ys3 ) ) ) ) ).

% split_list_first
thf(fact_880_split__list__last,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ? [Ys3: list_P5360711134766023690_a_b_b,Zs3: list_P5360711134766023690_a_b_b] :
          ( ( Xs
            = ( append86853766581025439_a_b_b @ Ys3 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs3 ) ) )
          & ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_881_split__list__last,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
     => ? [Ys3: list_dtree_a_b,Zs3: list_dtree_a_b] :
          ( ( Xs
            = ( append_dtree_a_b @ Ys3 @ ( cons_dtree_a_b @ X3 @ Zs3 ) ) )
          & ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_882_split__list,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ? [Ys3: list_P5360711134766023690_a_b_b,Zs3: list_P5360711134766023690_a_b_b] :
          ( Xs
          = ( append86853766581025439_a_b_b @ Ys3 @ ( cons_P2785074014425598660_a_b_b @ X3 @ Zs3 ) ) ) ) ).

% split_list
thf(fact_883_split__list,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
     => ? [Ys3: list_dtree_a_b,Zs3: list_dtree_a_b] :
          ( Xs
          = ( append_dtree_a_b @ Ys3 @ ( cons_dtree_a_b @ X3 @ Zs3 ) ) ) ) ).

% split_list
thf(fact_884_hd__in__set,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b] :
      ( ( Xs != nil_Pr5403147374433350260_a_b_b )
     => ( member4380921116106875537_a_b_b @ ( hd_Pro8093898422926754895_a_b_b @ Xs ) @ ( set_Pr8239206241032387877_a_b_b @ Xs ) ) ) ).

% hd_in_set
thf(fact_885_hd__in__set,axiom,
    ! [Xs: list_dtree_a_b] :
      ( ( Xs != nil_dtree_a_b )
     => ( member_dtree_a_b @ ( hd_dtree_a_b @ Xs ) @ ( set_dtree_a_b2 @ Xs ) ) ) ).

% hd_in_set
thf(fact_886_hd__in__set,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( member1426531481828664017od_a_b @ ( hd_Product_prod_a_b @ Xs ) @ ( set_Product_prod_a_b2 @ Xs ) ) ) ).

% hd_in_set
thf(fact_887_list_Oset__sel_I1_J,axiom,
    ! [A: list_P5360711134766023690_a_b_b] :
      ( ( A != nil_Pr5403147374433350260_a_b_b )
     => ( member4380921116106875537_a_b_b @ ( hd_Pro8093898422926754895_a_b_b @ A ) @ ( set_Pr8239206241032387877_a_b_b @ A ) ) ) ).

% list.set_sel(1)
thf(fact_888_list_Oset__sel_I1_J,axiom,
    ! [A: list_dtree_a_b] :
      ( ( A != nil_dtree_a_b )
     => ( member_dtree_a_b @ ( hd_dtree_a_b @ A ) @ ( set_dtree_a_b2 @ A ) ) ) ).

% list.set_sel(1)
thf(fact_889_list_Oset__sel_I1_J,axiom,
    ! [A: list_P1467974523212632366od_a_b] :
      ( ( A != nil_Product_prod_a_b )
     => ( member1426531481828664017od_a_b @ ( hd_Product_prod_a_b @ A ) @ ( set_Product_prod_a_b2 @ A ) ) ) ).

% list.set_sel(1)
thf(fact_890_last__in__set,axiom,
    ! [As2: list_P5360711134766023690_a_b_b] :
      ( ( As2 != nil_Pr5403147374433350260_a_b_b )
     => ( member4380921116106875537_a_b_b @ ( last_P1593854145880039067_a_b_b @ As2 ) @ ( set_Pr8239206241032387877_a_b_b @ As2 ) ) ) ).

% last_in_set
thf(fact_891_last__in__set,axiom,
    ! [As2: list_dtree_a_b] :
      ( ( As2 != nil_dtree_a_b )
     => ( member_dtree_a_b @ ( last_dtree_a_b @ As2 ) @ ( set_dtree_a_b2 @ As2 ) ) ) ).

% last_in_set
thf(fact_892_last__in__set,axiom,
    ! [As2: list_P1467974523212632366od_a_b] :
      ( ( As2 != nil_Product_prod_a_b )
     => ( member1426531481828664017od_a_b @ ( last_P8790725272581694279od_a_b @ As2 ) @ ( set_Product_prod_a_b2 @ As2 ) ) ) ).

% last_in_set
thf(fact_893_vwalk__arcs__set__nil,axiom,
    ! [X3: produc2233330766403592615od_a_b,P2: list_P1467974523212632366od_a_b] :
      ( ( member5065438833300252112od_a_b @ X3 @ ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ P2 ) ) )
     => ( P2 != nil_Product_prod_a_b ) ) ).

% vwalk_arcs_set_nil
thf(fact_894_butlast_Osimps_I2_J,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b] :
      ( ( ( Xs = nil_Product_prod_a_b )
       => ( ( butlas8142365734376493050od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
          = nil_Product_prod_a_b ) )
      & ( ( Xs != nil_Product_prod_a_b )
       => ( ( butlas8142365734376493050od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
          = ( cons_P7316939131009794654od_a_b @ X3 @ ( butlas8142365734376493050od_a_b @ Xs ) ) ) ) ) ).

% butlast.simps(2)
thf(fact_895_butlast__append,axiom,
    ! [Ys: list_P1467974523212632366od_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( ( Ys = nil_Product_prod_a_b )
       => ( ( butlas8142365734376493050od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( butlas8142365734376493050od_a_b @ Xs ) ) )
      & ( ( Ys != nil_Product_prod_a_b )
       => ( ( butlas8142365734376493050od_a_b @ ( append5335208823350062147od_a_b @ Xs @ Ys ) )
          = ( append5335208823350062147od_a_b @ Xs @ ( butlas8142365734376493050od_a_b @ Ys ) ) ) ) ) ).

% butlast_append
thf(fact_896_distinct__adj__singleton,axiom,
    ! [X3: product_prod_a_b] : ( distin2562679511629466758od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) ).

% distinct_adj_singleton
thf(fact_897_split__list__last__sep,axiom,
    ! [Y: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ( ( Y
         != ( last_P1593854145880039067_a_b_b @ Xs ) )
       => ? [As: list_P5360711134766023690_a_b_b,Bs: list_P5360711134766023690_a_b_b] :
            ( ( append86853766581025439_a_b_b @ As @ ( cons_P2785074014425598660_a_b_b @ Y @ ( append86853766581025439_a_b_b @ Bs @ ( cons_P2785074014425598660_a_b_b @ ( last_P1593854145880039067_a_b_b @ Xs ) @ nil_Pr5403147374433350260_a_b_b ) ) ) )
            = Xs ) ) ) ).

% split_list_last_sep
thf(fact_898_split__list__last__sep,axiom,
    ! [Y: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ Xs ) )
     => ( ( Y
         != ( last_dtree_a_b @ Xs ) )
       => ? [As: list_dtree_a_b,Bs: list_dtree_a_b] :
            ( ( append_dtree_a_b @ As @ ( cons_dtree_a_b @ Y @ ( append_dtree_a_b @ Bs @ ( cons_dtree_a_b @ ( last_dtree_a_b @ Xs ) @ nil_dtree_a_b ) ) ) )
            = Xs ) ) ) ).

% split_list_last_sep
thf(fact_899_split__list__last__sep,axiom,
    ! [Y: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ Y @ ( set_Product_prod_a_b2 @ Xs ) )
     => ( ( Y
         != ( last_P8790725272581694279od_a_b @ Xs ) )
       => ? [As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
            ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ Y @ ( append5335208823350062147od_a_b @ Bs @ ( cons_P7316939131009794654od_a_b @ ( last_P8790725272581694279od_a_b @ Xs ) @ nil_Product_prod_a_b ) ) ) )
            = Xs ) ) ) ).

% split_list_last_sep
thf(fact_900_split__list__not__last,axiom,
    ! [Y: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ Y @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ( ( Y
         != ( last_P1593854145880039067_a_b_b @ Xs ) )
       => ? [As: list_P5360711134766023690_a_b_b,Bs: list_P5360711134766023690_a_b_b] :
            ( ( ( append86853766581025439_a_b_b @ As @ ( cons_P2785074014425598660_a_b_b @ Y @ Bs ) )
              = Xs )
            & ( Bs != nil_Pr5403147374433350260_a_b_b ) ) ) ) ).

% split_list_not_last
thf(fact_901_split__list__not__last,axiom,
    ! [Y: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( member_dtree_a_b @ Y @ ( set_dtree_a_b2 @ Xs ) )
     => ( ( Y
         != ( last_dtree_a_b @ Xs ) )
       => ? [As: list_dtree_a_b,Bs: list_dtree_a_b] :
            ( ( ( append_dtree_a_b @ As @ ( cons_dtree_a_b @ Y @ Bs ) )
              = Xs )
            & ( Bs != nil_dtree_a_b ) ) ) ) ).

% split_list_not_last
thf(fact_902_split__list__not__last,axiom,
    ! [Y: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ Y @ ( set_Product_prod_a_b2 @ Xs ) )
     => ( ( Y
         != ( last_P8790725272581694279od_a_b @ Xs ) )
       => ? [As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
            ( ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ Y @ Bs ) )
              = Xs )
            & ( Bs != nil_Product_prod_a_b ) ) ) ) ).

% split_list_not_last
thf(fact_903_vwalk__arcs__butlast__empty,axiom,
    ! [Xs: list_P1467974523212632366od_a_b] :
      ( ( Xs != nil_Product_prod_a_b )
     => ( ( ( vertex3879532237292798496od_a_b @ Xs )
          = nil_Pr906174322249854893od_a_b )
       => ( ( vertex3879532237292798496od_a_b @ ( butlas8142365734376493050od_a_b @ Xs ) )
          = nil_Pr906174322249854893od_a_b ) ) ) ).

% vwalk_arcs_butlast_empty
thf(fact_904_distinct__adj__Cons,axiom,
    ! [X3: product_prod_a_b,Xs: list_P1467974523212632366od_a_b] :
      ( ( distin2562679511629466758od_a_b @ ( cons_P7316939131009794654od_a_b @ X3 @ Xs ) )
      = ( ( Xs = nil_Product_prod_a_b )
        | ( ( X3
           != ( hd_Product_prod_a_b @ Xs ) )
          & ( distin2562679511629466758od_a_b @ Xs ) ) ) ) ).

% distinct_adj_Cons
thf(fact_905_joinable__def,axiom,
    ( vertex7469968122360900522od_a_b
    = ( ^ [P4: list_P1467974523212632366od_a_b,Q3: list_P1467974523212632366od_a_b] :
          ( ( ( last_P8790725272581694279od_a_b @ P4 )
            = ( hd_Product_prod_a_b @ Q3 ) )
          & ( P4 != nil_Product_prod_a_b )
          & ( Q3 != nil_Product_prod_a_b ) ) ) ) ).

% joinable_def
thf(fact_906_snoc__eq__iff__butlast,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,X3: product_prod_a_b,Ys: list_P1467974523212632366od_a_b] :
      ( ( ( append5335208823350062147od_a_b @ Xs @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) )
        = Ys )
      = ( ( Ys != nil_Product_prod_a_b )
        & ( ( butlas8142365734376493050od_a_b @ Ys )
          = Xs )
        & ( ( last_P8790725272581694279od_a_b @ Ys )
          = X3 ) ) ) ).

% snoc_eq_iff_butlast
thf(fact_907_set__vwalk__arcs__snoc,axiom,
    ! [P2: list_P1467974523212632366od_a_b,A: product_prod_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ ( append5335208823350062147od_a_b @ P2 @ ( cons_P7316939131009794654od_a_b @ A @ nil_Product_prod_a_b ) ) ) )
        = ( insert7668604973114392439od_a_b @ ( produc6550459592057863831od_a_b @ ( last_P8790725272581694279od_a_b @ P2 ) @ A ) @ ( set_Pr5228040199190236220od_a_b @ ( vertex3879532237292798496od_a_b @ P2 ) ) ) ) ) ).

% set_vwalk_arcs_snoc
thf(fact_908_the__elem__set,axiom,
    ! [X3: product_prod_a_b] :
      ( ( the_el8589169213296894365od_a_b @ ( set_Product_prod_a_b2 @ ( cons_P7316939131009794654od_a_b @ X3 @ nil_Product_prod_a_b ) ) )
      = X3 ) ).

% the_elem_set
thf(fact_909_vwalk__join__split,axiom,
    ! [U2: produc4558475209616630778_a_b_b,P2: list_P5360711134766023690_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ U2 @ ( set_Pr8239206241032387877_a_b_b @ P2 ) )
     => ? [Q4: list_P5360711134766023690_a_b_b,R2: list_P5360711134766023690_a_b_b] :
          ( ( P2
            = ( vertex8382513469400993835_a_b_b @ Q4 @ R2 ) )
          & ( ( last_P1593854145880039067_a_b_b @ Q4 )
            = U2 )
          & ( ( hd_Pro8093898422926754895_a_b_b @ R2 )
            = U2 )
          & ( Q4 != nil_Pr5403147374433350260_a_b_b )
          & ( R2 != nil_Pr5403147374433350260_a_b_b ) ) ) ).

% vwalk_join_split
thf(fact_910_vwalk__join__split,axiom,
    ! [U2: dtree_a_b,P2: list_dtree_a_b] :
      ( ( member_dtree_a_b @ U2 @ ( set_dtree_a_b2 @ P2 ) )
     => ? [Q4: list_dtree_a_b,R2: list_dtree_a_b] :
          ( ( P2
            = ( vertex7288003445438391211ee_a_b @ Q4 @ R2 ) )
          & ( ( last_dtree_a_b @ Q4 )
            = U2 )
          & ( ( hd_dtree_a_b @ R2 )
            = U2 )
          & ( Q4 != nil_dtree_a_b )
          & ( R2 != nil_dtree_a_b ) ) ) ).

% vwalk_join_split
thf(fact_911_vwalk__join__split,axiom,
    ! [U2: product_prod_a_b,P2: list_P1467974523212632366od_a_b] :
      ( ( member1426531481828664017od_a_b @ U2 @ ( set_Product_prod_a_b2 @ P2 ) )
     => ? [Q4: list_P1467974523212632366od_a_b,R2: list_P1467974523212632366od_a_b] :
          ( ( P2
            = ( vertex9110485820359517623od_a_b @ Q4 @ R2 ) )
          & ( ( last_P8790725272581694279od_a_b @ Q4 )
            = U2 )
          & ( ( hd_Product_prod_a_b @ R2 )
            = U2 )
          & ( Q4 != nil_Product_prod_a_b )
          & ( R2 != nil_Product_prod_a_b ) ) ) ).

% vwalk_join_split
thf(fact_912_dtail__in__child__eq__child,axiom,
    ! [T: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,E: b,R: a,Def2: b > a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
     => ( ( member_b @ E @ ( darcs_a_b @ T ) )
       => ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
         => ( ( dtail_a_b @ ( node_a_b @ R @ Xs ) @ Def2 @ E )
            = ( dtail_a_b @ T @ Def2 @ E ) ) ) ) ) ).

% dtail_in_child_eq_child
thf(fact_913_insertCI,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( ~ ( member4380921116106875537_a_b_b @ A @ B4 )
       => ( A = B ) )
     => ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ B4 ) ) ) ).

% insertCI
thf(fact_914_insertCI,axiom,
    ! [A: dtree_a_b,B4: set_dtree_a_b,B: dtree_a_b] :
      ( ( ~ ( member_dtree_a_b @ A @ B4 )
       => ( A = B ) )
     => ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ B @ B4 ) ) ) ).

% insertCI
thf(fact_915_insert__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member4380921116106875537_a_b_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_916_insert__iff,axiom,
    ! [A: dtree_a_b,B: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ B @ A2 ) )
      = ( ( A = B )
        | ( member_dtree_a_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_917_singletonI,axiom,
    ! [A: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ) ).

% singletonI
thf(fact_918_singletonI,axiom,
    ! [A: dtree_a_b] : ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ A @ bot_bo8730652382759064772ee_a_b ) ) ).

% singletonI
thf(fact_919_Int__insert__left__if0,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ C2 )
     => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B4 ) @ C2 )
        = ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_920_Int__insert__left__if0,axiom,
    ! [A: dtree_a_b,C2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ A @ C2 )
     => ( ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ B4 ) @ C2 )
        = ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_921_Int__insert__left__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ C2 )
     => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B4 ) @ C2 )
        = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_922_Int__insert__left__if1,axiom,
    ! [A: dtree_a_b,C2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ C2 )
     => ( ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ B4 ) @ C2 )
        = ( insert_dtree_a_b @ A @ ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_923_Int__insert__right__if0,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ A2 )
     => ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ A @ B4 ) )
        = ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ).

% Int_insert_right_if0
thf(fact_924_Int__insert__right__if0,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ A @ A2 )
     => ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( insert_dtree_a_b @ A @ B4 ) )
        = ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ).

% Int_insert_right_if0
thf(fact_925_Int__insert__right__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A2 )
     => ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ A @ B4 ) )
        = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_926_Int__insert__right__if1,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ A2 )
     => ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( insert_dtree_a_b @ A @ B4 ) )
        = ( insert_dtree_a_b @ A @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_927_vwalk__join__Nil,axiom,
    ! [P2: list_P1467974523212632366od_a_b] :
      ( ( vertex9110485820359517623od_a_b @ P2 @ nil_Product_prod_a_b )
      = P2 ) ).

