%------------------------------------------------------------------------------
% File     : ITP128^1 : TPTP v8.2.0. Released v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer Monomorphic_Monad problem prob_47__7041882_1
% Version  : Especial.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : Monomorphic_Monad/prob_47__7041882_1 [Des21]

% Status   : Theorem
% Rating   : 0.10 v8.2.0, 0.00 v7.5.0
% Syntax   : Number of formulae    :  735 (  97 unt; 371 typ;   0 def)
%            Number of atoms       : 1443 ( 463 equ;   0 cnn)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives : 4482 (   0   ~;   1   |;  12   &;3946   @)
%                                         (   0 <=>; 523  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   9 avg)
%            Number of types       :   13 (  12 usr)
%            Number of type conns  : 7415 (7415   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  362 ( 359 usr;   2 con; 0-7 aty)
%            Number of variables   : 1860 ( 394   ^;1460   !;   6   ?;1860   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Sledgehammer 2021-02-23 15:29:58.508
%------------------------------------------------------------------------------
% Could-be-implicit typings (12)
thf(ty_n_t__Multiset__Omultiset_Itf__b_J,type,
    multiset_b: $tType ).

thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
    multiset_a: $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__d_J,type,
    set_d: $tType ).

thf(ty_n_t__Set__Oset_Itf__c_J,type,
    set_c: $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_tf__d,type,
    d: $tType ).

thf(ty_n_tf__c,type,
    c: $tType ).

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

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

% Explicit typings (359)
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_J,type,
    bNF_re19414301_d_d_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_Eo_J,type,
    bNF_re674980784_d_d_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    bNF_re1867846365_a_a_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J,type,
    bNF_re708047067_a_b_