% vwalk_join_Nil
thf(fact_928_insert__disjoint_I1_J,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ A2 ) @ B4 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B4 )
        & ( ( inf_in6138156342456174402_a_b_b @ A2 @ B4 )
          = bot_bo3721250822024684356_a_b_b ) ) ) ).

% insert_disjoint(1)
thf(fact_929_insert__disjoint_I1_J,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ A2 ) @ B4 )
        = bot_bo8730652382759064772ee_a_b )
      = ( ~ ( member_dtree_a_b @ A @ B4 )
        & ( ( inf_in5903708963019302594ee_a_b @ A2 @ B4 )
          = bot_bo8730652382759064772ee_a_b ) ) ) ).

% insert_disjoint(1)
thf(fact_930_insert__disjoint_I2_J,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ A2 ) @ B4 ) )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B4 )
        & ( bot_bo3721250822024684356_a_b_b
          = ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_931_insert__disjoint_I2_J,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( bot_bo8730652382759064772ee_a_b
        = ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ A2 ) @ B4 ) )
      = ( ~ ( member_dtree_a_b @ A @ B4 )
        & ( bot_bo8730652382759064772ee_a_b
          = ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_932_disjoint__insert_I1_J,axiom,
    ! [B4: set_Pr3012420139608375472_a_b_b,A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ B4 @ ( insert1613891728210272810_a_b_b @ A @ A2 ) )
        = bot_bo3721250822024684356_a_b_b )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B4 )
        & ( ( inf_in6138156342456174402_a_b_b @ B4 @ A2 )
          = bot_bo3721250822024684356_a_b_b ) ) ) ).

% disjoint_insert(1)
thf(fact_933_disjoint__insert_I1_J,axiom,
    ! [B4: set_dtree_a_b,A: dtree_a_b,A2: set_dtree_a_b] :
      ( ( ( inf_in5903708963019302594ee_a_b @ B4 @ ( insert_dtree_a_b @ A @ A2 ) )
        = bot_bo8730652382759064772ee_a_b )
      = ( ~ ( member_dtree_a_b @ A @ B4 )
        & ( ( inf_in5903708963019302594ee_a_b @ B4 @ A2 )
          = bot_bo8730652382759064772ee_a_b ) ) ) ).

% disjoint_insert(1)
thf(fact_934_disjoint__insert_I2_J,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( inf_in6138156342456174402_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ B @ B4 ) ) )
      = ( ~ ( member4380921116106875537_a_b_b @ B @ A2 )
        & ( bot_bo3721250822024684356_a_b_b
          = ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_935_disjoint__insert_I2_J,axiom,
    ! [A2: set_dtree_a_b,B: dtree_a_b,B4: set_dtree_a_b] :
      ( ( bot_bo8730652382759064772ee_a_b
        = ( inf_in5903708963019302594ee_a_b @ A2 @ ( insert_dtree_a_b @ B @ B4 ) ) )
      = ( ~ ( member_dtree_a_b @ B @ A2 )
        & ( bot_bo8730652382759064772ee_a_b
          = ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_936_finsert_Orep__eq,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ Xa ) )
      = ( insert1613891728210272810_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ Xa ) ) ) ).

% finsert.rep_eq
thf(fact_937_vwalk__join__Cons,axiom,
    ! [P2: list_P1467974523212632366od_a_b,U2: product_prod_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( vertex9110485820359517623od_a_b @ ( cons_P7316939131009794654od_a_b @ U2 @ P2 ) @ Q2 )
        = ( cons_P7316939131009794654od_a_b @ U2 @ ( vertex9110485820359517623od_a_b @ P2 @ Q2 ) ) ) ) ).

% vwalk_join_Cons
thf(fact_938_psubsetD,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,C: produc4558475209616630778_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A2 @ B4 )
     => ( ( member4380921116106875537_a_b_b @ C @ A2 )
       => ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% psubsetD
thf(fact_939_psubsetD,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,C: dtree_a_b] :
      ( ( ord_le1844933027578805380ee_a_b @ A2 @ B4 )
     => ( ( member_dtree_a_b @ C @ A2 )
       => ( member_dtree_a_b @ C @ B4 ) ) ) ).

% psubsetD
thf(fact_940_insertE,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member4380921116106875537_a_b_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_941_insertE,axiom,
    ! [A: dtree_a_b,B: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ B @ A2 ) )
     => ( ( A != B )
       => ( member_dtree_a_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_942_insertI1,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] : ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ A @ B4 ) ) ).

% insertI1
thf(fact_943_insertI1,axiom,
    ! [A: dtree_a_b,B4: set_dtree_a_b] : ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ A @ B4 ) ) ).

% insertI1
thf(fact_944_insertI2,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ B4 )
     => ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ B4 ) ) ) ).

% insertI2
thf(fact_945_insertI2,axiom,
    ! [A: dtree_a_b,B4: set_dtree_a_b,B: dtree_a_b] :
      ( ( member_dtree_a_b @ A @ B4 )
     => ( member_dtree_a_b @ A @ ( insert_dtree_a_b @ B @ B4 ) ) ) ).

% insertI2
thf(fact_946_Set_Oset__insert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ~ ! [B6: set_Pr3012420139608375472_a_b_b] :
            ( ( A2
              = ( insert1613891728210272810_a_b_b @ X3 @ B6 ) )
           => ( member4380921116106875537_a_b_b @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_947_Set_Oset__insert,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ A2 )
     => ~ ! [B6: set_dtree_a_b] :
            ( ( A2
              = ( insert_dtree_a_b @ X3 @ B6 ) )
           => ( member_dtree_a_b @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_948_insert__ident,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ~ ( member4380921116106875537_a_b_b @ X3 @ B4 )
       => ( ( ( insert1613891728210272810_a_b_b @ X3 @ A2 )
            = ( insert1613891728210272810_a_b_b @ X3 @ B4 ) )
          = ( A2 = B4 ) ) ) ) ).

% insert_ident
thf(fact_949_insert__ident,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ A2 )
     => ( ~ ( member_dtree_a_b @ X3 @ B4 )
       => ( ( ( insert_dtree_a_b @ X3 @ A2 )
            = ( insert_dtree_a_b @ X3 @ B4 ) )
          = ( A2 = B4 ) ) ) ) ).

% insert_ident
thf(fact_950_insert__absorb,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A2 )
     => ( ( insert1613891728210272810_a_b_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_951_insert__absorb,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ A2 )
     => ( ( insert_dtree_a_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_952_insert__eq__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ A2 )
     => ( ~ ( member4380921116106875537_a_b_b @ B @ B4 )
       => ( ( ( insert1613891728210272810_a_b_b @ A @ A2 )
            = ( insert1613891728210272810_a_b_b @ B @ B4 ) )
          = ( ( ( A = B )
             => ( A2 = B4 ) )
            & ( ( A != B )
             => ? [C3: set_Pr3012420139608375472_a_b_b] :
                  ( ( A2
                    = ( insert1613891728210272810_a_b_b @ B @ C3 ) )
                  & ~ ( member4380921116106875537_a_b_b @ B @ C3 )
                  & ( B4
                    = ( insert1613891728210272810_a_b_b @ A @ C3 ) )
                  & ~ ( member4380921116106875537_a_b_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_953_insert__eq__iff,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B: dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ A @ A2 )
     => ( ~ ( member_dtree_a_b @ B @ B4 )
       => ( ( ( insert_dtree_a_b @ A @ A2 )
            = ( insert_dtree_a_b @ B @ B4 ) )
          = ( ( ( A = B )
             => ( A2 = B4 ) )
            & ( ( A != B )
             => ? [C3: set_dtree_a_b] :
                  ( ( A2
                    = ( insert_dtree_a_b @ B @ C3 ) )
                  & ~ ( member_dtree_a_b @ B @ C3 )
                  & ( B4
                    = ( insert_dtree_a_b @ A @ C3 ) )
                  & ~ ( member_dtree_a_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_954_mk__disjoint__insert,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A2 )
     => ? [B6: set_Pr3012420139608375472_a_b_b] :
          ( ( A2
            = ( insert1613891728210272810_a_b_b @ A @ B6 ) )
          & ~ ( member4380921116106875537_a_b_b @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_955_mk__disjoint__insert,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ A2 )
     => ? [B6: set_dtree_a_b] :
          ( ( A2
            = ( insert_dtree_a_b @ A @ B6 ) )
          & ~ ( member_dtree_a_b @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_956_singleton__iff,axiom,
    ! [B: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ B @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_957_singleton__iff,axiom,
    ! [B: dtree_a_b,A: dtree_a_b] :
      ( ( member_dtree_a_b @ B @ ( insert_dtree_a_b @ A @ bot_bo8730652382759064772ee_a_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_958_singletonD,axiom,
    ! [B: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ B @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_959_singletonD,axiom,
    ! [B: dtree_a_b,A: dtree_a_b] :
      ( ( member_dtree_a_b @ B @ ( insert_dtree_a_b @ A @ bot_bo8730652382759064772ee_a_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_960_Int__insert__left,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ A @ C2 )
       => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B4 ) @ C2 )
          = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ A @ C2 )
       => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B4 ) @ C2 )
          = ( inf_in6138156342456174402_a_b_b @ B4 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_961_Int__insert__left,axiom,
    ! [A: dtree_a_b,C2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ( member_dtree_a_b @ A @ C2 )
       => ( ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ B4 ) @ C2 )
          = ( insert_dtree_a_b @ A @ ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) ) ) )
      & ( ~ ( member_dtree_a_b @ A @ C2 )
       => ( ( inf_in5903708963019302594ee_a_b @ ( insert_dtree_a_b @ A @ B4 ) @ C2 )
          = ( inf_in5903708963019302594ee_a_b @ B4 @ C2 ) ) ) ) ).

% Int_insert_left
thf(fact_962_Int__insert__right,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ A @ A2 )
       => ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ A @ B4 ) )
          = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ A @ A2 )
       => ( ( inf_in6138156342456174402_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ A @ B4 ) )
          = ( inf_in6138156342456174402_a_b_b @ A2 @ B4 ) ) ) ) ).

% Int_insert_right
thf(fact_963_Int__insert__right,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ( member_dtree_a_b @ A @ A2 )
       => ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( insert_dtree_a_b @ A @ B4 ) )
          = ( insert_dtree_a_b @ A @ ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) )
      & ( ~ ( member_dtree_a_b @ A @ A2 )
       => ( ( inf_in5903708963019302594ee_a_b @ A2 @ ( insert_dtree_a_b @ A @ B4 ) )
          = ( inf_in5903708963019302594ee_a_b @ A2 @ B4 ) ) ) ) ).

% Int_insert_right
thf(fact_964_vwalk__join__non__Nil,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( vertex9110485820359517623od_a_b @ P2 @ Q2 )
       != nil_Product_prod_a_b ) ) ).

% vwalk_join_non_Nil
thf(fact_965_vwalk__join__assoc_H,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b,R: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( Q2 != nil_Product_prod_a_b )
       => ( ( vertex9110485820359517623od_a_b @ ( vertex9110485820359517623od_a_b @ P2 @ Q2 ) @ R )
          = ( vertex9110485820359517623od_a_b @ P2 @ ( vertex9110485820359517623od_a_b @ Q2 @ R ) ) ) ) ) ).

% vwalk_join_assoc'
thf(fact_966_vwalk__join__hd_H,axiom,
    ! [P2: list_P1467974523212632366od_a_b,Q2: list_P1467974523212632366od_a_b] :
      ( ( P2 != nil_Product_prod_a_b )
     => ( ( hd_Product_prod_a_b @ ( vertex9110485820359517623od_a_b @ P2 @ Q2 ) )
        = ( hd_Product_prod_a_b @ P2 ) ) ) ).

% vwalk_join_hd'
thf(fact_967_fthe__elem_Orep__eq,axiom,
    ( fthe_e7442499522476018237_a_b_b
    = ( ^ [X4: fset_P5281107635120001194_a_b_b] : ( the_el4127461656392778949_a_b_b @ ( fset_P783253628892185035_a_b_b @ X4 ) ) ) ) ).

% fthe_elem.rep_eq
thf(fact_968_prod__set__simps_I1_J,axiom,
    ! [X3: dtree_a_b,Y: b] :
      ( ( basic_7578771248400840636_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y ) )
      = ( insert_dtree_a_b @ X3 @ bot_bo8730652382759064772ee_a_b ) ) ).

% prod_set_simps(1)
thf(fact_969_disjoint__darcs__if__wf__aux5,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T22: dtree_a_b,E22: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T22 @ E22 ) )
           => ( ( inf_inf_set_b @ ( sup_sup_set_b @ ( darcs_a_b @ T1 ) @ ( insert_b @ E1 @ bot_bot_set_b ) ) @ ( sup_sup_set_b @ ( darcs_a_b @ T22 ) @ ( insert_b @ E22 @ bot_bot_set_b ) ) )
              = bot_bot_set_b ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux5
thf(fact_970_wf__dtree_Odarc__in__sub__if__dtail__in__sub,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,Dt: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,E: produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,E1: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,T1: dtree_6636540493345571111_a_b_b,R: produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( ( dtail_367104560391499092_a_b_b @ T @ Dt @ E )
          = V )
       => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ T ) )
         => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E1 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
           => ( ( is_sub6703628162287821076_a_b_b @ T1 @ X3 )
             => ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
                  = T )
               => ( ( member4380921116106875537_a_b_b @ V @ ( dverts1640268204329280112_a_b_b @ T1 ) )
                 => ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ X3 ) ) ) ) ) ) ) ) ) ).

% wf_dtree.darc_in_sub_if_dtail_in_sub
thf(fact_971_wf__dtree_Odarc__in__sub__if__dtail__in__sub,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,Dt: produc4558475209616630778_a_b_b > dtree_a_b,E: produc4558475209616630778_a_b_b,V: dtree_a_b,X3: dtree_8397784528784866983_a_b_b,E1: produc4558475209616630778_a_b_b,Xs: fset_P8532786667068971368_a_b_b,T1: dtree_8397784528784866983_a_b_b,R: dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( ( dtail_2974526391675993812_a_b_b @ T @ Dt @ E )
          = V )
       => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ T ) )
         => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E1 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
           => ( ( is_sub3309389790737183380_a_b_b @ T1 @ X3 )
             => ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
                  = T )
               => ( ( member_dtree_a_b @ V @ ( dverts5490399362891984880_a_b_b @ T1 ) )
                 => ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ X3 ) ) ) ) ) ) ) ) ) ).

% wf_dtree.darc_in_sub_if_dtail_in_sub
thf(fact_972_wf__dtree_Odarc__in__sub__if__dtail__in__sub,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,Dt: dtree_a_b > produc4558475209616630778_a_b_b,E: dtree_a_b,V: produc4558475209616630778_a_b_b,X3: dtree_8690448868185853351ee_a_b,E1: dtree_a_b,Xs: fset_P1087233464713034472ee_a_b,T1: dtree_8690448868185853351ee_a_b,R: produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( ( dtail_456444732827996628ee_a_b @ T @ Dt @ E )
          = V )
       => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ T ) )
         => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E1 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
           => ( ( is_sub791308131889186196ee_a_b @ T1 @ X3 )
             => ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
                  = T )
               => ( ( member4380921116106875537_a_b_b @ V @ ( dverts2972317704043987696ee_a_b @ T1 ) )
                 => ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ X3 ) ) ) ) ) ) ) ) ) ).

% wf_dtree.darc_in_sub_if_dtail_in_sub
thf(fact_973_wf__dtree_Odarc__in__sub__if__dtail__in__sub,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,Dt: dtree_a_b > dtree_a_b,E: dtree_a_b,V: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,E1: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,T1: dtree_1861073144021109543ee_a_b,R: dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( ( dtail_6577300080304104276ee_a_b @ T @ Dt @ E )
          = V )
       => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ T ) )
         => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E1 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
           => ( ( is_sub7866859304860047124ee_a_b @ T1 @ X3 )
             => ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
                  = T )
               => ( ( member_dtree_a_b @ V @ ( dverts2436977245124431984ee_a_b @ T1 ) )
                 => ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ X3 ) ) ) ) ) ) ) ) ) ).

% wf_dtree.darc_in_sub_if_dtail_in_sub
thf(fact_974_wf__dtree_Odarc__in__sub__if__dtail__in__sub,axiom,
    ! [T: dtree_a_b,Dt: b > a,E: b,V: a,X3: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,R: a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( dtail_a_b @ T @ Dt @ E )
          = V )
       => ( ( member_b @ E @ ( darcs_a_b @ T ) )
         => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
           => ( ( is_subtree_a_b @ T1 @ X3 )
             => ( ( ( node_a_b @ R @ Xs )
                  = T )
               => ( ( member_a @ V @ ( dverts_a_b @ T1 ) )
                 => ( member_b @ E @ ( darcs_a_b @ X3 ) ) ) ) ) ) ) ) ) ).

% wf_dtree.darc_in_sub_if_dtail_in_sub
thf(fact_975_Un__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A2 @ B4 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A2 )
        | ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_976_Un__iff,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( sup_su8994539500306794332ee_a_b @ A2 @ B4 ) )
      = ( ( member_dtree_a_b @ C @ A2 )
        | ( member_dtree_a_b @ C @ B4 ) ) ) ).

% Un_iff
thf(fact_977_UnCI,axiom,
    ! [C: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( ~ ( member4380921116106875537_a_b_b @ C @ B4 )
       => ( member4380921116106875537_a_b_b @ C @ A2 ) )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A2 @ B4 ) ) ) ).

% UnCI
thf(fact_978_UnCI,axiom,
    ! [C: dtree_a_b,B4: set_dtree_a_b,A2: set_dtree_a_b] :
      ( ( ~ ( member_dtree_a_b @ C @ B4 )
       => ( member_dtree_a_b @ C @ A2 ) )
     => ( member_dtree_a_b @ C @ ( sup_su8994539500306794332ee_a_b @ A2 @ B4 ) ) ) ).

% UnCI
thf(fact_979_sup__bot__left,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ bot_bo2895716411488905534_a_b_b @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_980_sup__bot__right,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b )
      = X3 ) ).

% sup_bot_right
thf(fact_981_bot__eq__sup__iff,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y: fset_P5281107635120001194_a_b_b] :
      ( ( bot_bo2895716411488905534_a_b_b
        = ( sup_su860928060825958358_a_b_b @ X3 @ Y ) )
      = ( ( X3 = bot_bo2895716411488905534_a_b_b )
        & ( Y = bot_bo2895716411488905534_a_b_b ) ) ) ).

% bot_eq_sup_iff
thf(fact_982_sup__eq__bot__iff,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y: fset_P5281107635120001194_a_b_b] :
      ( ( ( sup_su860928060825958358_a_b_b @ X3 @ Y )
        = bot_bo2895716411488905534_a_b_b )
      = ( ( X3 = bot_bo2895716411488905534_a_b_b )
        & ( Y = bot_bo2895716411488905534_a_b_b ) ) ) ).

% sup_eq_bot_iff
thf(fact_983_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: fset_P5281107635120001194_a_b_b,B: fset_P5281107635120001194_a_b_b] :
      ( ( ( sup_su860928060825958358_a_b_b @ A @ B )
        = bot_bo2895716411488905534_a_b_b )
      = ( ( A = bot_bo2895716411488905534_a_b_b )
        & ( B = bot_bo2895716411488905534_a_b_b ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_984_sup__bot_Oleft__neutral,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ bot_bo2895716411488905534_a_b_b @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_985_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: fset_P5281107635120001194_a_b_b,B: fset_P5281107635120001194_a_b_b] :
      ( ( bot_bo2895716411488905534_a_b_b
        = ( sup_su860928060825958358_a_b_b @ A @ B ) )
      = ( ( A = bot_bo2895716411488905534_a_b_b )
        & ( B = bot_bo2895716411488905534_a_b_b ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_986_sup__bot_Oright__neutral,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ A @ bot_bo2895716411488905534_a_b_b )
      = A ) ).

% sup_bot.right_neutral
thf(fact_987_UnI2,axiom,
    ! [C: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ B4 )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A2 @ B4 ) ) ) ).

% UnI2
thf(fact_988_UnI2,axiom,
    ! [C: dtree_a_b,B4: set_dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ B4 )
     => ( member_dtree_a_b @ C @ ( sup_su8994539500306794332ee_a_b @ A2 @ B4 ) ) ) ).

% UnI2
thf(fact_989_UnI1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A2 )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A2 @ B4 ) ) ) ).

% UnI1
thf(fact_990_UnI1,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ A2 )
     => ( member_dtree_a_b @ C @ ( sup_su8994539500306794332ee_a_b @ A2 @ B4 ) ) ) ).

% UnI1
thf(fact_991_UnE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A2 @ B4 ) )
     => ( ~ ( member4380921116106875537_a_b_b @ C @ A2 )
       => ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% UnE
thf(fact_992_UnE,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( sup_su8994539500306794332ee_a_b @ A2 @ B4 ) )
     => ( ~ ( member_dtree_a_b @ C @ A2 )
       => ( member_dtree_a_b @ C @ B4 ) ) ) ).

% UnE
thf(fact_993_wf__dtree_Owf__verts,axiom,
    ! [T: dtree_a_b] :
      ( ( wf_dtree_a_b @ T )
     => ( wf_dverts_a_b @ T ) ) ).

% wf_dtree.wf_verts
thf(fact_994_wf__dtree_Ointro,axiom,
    ! [T: dtree_a_b] :
      ( ( wf_darcs_a_b @ T )
     => ( ( wf_dverts_a_b @ T )
       => ( wf_dtree_a_b @ T ) ) ) ).

% wf_dtree.intro
thf(fact_995_wf__dtree__def,axiom,
    ( wf_dtree_a_b
    = ( ^ [T4: dtree_a_b] :
          ( ( wf_darcs_a_b @ T4 )
          & ( wf_dverts_a_b @ T4 ) ) ) ) ).

% wf_dtree_def
thf(fact_996_wf__dtree_Owf__dtree__rec,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b,E: b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( node_a_b @ R @ Xs )
          = T )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( wf_dtree_a_b @ X3 ) ) ) ) ).

% wf_dtree.wf_dtree_rec
thf(fact_997_wf__dtree_Oarc__uneq__if__subtree__uneq,axiom,
    ! [T: dtree_a_b,X1: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,X22: dtree_a_b,E22: b,R: a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( X1 != X22 )
           => ( ( ( node_a_b @ R @ Xs )
                = T )
             => ( E1 != E22 ) ) ) ) ) ) ).

% wf_dtree.arc_uneq_if_subtree_uneq
thf(fact_998_wf__dtree_Osubtree__uneq__if__arc__uneq,axiom,
    ! [T: dtree_a_b,X1: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,X22: dtree_a_b,E22: b,R: a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X22 @ E22 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( E1 != E22 )
           => ( ( ( node_a_b @ R @ Xs )
                = T )
             => ( X1 != X22 ) ) ) ) ) ) ).

% wf_dtree.subtree_uneq_if_arc_uneq
thf(fact_999_wf__dtree_Odtail__in__dverts,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dtail_367104560391499092_a_b_b @ T @ Def2 @ E ) @ ( dverts1640268204329280112_a_b_b @ T ) ) ) ) ).

% wf_dtree.dtail_in_dverts
thf(fact_1000_wf__dtree_Odtail__in__dverts,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ T ) )
       => ( member_dtree_a_b @ ( dtail_2974526391675993812_a_b_b @ T @ Def2 @ E ) @ ( dverts5490399362891984880_a_b_b @ T ) ) ) ) ).

% wf_dtree.dtail_in_dverts
thf(fact_1001_wf__dtree_Odtail__in__dverts,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dtail_456444732827996628ee_a_b @ T @ Def2 @ E ) @ ( dverts2972317704043987696ee_a_b @ T ) ) ) ) ).

% wf_dtree.dtail_in_dverts
thf(fact_1002_wf__dtree_Odtail__in__dverts,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ T ) )
       => ( member_dtree_a_b @ ( dtail_6577300080304104276ee_a_b @ T @ Def2 @ E ) @ ( dverts2436977245124431984ee_a_b @ T ) ) ) ) ).

% wf_dtree.dtail_in_dverts
thf(fact_1003_wf__dtree_Ochild__arc__not__subtree,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b,E1: b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( node_a_b @ R @ Xs )
          = T )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ~ ( member_b @ E1 @ ( darcs_a_b @ X3 ) ) ) ) ) ).

% wf_dtree.child_arc_not_subtree
thf(fact_1004_wf__dtree_Osubtree__root__not__root,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b,E: b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( T
          = ( node_a_b @ R @ Xs ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( root_a_b @ X3 )
           != R ) ) ) ) ).

% wf_dtree.subtree_root_not_root
thf(fact_1005_wf__dtree_Odtail__in__subdverts,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ X3 ) )
       => ( ( is_sub6703628162287821076_a_b_b @ X3 @ T )
         => ( member4380921116106875537_a_b_b @ ( dtail_367104560391499092_a_b_b @ T @ Def2 @ E ) @ ( dverts1640268204329280112_a_b_b @ X3 ) ) ) ) ) ).

% wf_dtree.dtail_in_subdverts
thf(fact_1006_wf__dtree_Odtail__in__subdverts,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ X3 ) )
       => ( ( is_sub3309389790737183380_a_b_b @ X3 @ T )
         => ( member_dtree_a_b @ ( dtail_2974526391675993812_a_b_b @ T @ Def2 @ E ) @ ( dverts5490399362891984880_a_b_b @ X3 ) ) ) ) ) ).

% wf_dtree.dtail_in_subdverts
thf(fact_1007_wf__dtree_Odtail__in__subdverts,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ X3 ) )
       => ( ( is_sub791308131889186196ee_a_b @ X3 @ T )
         => ( member4380921116106875537_a_b_b @ ( dtail_456444732827996628ee_a_b @ T @ Def2 @ E ) @ ( dverts2972317704043987696ee_a_b @ X3 ) ) ) ) ) ).

% wf_dtree.dtail_in_subdverts
thf(fact_1008_wf__dtree_Odtail__in__subdverts,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ X3 ) )
       => ( ( is_sub7866859304860047124ee_a_b @ X3 @ T )
         => ( member_dtree_a_b @ ( dtail_6577300080304104276ee_a_b @ T @ Def2 @ E ) @ ( dverts2436977245124431984ee_a_b @ X3 ) ) ) ) ) ).

% wf_dtree.dtail_in_subdverts
thf(fact_1009_wf__dtree_Odtail__in__childverts,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,R: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ X3 ) )
       => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E3 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
         => ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dtail_367104560391499092_a_b_b @ T @ Def2 @ E ) @ ( dverts1640268204329280112_a_b_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dtail_in_childverts
thf(fact_1010_wf__dtree_Odtail__in__childverts,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P8532786667068971368_a_b_b,R: dtree_a_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ X3 ) )
       => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E3 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
         => ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dtail_2974526391675993812_a_b_b @ T @ Def2 @ E ) @ ( dverts5490399362891984880_a_b_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dtail_in_childverts
thf(fact_1011_wf__dtree_Odtail__in__childverts,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,E3: dtree_a_b,Xs: fset_P1087233464713034472ee_a_b,R: produc4558475209616630778_a_b_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ X3 ) )
       => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E3 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
         => ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dtail_456444732827996628ee_a_b @ T @ Def2 @ E ) @ ( dverts2972317704043987696ee_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dtail_in_childverts
thf(fact_1012_wf__dtree_Odtail__in__childverts,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,E3: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,R: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ X3 ) )
       => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E3 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
         => ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dtail_6577300080304104276ee_a_b @ T @ Def2 @ E ) @ ( dverts2436977245124431984ee_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dtail_in_childverts
thf(fact_1013_wf__dtree_Odtail__in__childverts,axiom,
    ! [T: dtree_a_b,E: b,X3: dtree_a_b,E3: b,Xs: fset_P5281107635120001194_a_b_b,R: a,Def2: b > a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member_b @ E @ ( darcs_a_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E3 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( node_a_b @ R @ Xs )
              = T )
           => ( member_a @ ( dtail_a_b @ T @ Def2 @ E ) @ ( dverts_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dtail_in_childverts
thf(fact_1014_wf__dtree_Oarc__in__subtree__if__tail__in__subtree,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,Dt: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,P2: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( dtail_367104560391499092_a_b_b @ T @ Dt @ P2 ) @ ( dverts1640268204329280112_a_b_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_2805522099973010655_a_b_b @ T ) )
         => ( ( T
              = ( node_P961815112480277940_a_b_b @ R @ Xs ) )
           => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
             => ( member4380921116106875537_a_b_b @ P2 @ ( darcs_2805522099973010655_a_b_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.arc_in_subtree_if_tail_in_subtree
thf(fact_1015_wf__dtree_Oarc__in__subtree__if__tail__in__subtree,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,Dt: dtree_a_b > produc4558475209616630778_a_b_b,P2: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,E: dtree_a_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( dtail_456444732827996628ee_a_b @ T @ Dt @ P2 ) @ ( dverts2972317704043987696ee_a_b @ X3 ) )
       => ( ( member_dtree_a_b @ P2 @ ( darcs_6860198329303686239ee_a_b @ T ) )
         => ( ( T
              = ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
           => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
             => ( member_dtree_a_b @ P2 @ ( darcs_6860198329303686239ee_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.arc_in_subtree_if_tail_in_subtree
thf(fact_1016_wf__dtree_Oarc__in__subtree__if__tail__in__subtree,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,Dt: produc4558475209616630778_a_b_b > dtree_a_b,P2: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,E: produc4558475209616630778_a_b_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member_dtree_a_b @ ( dtail_2974526391675993812_a_b_b @ T @ Dt @ P2 ) @ ( dverts5490399362891984880_a_b_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_154907951296907615_a_b_b @ T ) )
         => ( ( T
              = ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
           => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
             => ( member4380921116106875537_a_b_b @ P2 @ ( darcs_154907951296907615_a_b_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.arc_in_subtree_if_tail_in_subtree
thf(fact_1017_wf__dtree_Oarc__in__subtree__if__tail__in__subtree,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,Dt: dtree_a_b > dtree_a_b,P2: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,E: dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ ( dtail_6577300080304104276ee_a_b @ T @ Dt @ P2 ) @ ( dverts2436977245124431984ee_a_b @ X3 ) )
       => ( ( member_dtree_a_b @ P2 @ ( darcs_1812195894409408735ee_a_b @ T ) )
         => ( ( T
              = ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
           => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
             => ( member_dtree_a_b @ P2 @ ( darcs_1812195894409408735ee_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.arc_in_subtree_if_tail_in_subtree
thf(fact_1018_wf__dtree_Oarc__in__subtree__if__tail__in__subtree,axiom,
    ! [T: dtree_a_b,Dt: b > a,P2: b,X3: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,E: b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member_a @ ( dtail_a_b @ T @ Dt @ P2 ) @ ( dverts_a_b @ X3 ) )
       => ( ( member_b @ P2 @ ( darcs_a_b @ T ) )
         => ( ( T
              = ( node_a_b @ R @ Xs ) )
           => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
             => ( member_b @ P2 @ ( darcs_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.arc_in_subtree_if_tail_in_subtree
thf(fact_1019_wf__dtree_Odhead__in__verts__if__dtail,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,Dt: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,P2: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,R: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,E: produc4558475209616630778_a_b_b,Dh: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( dtail_367104560391499092_a_b_b @ T @ Dt @ P2 ) @ ( dverts1640268204329280112_a_b_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_2805522099973010655_a_b_b @ T ) )
         => ( ( T
              = ( node_P961815112480277940_a_b_b @ R @ Xs ) )
           => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
             => ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Dh @ P2 ) @ ( dverts1640268204329280112_a_b_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_verts_if_dtail
thf(fact_1020_wf__dtree_Odhead__in__verts__if__dtail,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,Dt: dtree_a_b > produc4558475209616630778_a_b_b,P2: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,R: produc4558475209616630778_a_b_b,Xs: fset_P1087233464713034472ee_a_b,E: dtree_a_b,Dh: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( dtail_456444732827996628ee_a_b @ T @ Dt @ P2 ) @ ( dverts2972317704043987696ee_a_b @ X3 ) )
       => ( ( member_dtree_a_b @ P2 @ ( darcs_6860198329303686239ee_a_b @ T ) )
         => ( ( T
              = ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
           => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
             => ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Dh @ P2 ) @ ( dverts2972317704043987696ee_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_verts_if_dtail
thf(fact_1021_wf__dtree_Odhead__in__verts__if__dtail,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,Dt: produc4558475209616630778_a_b_b > dtree_a_b,P2: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,R: dtree_a_b,Xs: fset_P8532786667068971368_a_b_b,E: produc4558475209616630778_a_b_b,Dh: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member_dtree_a_b @ ( dtail_2974526391675993812_a_b_b @ T @ Dt @ P2 ) @ ( dverts5490399362891984880_a_b_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_154907951296907615_a_b_b @ T ) )
         => ( ( T
              = ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
           => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
             => ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Dh @ P2 ) @ ( dverts5490399362891984880_a_b_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_verts_if_dtail
thf(fact_1022_wf__dtree_Odhead__in__verts__if__dtail,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,Dt: dtree_a_b > dtree_a_b,P2: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,R: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,E: dtree_a_b,Dh: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ ( dtail_6577300080304104276ee_a_b @ T @ Dt @ P2 ) @ ( dverts2436977245124431984ee_a_b @ X3 ) )
       => ( ( member_dtree_a_b @ P2 @ ( darcs_1812195894409408735ee_a_b @ T ) )
         => ( ( T
              = ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
           => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
             => ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Dh @ P2 ) @ ( dverts2436977245124431984ee_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_verts_if_dtail
thf(fact_1023_wf__dtree_Odhead__in__verts__if__dtail,axiom,
    ! [T: dtree_a_b,Dt: b > a,P2: b,X3: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,E: b,Dh: b > a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member_a @ ( dtail_a_b @ T @ Dt @ P2 ) @ ( dverts_a_b @ X3 ) )
       => ( ( member_b @ P2 @ ( darcs_a_b @ T ) )
         => ( ( T
              = ( node_a_b @ R @ Xs ) )
           => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
             => ( member_a @ ( dhead_a_b @ T @ Dh @ P2 ) @ ( dverts_a_b @ X3 ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_verts_if_dtail
thf(fact_1024_funion__fempty,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ( sup_su860928060825958358_a_b_b @ A2 @ B4 )
        = bot_bo2895716411488905534_a_b_b )
      = ( ( A2 = bot_bo2895716411488905534_a_b_b )
        & ( B4 = bot_bo2895716411488905534_a_b_b ) ) ) ).

% funion_fempty
thf(fact_1025_funion__finsert__right,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
      = ( finser8437519239679886002_a_b_b @ A @ ( sup_su860928060825958358_a_b_b @ A2 @ B4 ) ) ) ).

% funion_finsert_right
thf(fact_1026_funion__finsert__left,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b,C2: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ B4 ) @ C2 )
      = ( finser8437519239679886002_a_b_b @ A @ ( sup_su860928060825958358_a_b_b @ B4 @ C2 ) ) ) ).

% funion_finsert_left
thf(fact_1027_union__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( sup_su860928060825958358_a_b_b @ X3 @ Xa ) )
      = ( sup_su2887895092731772380_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa ) ) ) ).

% union_fset
thf(fact_1028_funion__fempty__right,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ A2 @ bot_bo2895716411488905534_a_b_b )
      = A2 ) ).

% funion_fempty_right
thf(fact_1029_funion__fempty__left,axiom,
    ! [B4: fset_P5281107635120001194_a_b_b] :
      ( ( sup_su860928060825958358_a_b_b @ bot_bo2895716411488905534_a_b_b @ B4 )
      = B4 ) ).

% funion_fempty_left
thf(fact_1030_funion__fsingleton__iff,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ( sup_su860928060825958358_a_b_b @ A2 @ B4 )
        = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
      = ( ( ( A2 = bot_bo2895716411488905534_a_b_b )
          & ( B4
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) )
        | ( ( A2
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
          & ( B4 = bot_bo2895716411488905534_a_b_b ) )
        | ( ( A2
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
          & ( B4
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ).

% funion_fsingleton_iff
thf(fact_1031_fsingleton__funion__iff,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b )
        = ( sup_su860928060825958358_a_b_b @ A2 @ B4 ) )
      = ( ( ( A2 = bot_bo2895716411488905534_a_b_b )
          & ( B4
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) )
        | ( ( A2
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
          & ( B4 = bot_bo2895716411488905534_a_b_b ) )
        | ( ( A2
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
          & ( B4
            = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ).

% fsingleton_funion_iff
thf(fact_1032_finsert__is__funion,axiom,
    ( finser8437519239679886002_a_b_b
    = ( ^ [A6: produc4558475209616630778_a_b_b] : ( sup_su860928060825958358_a_b_b @ ( finser8437519239679886002_a_b_b @ A6 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% finsert_is_funion
thf(fact_1033_is__singletonI_H,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ( A2 != bot_bo3721250822024684356_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
           => ( ( member4380921116106875537_a_b_b @ Y3 @ A2 )
             => ( X2 = Y3 ) ) )
       => ( is_sin1118336051388392454_a_b_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_1034_is__singletonI_H,axiom,
    ! [A2: set_dtree_a_b] :
      ( ( A2 != bot_bo8730652382759064772ee_a_b )
     => ( ! [X2: dtree_a_b,Y3: dtree_a_b] :
            ( ( member_dtree_a_b @ X2 @ A2 )
           => ( ( member_dtree_a_b @ Y3 @ A2 )
             => ( X2 = Y3 ) ) )
       => ( is_sin1157029654344370822ee_a_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_1035_wf__dtree_Odhead__in__dverts,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Def2 @ E ) @ ( dverts1640268204329280112_a_b_b @ T ) ) ) ) ).

% wf_dtree.dhead_in_dverts
thf(fact_1036_wf__dtree_Odhead__in__dverts,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ T ) )
       => ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Def2 @ E ) @ ( dverts5490399362891984880_a_b_b @ T ) ) ) ) ).

% wf_dtree.dhead_in_dverts
thf(fact_1037_wf__dtree_Odhead__in__dverts,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Def2 @ E ) @ ( dverts2972317704043987696ee_a_b @ T ) ) ) ) ).

% wf_dtree.dhead_in_dverts
thf(fact_1038_wf__dtree_Odhead__in__dverts,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ T ) )
       => ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Def2 @ E ) @ ( dverts2436977245124431984ee_a_b @ T ) ) ) ) ).

% wf_dtree.dhead_in_dverts
thf(fact_1039_dhead__in__child__eq__child,axiom,
    ! [T: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,E: b,R: a,Def2: b > a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
     => ( ( member_b @ E @ ( darcs_a_b @ T ) )
       => ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
         => ( ( dhead_a_b @ ( node_a_b @ R @ Xs ) @ Def2 @ E )
            = ( dhead_a_b @ T @ Def2 @ E ) ) ) ) ) ).

% dhead_in_child_eq_child
thf(fact_1040_dhead__in__set__eq__root,axiom,
    ! [T: dtree_a_b,E: b,Xs: fset_P5281107635120001194_a_b_b,R: a,Def2: b > a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
     => ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
       => ( ( dhead_a_b @ ( node_a_b @ R @ Xs ) @ Def2 @ E )
          = ( root_a_b @ T ) ) ) ) ).

% dhead_in_set_eq_root
thf(fact_1041_wf__dtree_Odhead__in__childverts,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,R: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ X3 ) )
       => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E3 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
         => ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Def2 @ E ) @ ( dverts1640268204329280112_a_b_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts
thf(fact_1042_wf__dtree_Odhead__in__childverts,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P8532786667068971368_a_b_b,R: dtree_a_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ X3 ) )
       => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E3 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
         => ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Def2 @ E ) @ ( dverts5490399362891984880_a_b_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts
thf(fact_1043_wf__dtree_Odhead__in__childverts,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,E3: dtree_a_b,Xs: fset_P1087233464713034472ee_a_b,R: produc4558475209616630778_a_b_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ X3 ) )
       => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E3 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
         => ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Def2 @ E ) @ ( dverts2972317704043987696ee_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts
thf(fact_1044_wf__dtree_Odhead__in__childverts,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,E3: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,R: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ X3 ) )
       => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E3 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
         => ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Def2 @ E ) @ ( dverts2436977245124431984ee_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts
thf(fact_1045_wf__dtree_Odhead__in__childverts,axiom,
    ! [T: dtree_a_b,E: b,X3: dtree_a_b,E3: b,Xs: fset_P5281107635120001194_a_b_b,R: a,Def2: b > a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member_b @ E @ ( darcs_a_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E3 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( node_a_b @ R @ Xs )
              = T )
           => ( member_a @ ( dhead_a_b @ T @ Def2 @ E ) @ ( dverts_a_b @ X3 ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts
thf(fact_1046_wf__dtree_Odhead__notin__subtree__wo__root,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,X3: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,P2: produc4558475209616630778_a_b_b,R: produc4558475209616630778_a_b_b,Dh: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
       => ( ~ ( member4380921116106875537_a_b_b @ P2 @ ( darcs_2805522099973010655_a_b_b @ X3 ) )
         => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_2805522099973010655_a_b_b @ T ) )
           => ( ( T
                = ( node_P961815112480277940_a_b_b @ R @ Xs ) )
             => ~ ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Dh @ P2 ) @ ( minus_1392386589478415753_a_b_b @ ( dverts1640268204329280112_a_b_b @ X3 ) @ ( insert1613891728210272810_a_b_b @ ( root_P204151722342556500_a_b_b @ X3 ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ) ) ) ).

% wf_dtree.dhead_notin_subtree_wo_root
thf(fact_1047_wf__dtree_Odhead__notin__subtree__wo__root,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,X3: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,Xs: fset_P8532786667068971368_a_b_b,P2: produc4558475209616630778_a_b_b,R: dtree_a_b,Dh: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
       => ( ~ ( member4380921116106875537_a_b_b @ P2 @ ( darcs_154907951296907615_a_b_b @ X3 ) )
         => ( ( member4380921116106875537_a_b_b @ P2 @ ( darcs_154907951296907615_a_b_b @ T ) )
           => ( ( T
                = ( node_d5271158820939511604_a_b_b @ R @ Xs ) )
             => ~ ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Dh @ P2 ) @ ( minus_3445990907098541065ee_a_b @ ( dverts5490399362891984880_a_b_b @ X3 ) @ ( insert_dtree_a_b @ ( root_d8071547644108387540_a_b_b @ X3 ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ) ) ) ).

% wf_dtree.dhead_notin_subtree_wo_root
thf(fact_1048_wf__dtree_Odhead__notin__subtree__wo__root,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,X3: dtree_8690448868185853351ee_a_b,E: dtree_a_b,Xs: fset_P1087233464713034472ee_a_b,P2: dtree_a_b,R: produc4558475209616630778_a_b_b,Dh: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
       => ( ~ ( member_dtree_a_b @ P2 @ ( darcs_6860198329303686239ee_a_b @ X3 ) )
         => ( ( member_dtree_a_b @ P2 @ ( darcs_6860198329303686239ee_a_b @ T ) )
           => ( ( T
                = ( node_P2753077162091514420ee_a_b @ R @ Xs ) )
             => ~ ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Dh @ P2 ) @ ( minus_1392386589478415753_a_b_b @ ( dverts2972317704043987696ee_a_b @ X3 ) @ ( insert1613891728210272810_a_b_b @ ( root_P5553465985260390356ee_a_b @ X3 ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ) ) ) ).

% wf_dtree.dhead_notin_subtree_wo_root
thf(fact_1049_wf__dtree_Odhead__notin__subtree__wo__root,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,X3: dtree_1861073144021109543ee_a_b,E: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,P2: dtree_a_b,R: dtree_a_b,Dh: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
       => ( ~ ( member_dtree_a_b @ P2 @ ( darcs_1812195894409408735ee_a_b @ X3 ) )
         => ( ( member_dtree_a_b @ P2 @ ( darcs_1812195894409408735ee_a_b @ T ) )
           => ( ( T
                = ( node_d7487230363575057332ee_a_b @ R @ Xs ) )
             => ~ ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Dh @ P2 ) @ ( minus_3445990907098541065ee_a_b @ ( dverts2436977245124431984ee_a_b @ X3 ) @ ( insert_dtree_a_b @ ( root_d1746759089207908692ee_a_b @ X3 ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ) ) ) ).

% wf_dtree.dhead_notin_subtree_wo_root
thf(fact_1050_wf__dtree_Odhead__notin__subtree__wo__root,axiom,
    ! [T: dtree_a_b,X3: dtree_a_b,E: b,Xs: fset_P5281107635120001194_a_b_b,P2: b,R: a,Dh: b > a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( ~ ( member_b @ P2 @ ( darcs_a_b @ X3 ) )
         => ( ( member_b @ P2 @ ( darcs_a_b @ T ) )
           => ( ( T
                = ( node_a_b @ R @ Xs ) )
             => ~ ( member_a @ ( dhead_a_b @ T @ Dh @ P2 ) @ ( minus_minus_set_a @ ( dverts_a_b @ X3 ) @ ( insert_a @ ( root_a_b @ X3 ) @ bot_bot_set_a ) ) ) ) ) ) ) ) ).

% wf_dtree.dhead_notin_subtree_wo_root
thf(fact_1051_wf__dtree_Odhead__in__childverts__no__root,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_6636540493345571111_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P271555816861255656_a_b_b,R: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ X3 ) )
       => ( ( member684607838164940587_a_b_b @ ( produc6281861845666676666_a_b_b @ X3 @ E3 ) @ ( fset_P8825802006873508977_a_b_b @ Xs ) )
         => ( ( ( node_P961815112480277940_a_b_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Def2 @ E ) @ ( minus_1392386589478415753_a_b_b @ ( dverts1640268204329280112_a_b_b @ X3 ) @ ( insert1613891728210272810_a_b_b @ ( root_P204151722342556500_a_b_b @ X3 ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts_no_root
thf(fact_1052_wf__dtree_Odhead__in__childverts__no__root,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,X3: dtree_8397784528784866983_a_b_b,E3: produc4558475209616630778_a_b_b,Xs: fset_P8532786667068971368_a_b_b,R: dtree_a_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ X3 ) )
       => ( ( member2386720262296790699_a_b_b @ ( produc74755587182097722_a_b_b @ X3 @ E3 ) @ ( fset_P4440376523358319089_a_b_b @ Xs ) )
         => ( ( ( node_d5271158820939511604_a_b_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Def2 @ E ) @ ( minus_3445990907098541065ee_a_b @ ( dverts5490399362891984880_a_b_b @ X3 ) @ ( insert_dtree_a_b @ ( root_d8071547644108387540_a_b_b @ X3 ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts_no_root
thf(fact_1053_wf__dtree_Odhead__in__childverts__no__root,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,X3: dtree_8690448868185853351ee_a_b,E3: dtree_a_b,Xs: fset_P1087233464713034472ee_a_b,R: produc4558475209616630778_a_b_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ X3 ) )
       => ( ( member5265136988498437675ee_a_b @ ( produc8867760425442229946ee_a_b @ X3 @ E3 ) @ ( fset_P3182333368011040625ee_a_b @ Xs ) )
         => ( ( ( node_P2753077162091514420ee_a_b @ R @ Xs )
              = T )
           => ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Def2 @ E ) @ ( minus_1392386589478415753_a_b_b @ ( dverts2972317704043987696ee_a_b @ X3 ) @ ( insert1613891728210272810_a_b_b @ ( root_P5553465985260390356ee_a_b @ X3 ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts_no_root
thf(fact_1054_wf__dtree_Odhead__in__childverts__no__root,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,X3: dtree_1861073144021109543ee_a_b,E3: dtree_a_b,Xs: fset_P5991447722532490344ee_a_b,R: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ X3 ) )
       => ( ( member1914986943068214699ee_a_b @ ( produc2775200505768408122ee_a_b @ X3 @ E3 ) @ ( fset_P4845137164202167537ee_a_b @ Xs ) )
         => ( ( ( node_d7487230363575057332ee_a_b @ R @ Xs )
              = T )
           => ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Def2 @ E ) @ ( minus_3445990907098541065ee_a_b @ ( dverts2436977245124431984ee_a_b @ X3 ) @ ( insert_dtree_a_b @ ( root_d1746759089207908692ee_a_b @ X3 ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts_no_root
thf(fact_1055_wf__dtree_Odhead__in__childverts__no__root,axiom,
    ! [T: dtree_a_b,E: b,X3: dtree_a_b,E3: b,Xs: fset_P5281107635120001194_a_b_b,R: a,Def2: b > a] :
      ( ( wf_dtree_a_b @ T )
     => ( ( member_b @ E @ ( darcs_a_b @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ E3 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
         => ( ( ( node_a_b @ R @ Xs )
              = T )
           => ( member_a @ ( dhead_a_b @ T @ Def2 @ E ) @ ( minus_minus_set_a @ ( dverts_a_b @ X3 ) @ ( insert_a @ ( root_a_b @ X3 ) @ bot_bot_set_a ) ) ) ) ) ) ) ).

% wf_dtree.dhead_in_childverts_no_root
thf(fact_1056_wf__dtree_Odhead__in__dverts__no__root,axiom,
    ! [T: dtree_6636540493345571111_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr8395680321066191539_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_2805522099973010655_a_b_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dhead_6575884314179264612_a_b_b @ T @ Def2 @ E ) @ ( minus_1392386589478415753_a_b_b @ ( dverts1640268204329280112_a_b_b @ T ) @ ( insert1613891728210272810_a_b_b @ ( root_P204151722342556500_a_b_b @ T ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ).

% wf_dtree.dhead_in_dverts_no_root
thf(fact_1057_wf__dtree_Odhead__in__dverts__no__root,axiom,
    ! [T: dtree_8397784528784866983_a_b_b,E: produc4558475209616630778_a_b_b,Def2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( wf_dtr5498106988402938675_a_b_b @ T )
     => ( ( member4380921116106875537_a_b_b @ E @ ( darcs_154907951296907615_a_b_b @ T ) )
       => ( member_dtree_a_b @ ( dhead_5693685568992248292_a_b_b @ T @ Def2 @ E ) @ ( minus_3445990907098541065ee_a_b @ ( dverts5490399362891984880_a_b_b @ T ) @ ( insert_dtree_a_b @ ( root_d8071547644108387540_a_b_b @ T ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ).

% wf_dtree.dhead_in_dverts_no_root
thf(fact_1058_wf__dtree_Odhead__in__dverts__no__root,axiom,
    ! [T: dtree_8690448868185853351ee_a_b,E: dtree_a_b,Def2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( wf_dtr2980025329554941491ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_6860198329303686239ee_a_b @ T ) )
       => ( member4380921116106875537_a_b_b @ ( dhead_3175603910144251108ee_a_b @ T @ Def2 @ E ) @ ( minus_1392386589478415753_a_b_b @ ( dverts2972317704043987696ee_a_b @ T ) @ ( insert1613891728210272810_a_b_b @ ( root_P5553465985260390356ee_a_b @ T ) @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ).

% wf_dtree.dhead_in_dverts_no_root
thf(fact_1059_wf__dtree_Odhead__in__dverts__no__root,axiom,
    ! [T: dtree_1861073144021109543ee_a_b,E: dtree_a_b,Def2: dtree_a_b > dtree_a_b] :
      ( ( wf_dtr6838629865543741107ee_a_b @ T )
     => ( ( member_dtree_a_b @ E @ ( darcs_1812195894409408735ee_a_b @ T ) )
       => ( member_dtree_a_b @ ( dhead_3390085853063673444ee_a_b @ T @ Def2 @ E ) @ ( minus_3445990907098541065ee_a_b @ ( dverts2436977245124431984ee_a_b @ T ) @ ( insert_dtree_a_b @ ( root_d1746759089207908692ee_a_b @ T ) @ bot_bo8730652382759064772ee_a_b ) ) ) ) ) ).

% wf_dtree.dhead_in_dverts_no_root
thf(fact_1060_Diff__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A2 )
        & ~ ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% Diff_iff
thf(fact_1061_Diff__iff,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) )
      = ( ( member_dtree_a_b @ C @ A2 )
        & ~ ( member_dtree_a_b @ C @ B4 ) ) ) ).

% Diff_iff
thf(fact_1062_DiffI,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A2 )
     => ( ~ ( member4380921116106875537_a_b_b @ C @ B4 )
       => ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) ) ) ) ).

% DiffI
thf(fact_1063_DiffI,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ A2 )
     => ( ~ ( member_dtree_a_b @ C @ B4 )
       => ( member_dtree_a_b @ C @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) ) ) ) ).

% DiffI
thf(fact_1064_Diff__insert0,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ( minus_1392386589478415753_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ B4 ) )
        = ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) ) ) ).

% Diff_insert0
thf(fact_1065_Diff__insert0,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ A2 )
     => ( ( minus_3445990907098541065ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ B4 ) )
        = ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) ) ) ).

% Diff_insert0
thf(fact_1066_insert__Diff1,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ B4 )
     => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A2 ) @ B4 )
        = ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) ) ) ).

% insert_Diff1
thf(fact_1067_insert__Diff1,axiom,
    ! [X3: dtree_a_b,B4: set_dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ B4 )
     => ( ( minus_3445990907098541065ee_a_b @ ( insert_dtree_a_b @ X3 @ A2 ) @ B4 )
        = ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) ) ) ).

% insert_Diff1
thf(fact_1068_DiffD2,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) )
     => ~ ( member4380921116106875537_a_b_b @ C @ B4 ) ) ).

% DiffD2
thf(fact_1069_DiffD2,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) )
     => ~ ( member_dtree_a_b @ C @ B4 ) ) ).

% DiffD2
thf(fact_1070_DiffD1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) )
     => ( member4380921116106875537_a_b_b @ C @ A2 ) ) ).

% DiffD1
thf(fact_1071_DiffD1,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) )
     => ( member_dtree_a_b @ C @ A2 ) ) ).

% DiffD1
thf(fact_1072_DiffE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) )
     => ~ ( ( member4380921116106875537_a_b_b @ C @ A2 )
         => ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% DiffE
thf(fact_1073_DiffE,axiom,
    ! [C: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( member_dtree_a_b @ C @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) )
     => ~ ( ( member_dtree_a_b @ C @ A2 )
         => ( member_dtree_a_b @ C @ B4 ) ) ) ).

% DiffE
thf(fact_1074_psubset__imp__ex__mem,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A2 @ B4 )
     => ? [B3: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ B3 @ ( minus_1392386589478415753_a_b_b @ B4 @ A2 ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1075_psubset__imp__ex__mem,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ord_le1844933027578805380ee_a_b @ A2 @ B4 )
     => ? [B3: dtree_a_b] : ( member_dtree_a_b @ B3 @ ( minus_3445990907098541065ee_a_b @ B4 @ A2 ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1076_insert__Diff__if,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ X3 @ B4 )
       => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A2 ) @ B4 )
          = ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ X3 @ B4 )
       => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A2 ) @ B4 )
          = ( insert1613891728210272810_a_b_b @ X3 @ ( minus_1392386589478415753_a_b_b @ A2 @ B4 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1077_insert__Diff__if,axiom,
    ! [X3: dtree_a_b,B4: set_dtree_a_b,A2: set_dtree_a_b] :
      ( ( ( member_dtree_a_b @ X3 @ B4 )
       => ( ( minus_3445990907098541065ee_a_b @ ( insert_dtree_a_b @ X3 @ A2 ) @ B4 )
          = ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) ) )
      & ( ~ ( member_dtree_a_b @ X3 @ B4 )
       => ( ( minus_3445990907098541065ee_a_b @ ( insert_dtree_a_b @ X3 @ A2 ) @ B4 )
          = ( insert_dtree_a_b @ X3 @ ( minus_3445990907098541065ee_a_b @ A2 @ B4 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1078_insert__Diff,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A2 )
     => ( ( insert1613891728210272810_a_b_b @ A @ ( minus_1392386589478415753_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1079_insert__Diff,axiom,
    ! [A: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ A @ A2 )
     => ( ( insert_dtree_a_b @ A @ ( minus_3445990907098541065ee_a_b @ A2 @ ( insert_dtree_a_b @ A @ bot_bo8730652382759064772ee_a_b ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1080_Diff__insert__absorb,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A2 ) @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1081_Diff__insert__absorb,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ A2 )
     => ( ( minus_3445990907098541065ee_a_b @ ( insert_dtree_a_b @ X3 @ A2 ) @ ( insert_dtree_a_b @ X3 @ bot_bo8730652382759064772ee_a_b ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1082_member__remove,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( remove1850832869696284629_a_b_b @ Y @ A2 ) )
      = ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
        & ( X3 != Y ) ) ) ).

% member_remove
thf(fact_1083_member__remove,axiom,
    ! [X3: dtree_a_b,Y: dtree_a_b,A2: set_dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( remove_dtree_a_b @ Y @ A2 ) )
      = ( ( member_dtree_a_b @ X3 @ A2 )
        & ( X3 != Y ) ) ) ).

% member_remove
thf(fact_1084_removeAll__id,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
     => ( ( remove1345892019315867374_a_b_b @ X3 @ Xs )
        = Xs ) ) ).

% removeAll_id
thf(fact_1085_removeAll__id,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) )
     => ( ( removeAll_dtree_a_b @ X3 @ Xs )
        = Xs ) ) ).

% removeAll_id
thf(fact_1086_removeAll_Osimps_I1_J,axiom,
    ! [X3: product_prod_a_b] :
      ( ( remove3678230900650767028od_a_b @ X3 @ nil_Product_prod_a_b )
      = nil_Product_prod_a_b ) ).

% removeAll.simps(1)
thf(fact_1087_FieldI2,axiom,
    ! [I: produc4558475209616630778_a_b_b,J: produc4558475209616630778_a_b_b,R4: set_Pr2755428042910921141_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R4 )
     => ( member4380921116106875537_a_b_b @ J @ ( field_2612910574630873453_a_b_b @ R4 ) ) ) ).

% FieldI2
thf(fact_1088_FieldI2,axiom,
    ! [I: dtree_a_b,J: dtree_a_b,R4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ I @ J ) @ R4 )
     => ( member_dtree_a_b @ J @ ( field_dtree_a_b @ R4 ) ) ) ).

% FieldI2
thf(fact_1089_FieldI1,axiom,
    ! [I: produc4558475209616630778_a_b_b,J: produc4558475209616630778_a_b_b,R4: set_Pr2755428042910921141_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R4 )
     => ( member4380921116106875537_a_b_b @ I @ ( field_2612910574630873453_a_b_b @ R4 ) ) ) ).

% FieldI1
thf(fact_1090_FieldI1,axiom,
    ! [I: dtree_a_b,J: dtree_a_b,R4: set_Pr8736279663640031669ee_a_b] :
      ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ I @ J ) @ R4 )
     => ( member_dtree_a_b @ I @ ( field_dtree_a_b @ R4 ) ) ) ).

% FieldI1
thf(fact_1091_partition_Osimps_I1_J,axiom,
    ! [P: product_prod_a_b > $o] :
      ( ( partit8484945486742549543od_a_b @ P @ nil_Product_prod_a_b )
      = ( produc5288560138351607191od_a_b @ nil_Product_prod_a_b @ nil_Product_prod_a_b ) ) ).

% partition.simps(1)
thf(fact_1092_pawalk__verts_Osimps_I1_J,axiom,
    ! [U2: product_prod_a_b] :
      ( ( pair_p1830641812483871010od_a_b @ U2 @ nil_Pr906174322249854893od_a_b )
      = ( cons_P7316939131009794654od_a_b @ U2 @ nil_Product_prod_a_b ) ) ).

% pawalk_verts.simps(1)
thf(fact_1093_subsetI,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
         => ( member4380921116106875537_a_b_b @ X2 @ B4 ) )
     => ( ord_le146215904626753808_a_b_b @ A2 @ B4 ) ) ).

% subsetI
thf(fact_1094_subsetI,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ! [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ A2 )
         => ( member_dtree_a_b @ X2 @ B4 ) )
     => ( ord_le6340955050456522384ee_a_b @ A2 @ B4 ) ) ).

% subsetI
thf(fact_1095_insert__subset,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A2 ) @ B4 )
      = ( ( member4380921116106875537_a_b_b @ X3 @ B4 )
        & ( ord_le146215904626753808_a_b_b @ A2 @ B4 ) ) ) ).

% insert_subset
thf(fact_1096_insert__subset,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ ( insert_dtree_a_b @ X3 @ A2 ) @ B4 )
      = ( ( member_dtree_a_b @ X3 @ B4 )
        & ( ord_le6340955050456522384ee_a_b @ A2 @ B4 ) ) ) ).

% insert_subset
thf(fact_1097_bot_Oextremum__uniqueI,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A @ bot_bo2895716411488905534_a_b_b )
     => ( A = bot_bo2895716411488905534_a_b_b ) ) ).

% bot.extremum_uniqueI
thf(fact_1098_bot_Oextremum__unique,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A @ bot_bo2895716411488905534_a_b_b )
      = ( A = bot_bo2895716411488905534_a_b_b ) ) ).

% bot.extremum_unique
thf(fact_1099_bot_Oextremum,axiom,
    ! [A: fset_P5281107635120001194_a_b_b] : ( ord_le789900035998834954_a_b_b @ bot_bo2895716411488905534_a_b_b @ A ) ).

% bot.extremum
thf(fact_1100_subrelI,axiom,
    ! [R: set_Pr3012420139608375472_a_b_b,S4: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: dtree_a_b,Y3: b] :
          ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X2 @ Y3 ) @ R )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X2 @ Y3 ) @ S4 ) )
     => ( ord_le146215904626753808_a_b_b @ R @ S4 ) ) ).

% subrelI
thf(fact_1101_subset__iff,axiom,
    ( ord_le146215904626753808_a_b_b
    = ( ^ [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
        ! [T4: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ T4 @ A5 )
         => ( member4380921116106875537_a_b_b @ T4 @ B5 ) ) ) ) ).

% subset_iff
thf(fact_1102_subset__iff,axiom,
    ( ord_le6340955050456522384ee_a_b
    = ( ^ [A5: set_dtree_a_b,B5: set_dtree_a_b] :
        ! [T4: dtree_a_b] :
          ( ( member_dtree_a_b @ T4 @ A5 )
         => ( member_dtree_a_b @ T4 @ B5 ) ) ) ) ).

% subset_iff
thf(fact_1103_subset__eq,axiom,
    ( ord_le146215904626753808_a_b_b
    = ( ^ [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
        ! [X4: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X4 @ A5 )
         => ( member4380921116106875537_a_b_b @ X4 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_1104_subset__eq,axiom,
    ( ord_le6340955050456522384ee_a_b
    = ( ^ [A5: set_dtree_a_b,B5: set_dtree_a_b] :
        ! [X4: dtree_a_b] :
          ( ( member_dtree_a_b @ X4 @ A5 )
         => ( member_dtree_a_b @ X4 @ B5 ) ) ) ) ).

% subset_eq
thf(fact_1105_subsetD,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,C: produc4558475209616630778_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A2 @ B4 )
     => ( ( member4380921116106875537_a_b_b @ C @ A2 )
       => ( member4380921116106875537_a_b_b @ C @ B4 ) ) ) ).

% subsetD
thf(fact_1106_subsetD,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,C: dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ A2 @ B4 )
     => ( ( member_dtree_a_b @ C @ A2 )
       => ( member_dtree_a_b @ C @ B4 ) ) ) ).

% subsetD
thf(fact_1107_in__mono,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A2 @ B4 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
       => ( member4380921116106875537_a_b_b @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_1108_in__mono,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,X3: dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ A2 @ B4 )
     => ( ( member_dtree_a_b @ X3 @ A2 )
       => ( member_dtree_a_b @ X3 @ B4 ) ) ) ).

% in_mono
thf(fact_1109_Int__Collect__mono,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,P: produc4558475209616630778_a_b_b > $o,Q: produc4558475209616630778_a_b_b > $o] :
      ( ( ord_le146215904626753808_a_b_b @ A2 @ B4 )
     => ( ! [X2: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
           => ( ( P @ X2 )
             => ( Q @ X2 ) ) )
       => ( ord_le146215904626753808_a_b_b @ ( inf_in6138156342456174402_a_b_b @ A2 @ ( collec1368399972772960719_a_b_b @ P ) ) @ ( inf_in6138156342456174402_a_b_b @ B4 @ ( collec1368399972772960719_a_b_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1110_Int__Collect__mono,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,P: dtree_a_b > $o,Q: dtree_a_b > $o] :
      ( ( ord_le6340955050456522384ee_a_b @ A2 @ B4 )
     => ( ! [X2: dtree_a_b] :
            ( ( member_dtree_a_b @ X2 @ A2 )
           => ( ( P @ X2 )
             => ( Q @ X2 ) ) )
       => ( ord_le6340955050456522384ee_a_b @ ( inf_in5903708963019302594ee_a_b @ A2 @ ( collect_dtree_a_b @ P ) ) @ ( inf_in5903708963019302594ee_a_b @ B4 @ ( collect_dtree_a_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1111_subset__code_I1_J,axiom,
    ! [Xs: list_P5360711134766023690_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ ( set_Pr8239206241032387877_a_b_b @ Xs ) @ B4 )
      = ( ! [X4: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X4 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) )
           => ( member4380921116106875537_a_b_b @ X4 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_1112_subset__code_I1_J,axiom,
    ! [Xs: list_dtree_a_b,B4: set_dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ ( set_dtree_a_b2 @ Xs ) @ B4 )
      = ( ! [X4: dtree_a_b] :
            ( ( member_dtree_a_b @ X4 @ ( set_dtree_a_b2 @ Xs ) )
           => ( member_dtree_a_b @ X4 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_1113_subset__insert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ( ord_le146215904626753808_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ B4 ) )
        = ( ord_le146215904626753808_a_b_b @ A2 @ B4 ) ) ) ).

% subset_insert
thf(fact_1114_subset__insert,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B4: set_dtree_a_b] :
      ( ~ ( member_dtree_a_b @ X3 @ A2 )
     => ( ( ord_le6340955050456522384ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ B4 ) )
        = ( ord_le6340955050456522384ee_a_b @ A2 @ B4 ) ) ) ).

% subset_insert
thf(fact_1115_subset__Diff__insert,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,B4: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,C2: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A2 @ ( minus_1392386589478415753_a_b_b @ B4 @ ( insert1613891728210272810_a_b_b @ X3 @ C2 ) ) )
      = ( ( ord_le146215904626753808_a_b_b @ A2 @ ( minus_1392386589478415753_a_b_b @ B4 @ C2 ) )
        & ~ ( member4380921116106875537_a_b_b @ X3 @ A2 ) ) ) ).

% subset_Diff_insert
thf(fact_1116_subset__Diff__insert,axiom,
    ! [A2: set_dtree_a_b,B4: set_dtree_a_b,X3: dtree_a_b,C2: set_dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ A2 @ ( minus_3445990907098541065ee_a_b @ B4 @ ( insert_dtree_a_b @ X3 @ C2 ) ) )
      = ( ( ord_le6340955050456522384ee_a_b @ A2 @ ( minus_3445990907098541065ee_a_b @ B4 @ C2 ) )
        & ~ ( member_dtree_a_b @ X3 @ A2 ) ) ) ).

% subset_Diff_insert
thf(fact_1117_maps__simps_I2_J,axiom,
    ! [F2: product_prod_a_b > list_P1467974523212632366od_a_b] :
      ( ( maps_P4858162816583320641od_a_b @ F2 @ nil_Product_prod_a_b )
      = nil_Product_prod_a_b ) ).

% maps_simps(2)
thf(fact_1118_subset__insert__iff,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ B4 ) )
      = ( ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
         => ( ord_le146215904626753808_a_b_b @ ( minus_1392386589478415753_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) @ B4 ) )
        & ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
         => ( ord_le146215904626753808_a_b_b @ A2 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1119_subset__insert__iff,axiom,
    ! [A2: set_dtree_a_b,X3: dtree_a_b,B4: set_dtree_a_b] :
      ( ( ord_le6340955050456522384ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ B4 ) )
      = ( ( ( member_dtree_a_b @ X3 @ A2 )
         => ( ord_le6340955050456522384ee_a_b @ ( minus_3445990907098541065ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ bot_bo8730652382759064772ee_a_b ) ) @ B4 ) )
        & ( ~ ( member_dtree_a_b @ X3 @ A2 )
         => ( ord_le6340955050456522384ee_a_b @ A2 @ B4 ) ) ) ) ).

% subset_insert_iff
thf(fact_1120_psubset__insert__iff,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ B4 ) )
      = ( ( ( member4380921116106875537_a_b_b @ X3 @ B4 )
         => ( ord_le3723863380492978948_a_b_b @ A2 @ B4 ) )
        & ( ~ ( member4380921116106875537_a_b_b @ X3 @ B4 )
         => ( ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
             => ( ord_le3723863380492978948_a_b_b @ ( minus_1392386589478415753_a_b_b @ A2 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) @ B4 ) )
            & ( ~ ( member4380921116106875537_a_b_b @ X3 @ A2 )
             => ( ord_le146215904626753808_a_b_b @ A2 @ B4 ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1121_psubset__insert__iff,axiom,
    ! [A2: set_dtree_a_b,X3: dtree_a_b,B4: set_dtree_a_b] :
      ( ( ord_le1844933027578805380ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ B4 ) )
      = ( ( ( member_dtree_a_b @ X3 @ B4 )
         => ( ord_le1844933027578805380ee_a_b @ A2 @ B4 ) )
        & ( ~ ( member_dtree_a_b @ X3 @ B4 )
         => ( ( ( member_dtree_a_b @ X3 @ A2 )
             => ( ord_le1844933027578805380ee_a_b @ ( minus_3445990907098541065ee_a_b @ A2 @ ( insert_dtree_a_b @ X3 @ bot_bo8730652382759064772ee_a_b ) ) @ B4 ) )
            & ( ~ ( member_dtree_a_b @ X3 @ A2 )
             => ( ord_le6340955050456522384ee_a_b @ A2 @ B4 ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1122_subset__emptyI,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ~ ( member4380921116106875537_a_b_b @ X2 @ A2 )
     => ( ord_le146215904626753808_a_b_b @ A2 @ bot_bo3721250822024684356_a_b_b ) ) ).

% subset_emptyI
thf(fact_1123_subset__emptyI,axiom,
    ! [A2: set_dtree_a_b] :
      ( ! [X2: dtree_a_b] :
          ~ ( member_dtree_a_b @ X2 @ A2 )
     => ( ord_le6340955050456522384ee_a_b @ A2 @ bot_bo8730652382759064772ee_a_b ) ) ).

% subset_emptyI
thf(fact_1124_fempty__fsubsetI,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b] : ( ord_le789900035998834954_a_b_b @ bot_bo2895716411488905534_a_b_b @ X3 ) ).

% fempty_fsubsetI
thf(fact_1125_fsubset__fempty,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A2 @ bot_bo2895716411488905534_a_b_b )
      = ( A2 = bot_bo2895716411488905534_a_b_b ) ) ).

% fsubset_fempty
thf(fact_1126_fempty__fminus,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( minus_1250967532242559235_a_b_b @ bot_bo2895716411488905534_a_b_b @ A2 )
      = bot_bo2895716411488905534_a_b_b ) ).

% fempty_fminus
thf(fact_1127_fminus__cancel,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( minus_1250967532242559235_a_b_b @ A2 @ A2 )
      = bot_bo2895716411488905534_a_b_b ) ).

% fminus_cancel
thf(fact_1128_fminus__fempty,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( minus_1250967532242559235_a_b_b @ A2 @ bot_bo2895716411488905534_a_b_b )
      = A2 ) ).

% fminus_fempty
thf(fact_1129_minus__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( minus_1250967532242559235_a_b_b @ X3 @ Xa ) )
      = ( minus_1392386589478415753_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa ) ) ) ).

% minus_fset
thf(fact_1130_finsert__fminus__single,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( finser8437519239679886002_a_b_b @ A @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ) )
      = ( finser8437519239679886002_a_b_b @ A @ A2 ) ) ).

% finsert_fminus_single
thf(fact_1131_fminus__disjoint,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( inf_in7138637532943773244_a_b_b @ A2 @ ( minus_1250967532242559235_a_b_b @ B4 @ A2 ) )
      = bot_bo2895716411488905534_a_b_b ) ).

% fminus_disjoint
thf(fact_1132_size__le__if__child__subset,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,Ys: fset_P5281107635120001194_a_b_b,R: a,V: a] :
      ( ( ord_le789900035998834954_a_b_b @ Xs @ Ys )
     => ( ord_less_eq_nat @ ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs ) ) @ ( size_size_dtree_a_b @ ( node_a_b @ V @ Ys ) ) ) ) ).

% size_le_if_child_subset
thf(fact_1133_fsubset__finsertI2,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A2 @ B4 )
     => ( ord_le789900035998834954_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ B @ B4 ) ) ) ).

% fsubset_finsertI2
thf(fact_1134_fsubset__finsertI,axiom,
    ! [B4: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b] : ( ord_le789900035998834954_a_b_b @ B4 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) ) ).

% fsubset_finsertI
thf(fact_1135_finsert__mono,axiom,
    ! [C2: fset_P5281107635120001194_a_b_b,D2: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ C2 @ D2 )
     => ( ord_le789900035998834954_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ C2 ) @ ( finser8437519239679886002_a_b_b @ A @ D2 ) ) ) ).

% finsert_mono
thf(fact_1136_fminus__single__finsert,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) @ B4 )
     => ( ord_le789900035998834954_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ B4 ) ) ) ).

% fminus_single_finsert
thf(fact_1137_refl__onD2,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,X3: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A2 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y ) @ R )
       => ( member4380921116106875537_a_b_b @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_1138_refl__onD2,axiom,
    ! [A2: set_dtree_a_b,R: set_Pr8736279663640031669ee_a_b,X3: dtree_a_b,Y: dtree_a_b] :
      ( ( refl_on_dtree_a_b @ A2 @ R )
     => ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ X3 @ Y ) @ R )
       => ( member_dtree_a_b @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_1139_refl__onD1,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,X3: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A2 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y ) @ R )
       => ( member4380921116106875537_a_b_b @ X3 @ A2 ) ) ) ).

% refl_onD1
thf(fact_1140_refl__onD1,axiom,
    ! [A2: set_dtree_a_b,R: set_Pr8736279663640031669ee_a_b,X3: dtree_a_b,Y: dtree_a_b] :
      ( ( refl_on_dtree_a_b @ A2 @ R )
     => ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ X3 @ Y ) @ R )
       => ( member_dtree_a_b @ X3 @ A2 ) ) ) ).

% refl_onD1
thf(fact_1141_refl__onD,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A2 @ R )
     => ( ( member4380921116106875537_a_b_b @ A @ A2 )
       => ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_1142_refl__onD,axiom,
    ! [A2: set_dtree_a_b,R: set_Pr8736279663640031669ee_a_b,A: dtree_a_b] :
      ( ( refl_on_dtree_a_b @ A2 @ R )
     => ( ( member_dtree_a_b @ A @ A2 )
       => ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_1143_less__eq__fset_Orep__eq,axiom,
    ( ord_le789900035998834954_a_b_b
    = ( ^ [X4: fset_P5281107635120001194_a_b_b,Xa3: fset_P5281107635120001194_a_b_b] : ( ord_le146215904626753808_a_b_b @ ( fset_P783253628892185035_a_b_b @ X4 ) @ ( fset_P783253628892185035_a_b_b @ Xa3 ) ) ) ) ).

% less_eq_fset.rep_eq
thf(fact_1144_fminus__finsert2,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
      = ( minus_1250967532242559235_a_b_b @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ) @ B4 ) ) ).

% fminus_finsert2
thf(fact_1145_fminus__finsert,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
      = ( minus_1250967532242559235_a_b_b @ ( minus_1250967532242559235_a_b_b @ A2 @ B4 ) @ ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ) ) ).

% fminus_finsert
thf(fact_1146_fminus__triv,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ( inf_in7138637532943773244_a_b_b @ A2 @ B4 )
        = bot_bo2895716411488905534_a_b_b )
     => ( ( minus_1250967532242559235_a_b_b @ A2 @ B4 )
        = A2 ) ) ).

% fminus_triv
thf(fact_1147_fsubset__fsingletonD,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
     => ( ( A2 = bot_bo2895716411488905534_a_b_b )
        | ( A2
          = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% fsubset_fsingletonD
thf(fact_1148_wf__darcs__sub,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,Ys: fset_P5281107635120001194_a_b_b,R3: a,R: a] :
      ( ( ord_le789900035998834954_a_b_b @ Xs @ Ys )
     => ( ( wf_darcs_a_b @ ( node_a_b @ R3 @ Ys ) )
       => ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% wf_darcs_sub
thf(fact_1149_wf__dverts__sub,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,Ys: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( ord_le789900035998834954_a_b_b @ Xs @ Ys )
     => ( ( wf_dverts_a_b @ ( node_a_b @ R @ Ys ) )
       => ( wf_dverts_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% wf_dverts_sub
thf(fact_1150_strict__subtree__subset,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,Ys: fset_P5281107635120001194_a_b_b] :
      ( ( strict_subtree_a_b @ T @ ( node_a_b @ R @ Xs ) )
     => ( ( ord_le789900035998834954_a_b_b @ Xs @ Ys )
       => ( strict_subtree_a_b @ T @ ( node_a_b @ R @ Ys ) ) ) ) ).

% strict_subtree_subset
thf(fact_1151_ssubst__Pair__rhs,axiom,
    ! [R: dtree_a_b,S4: b,R4: set_Pr3012420139608375472_a_b_b,S5: b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ R @ S4 ) @ R4 )
     => ( ( S5 = S4 )
       => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ R @ S5 ) @ R4 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_1152_refl__on__domain,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A2 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ B ) @ R )
       => ( ( member4380921116106875537_a_b_b @ A @ A2 )
          & ( member4380921116106875537_a_b_b @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_1153_refl__on__domain,axiom,
    ! [A2: set_dtree_a_b,R: set_Pr8736279663640031669ee_a_b,A: dtree_a_b,B: dtree_a_b] :
      ( ( refl_on_dtree_a_b @ A2 @ R )
     => ( ( member2060280516343777534ee_a_b @ ( produc7805419539522982029ee_a_b @ A @ B ) @ R )
       => ( ( member_dtree_a_b @ A @ A2 )
          & ( member_dtree_a_b @ B @ A2 ) ) ) ) ).

% refl_on_domain
thf(fact_1154_mdeg__child__sucs__le,axiom,
    ! [V: a,T: dtree_a_b,R: a,E: b] : ( ord_less_eq_nat @ ( max_deg_a_b @ ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) @ ( max_deg_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% mdeg_child_sucs_le
thf(fact_1155_mdeg__root,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V: a] :
      ( ( max_deg_a_b @ ( node_a_b @ R @ Xs ) )
      = ( max_deg_a_b @ ( node_a_b @ V @ Xs ) ) ) ).

% mdeg_root
thf(fact_1156_mdeg__ge__child,axiom,
    ! [T1: dtree_a_b,E1: b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs ) )
     => ( ord_less_eq_nat @ ( max_deg_a_b @ T1 ) @ ( max_deg_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% mdeg_ge_child
thf(fact_1157_subtree__child__if__dvert__notroot__mdeg__le1,axiom,
    ! [T: dtree_a_b,V: a] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( V
         != ( root_a_b @ T ) )
       => ( ( member_a @ V @ ( dverts_a_b @ T ) )
         => ? [R5: a,E2: b,Zs3: fset_P5281107635120001194_a_b_b] : ( is_subtree_a_b @ ( node_a_b @ R5 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ ( node_a_b @ V @ Zs3 ) @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) @ T ) ) ) ) ).

% subtree_child_if_dvert_notroot_mdeg_le1
thf(fact_1158_subtree__child__if__dvert__notr__mdeg__le1,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V: a] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ ( node_a_b @ R @ Xs ) ) @ one_one_nat )
     => ( ( V != R )
       => ( ( member_a @ V @ ( dverts_a_b @ ( node_a_b @ R @ Xs ) ) )
         => ? [R5: a,E2: b,Zs3: fset_P5281107635120001194_a_b_b] : ( is_subtree_a_b @ ( node_a_b @ R5 @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ ( node_a_b @ V @ Zs3 ) @ E2 ) @ bot_bo2895716411488905534_a_b_b ) ) @ ( node_a_b @ R @ Xs ) ) ) ) ) ).

% subtree_child_if_dvert_notr_mdeg_le1
thf(fact_1159_num__leaves__ge1,axiom,
    ! [T: dtree_a_b] : ( ord_less_eq_nat @ one_one_nat @ ( num_leaves_a_b @ T ) ) ).

% num_leaves_ge1
thf(fact_1160_dtree__from__list__deg__1,axiom,
    ! [Xs: list_P1467974523212632366od_a_b,R: a] :
      ( ( Xs != nil_Product_prod_a_b )
      = ( ( max_deg_a_b @ ( dtree_from_list_a_b @ R @ Xs ) )
        = one_one_nat ) ) ).

% dtree_from_list_deg_1
thf(fact_1161_num__leaves__1__if__mdeg__1,axiom,
    ! [T: dtree_a_b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( num_leaves_a_b @ T )
        = one_one_nat ) ) ).

% num_leaves_1_if_mdeg_1
thf(fact_1162_mdeg__1__singleton,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b] :
      ( ( ( max_deg_a_b @ ( node_a_b @ R @ Xs ) )
        = one_one_nat )
     => ? [X2: produc4558475209616630778_a_b_b] :
          ( Xs
          = ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) ) ) ).

% mdeg_1_singleton
thf(fact_1163_empty__fset__if__mdeg__le1__not__single,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( Xs
         != ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) )
     => ( ( ord_less_eq_nat @ ( max_deg_a_b @ ( node_a_b @ R @ Xs ) ) @ one_one_nat )
       => ( Xs = bot_bo2895716411488905534_a_b_b ) ) ) ).

% empty_fset_if_mdeg_le1_not_single
thf(fact_1164_empty__fset__if__mdeg__le1__not__single__suc,axiom,
    ! [T: dtree_a_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( sucs_a_b @ T )
         != ( finser8437519239679886002_a_b_b @ X2 @ bot_bo2895716411488905534_a_b_b ) )
     => ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
       => ( ( sucs_a_b @ T )
          = bot_bo2895716411488905534_a_b_b ) ) ) ).

% empty_fset_if_mdeg_le1_not_single_suc
thf(fact_1165_dtree__from__to__list__id,axiom,
    ! [T: dtree_a_b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( dtree_from_list_a_b @ ( root_a_b @ T ) @ ( dtree_to_list_a_b @ T ) )
        = T ) ) ).

% dtree_from_to_list_id
thf(fact_1166_singleton__if__mdeg__le1__elem,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ ( node_a_b @ R @ Xs ) ) @ one_one_nat )
     => ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ Xs ) )
       => ( Xs
          = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% singleton_if_mdeg_le1_elem
thf(fact_1167_mdeg__eq__child__if__singleton__gt1,axiom,
    ! [R: a,T1: dtree_a_b,E1: b] :
      ( ( ord_less_nat @ one_one_nat @ ( max_deg_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ bot_bo2895716411488905534_a_b_b ) ) ) )
     => ( ( max_deg_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ bot_bo2895716411488905534_a_b_b ) ) )
        = ( max_deg_a_b @ T1 ) ) ) ).

% mdeg_eq_child_if_singleton_gt1
thf(fact_1168_singleton__if__mdeg__le1__elem__suc,axiom,
    ! [T: dtree_a_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) )
       => ( ( sucs_a_b @ T )
          = ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ).

% singleton_if_mdeg_le1_elem_suc
thf(fact_1169_mdeg__child__sucs__eq__if__gt1,axiom,
    ! [R: a,T: dtree_a_b,E: b,V: a] :
      ( ( ord_less_nat @ one_one_nat @ ( max_deg_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) ) )
     => ( ( max_deg_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) )
        = ( max_deg_a_b @ ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) ) ) ).

% mdeg_child_sucs_eq_if_gt1
thf(fact_1170_fset__of__list__simps_I2_J,axiom,
    ! [X21: produc4558475209616630778_a_b_b,X222: list_P5360711134766023690_a_b_b] :
      ( ( fset_o8043272628024912308_a_b_b @ ( cons_P2785074014425598660_a_b_b @ X21 @ X222 ) )
      = ( finser8437519239679886002_a_b_b @ X21 @ ( fset_o8043272628024912308_a_b_b @ X222 ) ) ) ).

% fset_of_list_simps(2)
thf(fact_1171_fset__of__list__simps_I1_J,axiom,
    ( ( fset_o3702720909373460334od_a_b @ nil_Product_prod_a_b )
    = bot_bo757577729753943290od_a_b ) ).

% fset_of_list_simps(1)
thf(fact_1172_fset__of__list__simps_I1_J,axiom,
    ( ( fset_o8043272628024912308_a_b_b @ nil_Pr5403147374433350260_a_b_b )
    = bot_bo2895716411488905534_a_b_b ) ).

% fset_of_list_simps(1)
thf(fact_1173_fset__of__list_Orep__eq,axiom,
    ! [X3: list_P5360711134766023690_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( fset_o8043272628024912308_a_b_b @ X3 ) )
      = ( set_Pr8239206241032387877_a_b_b @ X3 ) ) ).

% fset_of_list.rep_eq
thf(fact_1174_dtree__to__list__eq__dverts,axiom,
    ! [T: dtree_a_b] :
      ( ( wf_dverts_a_b @ T )
     => ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
       => ( ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ ( dtree_to_list_a_b @ T ) ) )
          = ( minus_minus_set_a @ ( dverts_a_b @ T ) @ ( insert_a @ ( root_a_b @ T ) @ bot_bot_set_a ) ) ) ) ) ).

% dtree_to_list_eq_dverts
thf(fact_1175_pfsubset__finsert__iff,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le7001451600920047870_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ B4 ) )
      = ( ( ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
         => ( ord_le7001451600920047870_a_b_b @ A2 @ B4 ) )
        & ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
         => ( ( ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
             => ( ord_le7001451600920047870_a_b_b @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) @ B4 ) )
            & ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
             => ( ord_le789900035998834954_a_b_b @ A2 @ B4 ) ) ) ) ) ) ).

% pfsubset_finsert_iff
thf(fact_1176_image__eqI,axiom,
    ! [B: produc4558475209616630778_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
       => ( member4380921116106875537_a_b_b @ B @ ( image_6081965176830705659_a_b_b @ F2 @ A2 ) ) ) ) ).

% image_eqI
thf(fact_1177_image__eqI,axiom,
    ! [B: dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
       => ( member_dtree_a_b @ B @ ( image_7065894828672115579ee_a_b @ F2 @ A2 ) ) ) ) ).

% image_eqI
thf(fact_1178_image__eqI,axiom,
    ! [B: produc4558475209616630778_a_b_b,F2: dtree_a_b > produc4558475209616630778_a_b_b,X3: dtree_a_b,A2: set_dtree_a_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_dtree_a_b @ X3 @ A2 )
       => ( member4380921116106875537_a_b_b @ B @ ( image_360604450665336955_a_b_b @ F2 @ A2 ) ) ) ) ).

% image_eqI
thf(fact_1179_image__eqI,axiom,
    ! [B: dtree_a_b,F2: dtree_a_b > dtree_a_b,X3: dtree_a_b,A2: set_dtree_a_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_dtree_a_b @ X3 @ A2 )
       => ( member_dtree_a_b @ B @ ( image_1160270813240538107ee_a_b @ F2 @ A2 ) ) ) ) ).

% image_eqI
thf(fact_1180_all__not__fin__conv,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( ! [X4: produc4558475209616630778_a_b_b] :
            ~ ( fmembe3173364709796808819_a_b_b @ X4 @ A2 ) )
      = ( A2 = bot_bo2895716411488905534_a_b_b ) ) ).

% all_not_fin_conv
thf(fact_1181_fempty__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b] :
      ~ ( fmembe3173364709796808819_a_b_b @ C @ bot_bo2895716411488905534_a_b_b ) ).

% fempty_iff
thf(fact_1182_finsertCI,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( ~ ( fmembe3173364709796808819_a_b_b @ A @ B4 )
       => ( A = B ) )
     => ( fmembe3173364709796808819_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ B @ B4 ) ) ) ).

% finsertCI
thf(fact_1183_finsert__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ B @ A2 ) )
      = ( ( A = B )
        | ( fmembe3173364709796808819_a_b_b @ A @ A2 ) ) ) ).

% finsert_iff
thf(fact_1184_finsert__fsubset,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) @ B4 )
      = ( ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
        & ( ord_le789900035998834954_a_b_b @ A2 @ B4 ) ) ) ).

% finsert_fsubset
thf(fact_1185_finter__finsert__right__ifffempty,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ( ( inf_in7138637532943773244_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
        = ( inf_in7138637532943773244_a_b_b @ A2 @ B4 ) ) ) ).

% finter_finsert_right_ifffempty
thf(fact_1186_finter__finsert__left__ifffempty,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ A @ C2 )
     => ( ( inf_in7138637532943773244_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ B4 ) @ C2 )
        = ( inf_in7138637532943773244_a_b_b @ B4 @ C2 ) ) ) ).

% finter_finsert_left_ifffempty
thf(fact_1187_finter__finsert__right__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ( ( inf_in7138637532943773244_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
        = ( finser8437519239679886002_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ A2 @ B4 ) ) ) ) ).

% finter_finsert_right_if1
thf(fact_1188_finter__finsert__left__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ C2 )
     => ( ( inf_in7138637532943773244_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ B4 ) @ C2 )
        = ( finser8437519239679886002_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ B4 @ C2 ) ) ) ) ).

% finter_finsert_left_if1
thf(fact_1189_finsert__fminus1,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
     => ( ( minus_1250967532242559235_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) @ B4 )
        = ( minus_1250967532242559235_a_b_b @ A2 @ B4 ) ) ) ).

% finsert_fminus1
thf(fact_1190_fset__of__list__elem,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xs: list_P5360711134766023690_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ X3 @ ( fset_o8043272628024912308_a_b_b @ Xs ) )
      = ( member4380921116106875537_a_b_b @ X3 @ ( set_Pr8239206241032387877_a_b_b @ Xs ) ) ) ).

% fset_of_list_elem
thf(fact_1191_fset__of__list__elem,axiom,
    ! [X3: dtree_a_b,Xs: list_dtree_a_b] :
      ( ( fmember_dtree_a_b @ X3 @ ( fset_o5204176837177470516ee_a_b @ Xs ) )
      = ( member_dtree_a_b @ X3 @ ( set_dtree_a_b2 @ Xs ) ) ) ).

% fset_of_list_elem
thf(fact_1192_image__subsetI,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
         => ( member4380921116106875537_a_b_b @ ( F2 @ X2 ) @ B4 ) )
     => ( ord_le146215904626753808_a_b_b @ ( image_6081965176830705659_a_b_b @ F2 @ A2 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1193_image__subsetI,axiom,
    ! [A2: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,B4: set_dtree_a_b] :
      ( ! [X2: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X2 @ A2 )
         => ( member_dtree_a_b @ ( F2 @ X2 ) @ B4 ) )
     => ( ord_le6340955050456522384ee_a_b @ ( image_7065894828672115579ee_a_b @ F2 @ A2 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1194_image__subsetI,axiom,
    ! [A2: set_dtree_a_b,F2: dtree_a_b > produc4558475209616630778_a_b_b,B4: set_Pr3012420139608375472_a_b_b] :
      ( ! [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ A2 )
         => ( member4380921116106875537_a_b_b @ ( F2 @ X2 ) @ B4 ) )
     => ( ord_le146215904626753808_a_b_b @ ( image_360604450665336955_a_b_b @ F2 @ A2 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1195_image__subsetI,axiom,
    ! [A2: set_dtree_a_b,F2: dtree_a_b > dtree_a_b,B4: set_dtree_a_b] :
      ( ! [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ A2 )
         => ( member_dtree_a_b @ ( F2 @ X2 ) @ B4 ) )
     => ( ord_le6340955050456522384ee_a_b @ ( image_1160270813240538107ee_a_b @ F2 @ A2 ) @ B4 ) ) ).

% image_subsetI
thf(fact_1196_mdeg__ge__child_H,axiom,
    ! [T1: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ord_less_eq_nat @ ( max_deg_a_b @ T1 ) @ ( max_deg_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% mdeg_ge_child'
thf(fact_1197_fsubset__finsert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
     => ( ( ord_le789900035998834954_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ B4 ) )
        = ( ord_le789900035998834954_a_b_b @ A2 @ B4 ) ) ) ).

% fsubset_finsert
thf(fact_1198_finsert__fminus__if,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
       => ( ( minus_1250967532242559235_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) @ B4 )
          = ( minus_1250967532242559235_a_b_b @ A2 @ B4 ) ) )
      & ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
       => ( ( minus_1250967532242559235_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) @ B4 )
          = ( finser8437519239679886002_a_b_b @ X3 @ ( minus_1250967532242559235_a_b_b @ A2 @ B4 ) ) ) ) ) ).

% finsert_fminus_if
thf(fact_1199_darcs__child__subseteq,axiom,
    ! [X3: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ord_less_eq_set_b @ ( darcs_a_b @ X3 ) @ ( darcs_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% darcs_child_subseteq
thf(fact_1200_dverts__child__subseteq,axiom,
    ! [X3: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ord_less_eq_set_a @ ( dverts_a_b @ X3 ) @ ( dverts_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% dverts_child_subseteq
thf(fact_1201_dverts__suc__subseteq,axiom,
    ! [X3: dtree_a_b,T: dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( ord_less_eq_set_a @ ( dverts_a_b @ X3 ) @ ( dverts_a_b @ T ) ) ) ).

% dverts_suc_subseteq
thf(fact_1202_dtree__size__decr__aux_H,axiom,
    ! [T1: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ord_less_nat @ ( size_size_dtree_a_b @ T1 ) @ ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs ) ) ) ) ).

% dtree_size_decr_aux'
thf(fact_1203_finter__finsert__left,axiom,
    ! [A: produc4558475209616630778_a_b_b,C2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ( fmembe3173364709796808819_a_b_b @ A @ C2 )
       => ( ( inf_in7138637532943773244_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ B4 ) @ C2 )
          = ( finser8437519239679886002_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ B4 @ C2 ) ) ) )
      & ( ~ ( fmembe3173364709796808819_a_b_b @ A @ C2 )
       => ( ( inf_in7138637532943773244_a_b_b @ ( finser8437519239679886002_a_b_b @ A @ B4 ) @ C2 )
          = ( inf_in7138637532943773244_a_b_b @ B4 @ C2 ) ) ) ) ).

% finter_finsert_left
thf(fact_1204_finter__finsert__right,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ( fmembe3173364709796808819_a_b_b @ A @ A2 )
       => ( ( inf_in7138637532943773244_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
          = ( finser8437519239679886002_a_b_b @ A @ ( inf_in7138637532943773244_a_b_b @ A2 @ B4 ) ) ) )
      & ( ~ ( fmembe3173364709796808819_a_b_b @ A @ A2 )
       => ( ( inf_in7138637532943773244_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ B4 ) )
          = ( inf_in7138637532943773244_a_b_b @ A2 @ B4 ) ) ) ) ).

% finter_finsert_right
thf(fact_1205_wf__dtree_Odarcs__child__subset,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( node_a_b @ R @ Xs )
          = T )
       => ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
         => ( ord_less_set_b @ ( darcs_a_b @ X3 ) @ ( darcs_a_b @ T ) ) ) ) ) ).

% wf_dtree.darcs_child_subset
thf(fact_1206_wf__dtree_Odverts__child__subset,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( node_a_b @ R @ Xs )
          = T )
       => ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
         => ( ord_less_set_a @ ( dverts_a_b @ X3 ) @ ( dverts_a_b @ T ) ) ) ) ) ).

% wf_dtree.dverts_child_subset
thf(fact_1207_subtree__child__if__dvert__notelem,axiom,
    ! [V: a,T: dtree_a_b] :
      ( ( V
       != ( root_a_b @ T ) )
     => ( ( member_a @ V @ ( dverts_a_b @ T ) )
       => ? [R5: a,Ys3: fset_P5281107635120001194_a_b_b,Zs3: fset_P5281107635120001194_a_b_b] :
            ( ( is_subtree_a_b @ ( node_a_b @ R5 @ Ys3 ) @ T )
            & ( member_dtree_a_b @ ( node_a_b @ V @ Zs3 ) @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Ys3 ) ) ) ) ) ) ).

% subtree_child_if_dvert_notelem
thf(fact_1208_wf__list__verts_Oelims_I2_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ( wf_list_verts_a_b @ X3 )
     => ( ( X3 != nil_Product_prod_a_b )
       => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
              ( ( X3
                = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ~ ( ~ ( member_a @ V2 @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Xs2 ) ) )
                  & ( wf_list_verts_a_b @ Xs2 ) ) ) ) ) ).

% wf_list_verts.elims(2)
thf(fact_1209_wf__list__verts_Oelims_I1_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b,Y: $o] :
      ( ( ( wf_list_verts_a_b @ X3 )
        = Y )
     => ( ( ( X3 = nil_Product_prod_a_b )
         => ~ Y )
       => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
              ( ( X3
                = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) )
             => ( Y
                = ( ~ ( ~ ( member_a @ V2 @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Xs2 ) ) )
                      & ( wf_list_verts_a_b @ Xs2 ) ) ) ) ) ) ) ).

% wf_list_verts.elims(1)
thf(fact_1210_equalsffemptyI,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ! [Y3: produc4558475209616630778_a_b_b] :
          ~ ( fmembe3173364709796808819_a_b_b @ Y3 @ A2 )
     => ( A2 = bot_bo2895716411488905534_a_b_b ) ) ).

% equalsffemptyI
thf(fact_1211_equalsffemptyD,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( A2 = bot_bo2895716411488905534_a_b_b )
     => ~ ( fmembe3173364709796808819_a_b_b @ A @ A2 ) ) ).

% equalsffemptyD
thf(fact_1212_ex__fin__conv,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b] :
      ( ( ? [X4: produc4558475209616630778_a_b_b] : ( fmembe3173364709796808819_a_b_b @ X4 @ A2 ) )
      = ( A2 != bot_bo2895716411488905534_a_b_b ) ) ).

% ex_fin_conv
thf(fact_1213_femptyE,axiom,
    ! [A: produc4558475209616630778_a_b_b] :
      ~ ( fmembe3173364709796808819_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ).

% femptyE
thf(fact_1214_child__uneq,axiom,
    ! [T: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ( node_a_b @ R @ Xs )
       != T ) ) ).

% child_uneq
thf(fact_1215_imageI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( member4380921116106875537_a_b_b @ ( F2 @ X3 ) @ ( image_6081965176830705659_a_b_b @ F2 @ A2 ) ) ) ).

% imageI
thf(fact_1216_imageI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( member_dtree_a_b @ ( F2 @ X3 ) @ ( image_7065894828672115579ee_a_b @ F2 @ A2 ) ) ) ).

% imageI
thf(fact_1217_imageI,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,F2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( member_dtree_a_b @ X3 @ A2 )
     => ( member4380921116106875537_a_b_b @ ( F2 @ X3 ) @ ( image_360604450665336955_a_b_b @ F2 @ A2 ) ) ) ).

% imageI
thf(fact_1218_imageI,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,F2: dtree_a_b > dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ A2 )
     => ( member_dtree_a_b @ ( F2 @ X3 ) @ ( image_1160270813240538107ee_a_b @ F2 @ A2 ) ) ) ).

% imageI
thf(fact_1219_rev__image__eqI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member4380921116106875537_a_b_b @ B @ ( image_6081965176830705659_a_b_b @ F2 @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_1220_rev__image__eqI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: set_Pr3012420139608375472_a_b_b,B: dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A2 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_dtree_a_b @ B @ ( image_7065894828672115579ee_a_b @ F2 @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_1221_rev__image__eqI,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B: produc4558475209616630778_a_b_b,F2: dtree_a_b > produc4558475209616630778_a_b_b] :
      ( ( member_dtree_a_b @ X3 @ A2 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member4380921116106875537_a_b_b @ B @ ( image_360604450665336955_a_b_b @ F2 @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_1222_rev__image__eqI,axiom,
    ! [X3: dtree_a_b,A2: set_dtree_a_b,B: dtree_a_b,F2: dtree_a_b > dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ A2 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_dtree_a_b @ B @ ( image_1160270813240538107ee_a_b @ F2 @ A2 ) ) ) ) ).

% rev_image_eqI
thf(fact_1223_finsertE,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ B @ A2 ) )
     => ( ( A != B )
       => ( fmembe3173364709796808819_a_b_b @ A @ A2 ) ) ) ).

% finsertE
thf(fact_1224_finsertI1,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] : ( fmembe3173364709796808819_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ A @ B4 ) ) ).

% finsertI1
thf(fact_1225_finsertI2,axiom,
    ! [A: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ B4 )
     => ( fmembe3173364709796808819_a_b_b @ A @ ( finser8437519239679886002_a_b_b @ B @ B4 ) ) ) ).

% finsertI2
thf(fact_1226_set__finsert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
     => ~ ! [B6: fset_P5281107635120001194_a_b_b] :
            ( ( A2
              = ( finser8437519239679886002_a_b_b @ X3 @ B6 ) )
           => ( fmembe3173364709796808819_a_b_b @ X3 @ B6 ) ) ) ).

% set_finsert
thf(fact_1227_finsert__ident,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
     => ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ B4 )
       => ( ( ( finser8437519239679886002_a_b_b @ X3 @ A2 )
            = ( finser8437519239679886002_a_b_b @ X3 @ B4 ) )
          = ( A2 = B4 ) ) ) ) ).

% finsert_ident
thf(fact_1228_finsert__absorb,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ( ( finser8437519239679886002_a_b_b @ A @ A2 )
        = A2 ) ) ).

% finsert_absorb
thf(fact_1229_finsert__eq__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b,B: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ( ~ ( fmembe3173364709796808819_a_b_b @ B @ B4 )
       => ( ( ( finser8437519239679886002_a_b_b @ A @ A2 )
            = ( finser8437519239679886002_a_b_b @ B @ B4 ) )
          = ( ( ( A = B )
             => ( A2 = B4 ) )
            & ( ( A != B )
             => ? [C3: fset_P5281107635120001194_a_b_b] :
                  ( ( A2
                    = ( finser8437519239679886002_a_b_b @ B @ C3 ) )
                  & ~ ( fmembe3173364709796808819_a_b_b @ B @ C3 )
                  & ( B4
                    = ( finser8437519239679886002_a_b_b @ A @ C3 ) )
                  & ~ ( fmembe3173364709796808819_a_b_b @ A @ C3 ) ) ) ) ) ) ) ).

% finsert_eq_iff
thf(fact_1230_mk__disjoint__finsert,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ? [B6: fset_P5281107635120001194_a_b_b] :
          ( ( A2
            = ( finser8437519239679886002_a_b_b @ A @ B6 ) )
          & ~ ( fmembe3173364709796808819_a_b_b @ A @ B6 ) ) ) ).

% mk_disjoint_finsert
thf(fact_1231_fmember_Orep__eq,axiom,
    ( fmember_dtree_a_b
    = ( ^ [X4: dtree_a_b,Xa3: fset_dtree_a_b] : ( member_dtree_a_b @ X4 @ ( fset_dtree_a_b2 @ Xa3 ) ) ) ) ).

% fmember.rep_eq
thf(fact_1232_fmember_Orep__eq,axiom,
    ( fmembe3173364709796808819_a_b_b
    = ( ^ [X4: produc4558475209616630778_a_b_b,Xa3: fset_P5281107635120001194_a_b_b] : ( member4380921116106875537_a_b_b @ X4 @ ( fset_P783253628892185035_a_b_b @ Xa3 ) ) ) ) ).

% fmember.rep_eq
thf(fact_1233_notin__fset,axiom,
    ! [X3: dtree_a_b,S: fset_dtree_a_b] :
      ( ( ~ ( fmember_dtree_a_b @ X3 @ S ) )
      = ( ~ ( member_dtree_a_b @ X3 @ ( fset_dtree_a_b2 @ S ) ) ) ) ).

% notin_fset
thf(fact_1234_notin__fset,axiom,
    ! [X3: produc4558475209616630778_a_b_b,S: fset_P5281107635120001194_a_b_b] :
      ( ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ S ) )
      = ( ~ ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ S ) ) ) ) ).

% notin_fset
thf(fact_1235_fmember__iff__member__fset,axiom,
    ( fmember_dtree_a_b
    = ( ^ [X4: dtree_a_b,A5: fset_dtree_a_b] : ( member_dtree_a_b @ X4 @ ( fset_dtree_a_b2 @ A5 ) ) ) ) ).

% fmember_iff_member_fset
thf(fact_1236_fmember__iff__member__fset,axiom,
    ( fmembe3173364709796808819_a_b_b
    = ( ^ [X4: produc4558475209616630778_a_b_b,A5: fset_P5281107635120001194_a_b_b] : ( member4380921116106875537_a_b_b @ X4 @ ( fset_P783253628892185035_a_b_b @ A5 ) ) ) ) ).

% fmember_iff_member_fset
thf(fact_1237_suc__uneq,axiom,
    ! [T1: dtree_a_b,T: dtree_a_b] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( T != T1 ) ) ).

% suc_uneq
thf(fact_1238_subtree__if__suc,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T22 ) ) ) )
     => ( is_subtree_a_b @ T1 @ T22 ) ) ).

% subtree_if_suc
thf(fact_1239_wf__dverts__rec,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
       => ( wf_dverts_a_b @ T1 ) ) ) ).

% wf_dverts_rec
thf(fact_1240_suc__uneq_H,axiom,
    ! [T1: dtree_a_b,T: dtree_a_b,V: a] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( T
       != ( node_a_b @ V @ ( sucs_a_b @ T1 ) ) ) ) ).

% suc_uneq'
thf(fact_1241_child__uneq_H,axiom,
    ! [T: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a,V: a] :
      ( ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( ( node_a_b @ R @ Xs )
       != ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) ) ).

% child_uneq'
thf(fact_1242_wf__darcs__rec,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,T1: dtree_a_b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs ) )
     => ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
       => ( wf_darcs_a_b @ T1 ) ) ) ).

% wf_darcs_rec
thf(fact_1243_subtree__if__child,axiom,
    ! [X3: dtree_a_b,Xs: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
     => ( is_subtree_a_b @ X3 @ ( node_a_b @ R @ Xs ) ) ) ).

% subtree_if_child
thf(fact_1244_dverts__child__if__not__root,axiom,
    ! [V: a,R: a,Xs: fset_P5281107635120001194_a_b_b] :
      ( ( member_a @ V @ ( dverts_a_b @ ( node_a_b @ R @ Xs ) ) )
     => ( ( V != R )
       => ? [X2: dtree_a_b] :
            ( ( member_dtree_a_b @ X2 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
            & ( member_a @ V @ ( dverts_a_b @ X2 ) ) ) ) ) ).

% dverts_child_if_not_root
thf(fact_1245_wf__dverts__iff__wf__list__verts,axiom,
    ! [R: a,Xs: list_P1467974523212632366od_a_b] :
      ( ( ~ ( member_a @ R @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Xs ) ) )
        & ( wf_list_verts_a_b @ Xs ) )
      = ( wf_dverts_a_b @ ( dtree_from_list_a_b @ R @ Xs ) ) ) ).

% wf_dverts_iff_wf_list_verts
thf(fact_1246_suc__sub__if__strict__subtree,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b] :
      ( ( strict_subtree_a_b @ T1 @ T22 )
     => ? [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T22 ) ) ) )
          & ( is_subtree_a_b @ T1 @ X2 ) ) ) ).

% suc_sub_if_strict_subtree
thf(fact_1247_subtree__child__if__strict__subtree,axiom,
    ! [T1: dtree_a_b,T22: dtree_a_b] :
      ( ( strict_subtree_a_b @ T1 @ T22 )
     => ? [R2: a,Xs2: fset_P5281107635120001194_a_b_b] :
          ( ( is_subtree_a_b @ ( node_a_b @ R2 @ Xs2 ) @ T22 )
          & ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) ) ) ) ).

% subtree_child_if_strict_subtree
thf(fact_1248_child__sub__if__strict__subtree,axiom,
    ! [T1: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b] :
      ( ( strict_subtree_a_b @ T1 @ ( node_a_b @ R @ Xs ) )
     => ? [X2: dtree_a_b] :
          ( ( member_dtree_a_b @ X2 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
          & ( is_subtree_a_b @ T1 @ X2 ) ) ) ).

% child_sub_if_strict_subtree
thf(fact_1249_fset__induct2,axiom,
    ! [P: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $o,Xsa: fset_P5281107635120001194_a_b_b,Ysa: fset_P5281107635120001194_a_b_b] :
      ( ( P @ bot_bo2895716411488905534_a_b_b @ bot_bo2895716411488905534_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b,Xs2: fset_P5281107635120001194_a_b_b] :
            ( ~ ( fmembe3173364709796808819_a_b_b @ X2 @ Xs2 )
           => ( P @ ( finser8437519239679886002_a_b_b @ X2 @ Xs2 ) @ bot_bo2895716411488905534_a_b_b ) )
       => ( ! [Y3: produc4558475209616630778_a_b_b,Ys3: fset_P5281107635120001194_a_b_b] :
              ( ~ ( fmembe3173364709796808819_a_b_b @ Y3 @ Ys3 )
             => ( P @ bot_bo2895716411488905534_a_b_b @ ( finser8437519239679886002_a_b_b @ Y3 @ Ys3 ) ) )
         => ( ! [X2: produc4558475209616630778_a_b_b,Xs2: fset_P5281107635120001194_a_b_b,Y3: produc4558475209616630778_a_b_b,Ys3: fset_P5281107635120001194_a_b_b] :
                ( ( P @ Xs2 @ Ys3 )
               => ( ~ ( fmembe3173364709796808819_a_b_b @ X2 @ Xs2 )
                 => ( ~ ( fmembe3173364709796808819_a_b_b @ Y3 @ Ys3 )
                   => ( P @ ( finser8437519239679886002_a_b_b @ X2 @ Xs2 ) @ ( finser8437519239679886002_a_b_b @ Y3 @ Ys3 ) ) ) ) )
           => ( P @ Xsa @ Ysa ) ) ) ) ) ).

% fset_induct2
thf(fact_1250_fsingleton__iff,axiom,
    ! [B: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ B @ ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) )
      = ( B = A ) ) ).

% fsingleton_iff
thf(fact_1251_fset__strong__cases,axiom,
    ! [Xs: fset_P5281107635120001194_a_b_b] :
      ( ( Xs != bot_bo2895716411488905534_a_b_b )
     => ~ ! [Ys3: fset_P5281107635120001194_a_b_b,X2: produc4558475209616630778_a_b_b] :
            ( ~ ( fmembe3173364709796808819_a_b_b @ X2 @ Ys3 )
           => ( Xs
             != ( finser8437519239679886002_a_b_b @ X2 @ Ys3 ) ) ) ) ).

% fset_strong_cases
thf(fact_1252_fset__induct__stronger,axiom,
    ! [P: fset_P5281107635120001194_a_b_b > $o,S: fset_P5281107635120001194_a_b_b] :
      ( ( P @ bot_bo2895716411488905534_a_b_b )
     => ( ! [X2: produc4558475209616630778_a_b_b,S2: fset_P5281107635120001194_a_b_b] :
            ( ~ ( fmembe3173364709796808819_a_b_b @ X2 @ S2 )
           => ( ( P @ S2 )
             => ( P @ ( finser8437519239679886002_a_b_b @ X2 @ S2 ) ) ) )
       => ( P @ S ) ) ) ).

% fset_induct_stronger
thf(fact_1253_wf__list__verts_Oelims_I3_J,axiom,
    ! [X3: list_P1467974523212632366od_a_b] :
      ( ~ ( wf_list_verts_a_b @ X3 )
     => ~ ! [V2: a,E2: b,Xs2: list_P1467974523212632366od_a_b] :
            ( ( X3
              = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V2 @ E2 ) @ Xs2 ) )
           => ( ~ ( member_a @ V2 @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Xs2 ) ) )
              & ( wf_list_verts_a_b @ Xs2 ) ) ) ) ).

% wf_list_verts.elims(3)
thf(fact_1254_wf__list__verts_Osimps_I2_J,axiom,
    ! [V: a,E: b,Xs: list_P1467974523212632366od_a_b] :
      ( ( wf_list_verts_a_b @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V @ E ) @ Xs ) )
      = ( ~ ( member_a @ V @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Xs ) ) )
        & ( wf_list_verts_a_b @ Xs ) ) ) ).

% wf_list_verts.simps(2)
thf(fact_1255_dverts__suc__if__not__root,axiom,
    ! [V: a,T: dtree_a_b] :
      ( ( member_a @ V @ ( dverts_a_b @ T ) )
     => ( ( V
         != ( root_a_b @ T ) )
       => ? [X2: dtree_a_b] :
            ( ( member_dtree_a_b @ X2 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
            & ( member_a @ V @ ( dverts_a_b @ X2 ) ) ) ) ) ).

% dverts_suc_if_not_root
thf(fact_1256_wf__dtree_Oroot__not__subtree,axiom,
    ! [T: dtree_a_b,R: a,Xs: fset_P5281107635120001194_a_b_b,X3: dtree_a_b] :
      ( ( wf_dtree_a_b @ T )
     => ( ( ( node_a_b @ R @ Xs )
          = T )
       => ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs ) ) )
         => ~ ( member_a @ R @ ( dverts_a_b @ X3 ) ) ) ) ) ).

% wf_dtree.root_not_subtree
thf(fact_1257_subtree__child__if__dvert__notroot,axiom,
    ! [V: a,R: a,Xs: fset_P5281107635120001194_a_b_b] :
      ( ( V != R )
     => ( ( member_a @ V @ ( dverts_a_b @ ( node_a_b @ R @ Xs ) ) )
       => ? [R5: a,Ys3: fset_P5281107635120001194_a_b_b,Zs3: fset_P5281107635120001194_a_b_b] :
            ( ( is_subtree_a_b @ ( node_a_b @ R5 @ Ys3 ) @ ( node_a_b @ R @ Xs ) )
            & ( member_dtree_a_b @ ( node_a_b @ V @ Zs3 ) @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Ys3 ) ) ) ) ) ) ).

% subtree_child_if_dvert_notroot
thf(fact_1258_dtree__to__list__sub__dverts__ins,axiom,
    ! [T: dtree_a_b] : ( ord_less_eq_set_a @ ( insert_a @ ( root_a_b @ T ) @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ ( dtree_to_list_a_b @ T ) ) ) ) @ ( dverts_a_b @ T ) ) ).

% dtree_to_list_sub_dverts_ins
thf(fact_1259_singleton__suc,axiom,
    ! [T: dtree_a_b,R: a,E: b] : ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ) ).

% singleton_suc
thf(fact_1260_fminus__finsert__absorb,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
     => ( ( minus_1250967532242559235_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ A2 ) @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) )
        = A2 ) ) ).

% fminus_finsert_absorb
thf(fact_1261_finsert__fminus,axiom,
    ! [A: produc4558475209616630778_a_b_b,A2: fset_P5281107635120001194_a_b_b] :
      ( ( fmembe3173364709796808819_a_b_b @ A @ A2 )
     => ( ( finser8437519239679886002_a_b_b @ A @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ A @ bot_bo2895716411488905534_a_b_b ) ) )
        = A2 ) ) ).

% finsert_fminus
thf(fact_1262_dtree__to__list__eq__dverts__ins,axiom,
    ! [T: dtree_a_b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( insert_a @ ( root_a_b @ T ) @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ ( dtree_to_list_a_b @ T ) ) ) )
        = ( dverts_a_b @ T ) ) ) ).

% dtree_to_list_eq_dverts_ins
thf(fact_1263_fsubset__finsert__iff,axiom,
    ! [A2: fset_P5281107635120001194_a_b_b,X3: produc4558475209616630778_a_b_b,B4: fset_P5281107635120001194_a_b_b] :
      ( ( ord_le789900035998834954_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ B4 ) )
      = ( ( ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
         => ( ord_le789900035998834954_a_b_b @ ( minus_1250967532242559235_a_b_b @ A2 @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) @ B4 ) )
        & ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ A2 )
         => ( ord_le789900035998834954_a_b_b @ A2 @ B4 ) ) ) ) ).

% fsubset_finsert_iff
thf(fact_1264_strict__subtree__singleton,axiom,
    ! [T: dtree_a_b,R: a,X3: produc4558475209616630778_a_b_b,Xs: fset_P5281107635120001194_a_b_b] :
      ( ( strict_subtree_a_b @ T @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) )
     => ( ( fmembe3173364709796808819_a_b_b @ X3 @ Xs )
       => ( strict_subtree_a_b @ T @ ( node_a_b @ R @ Xs ) ) ) ) ).

% strict_subtree_singleton
thf(fact_1265_dtree__to__list__sub__dverts,axiom,
    ! [T: dtree_a_b] :
      ( ( wf_dverts_a_b @ T )
     => ( ord_less_eq_set_a @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ ( dtree_to_list_a_b @ T ) ) ) @ ( minus_minus_set_a @ ( dverts_a_b @ T ) @ ( insert_a @ ( root_a_b @ T ) @ bot_bot_set_a ) ) ) ) ).

% dtree_to_list_sub_dverts
thf(fact_1266_dtree__from__list__sequence__dverts,axiom,
    ! [R: a,Xs: fset_P5281107635120001194_a_b_b,V1: a,Ys: list_P1467974523212632366od_a_b,E1: b] :
      ( ( is_subtree_a_b @ ( node_a_b @ R @ Xs ) @ ( dtree_from_list_a_b @ V1 @ Ys ) )
     => ? [E2: b,As: list_P1467974523212632366od_a_b,Bs: list_P1467974523212632366od_a_b] :
          ( ( ( append5335208823350062147od_a_b @ As @ ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ R @ E2 ) @ Bs ) )
            = ( cons_P7316939131009794654od_a_b @ ( product_Pair_a_b @ V1 @ E1 ) @ Ys ) )
          & ( ( dverts_a_b @ ( node_a_b @ R @ Xs ) )
            = ( insert_a @ R @ ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ Bs ) ) ) ) ) ) ).

% dtree_from_list_sequence_dverts
thf(fact_1267_dtree__to__list__eq__dverts__single,axiom,
    ! [T: dtree_a_b,T1: dtree_a_b,E1: b] :
      ( ( ord_less_eq_nat @ ( max_deg_a_b @ T ) @ one_one_nat )
     => ( ( ( sucs_a_b @ T )
          = ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ bot_bo2895716411488905534_a_b_b ) )
       => ( ( image_2802296252294471259_a_b_a @ product_fst_a_b @ ( set_Product_prod_a_b2 @ ( dtree_to_list_a_b @ T ) ) )
          = ( dverts_a_b @ T1 ) ) ) ) ).

% dtree_to_list_eq_dverts_single

% Conjectures (1)
thf(conj_0,conjecture,
    wf_list_verts_a_b @ ( dtree_to_list_a_b @ ( node_a_b @ r @ xs ) ) ).

%------------------------------------------------------------------------------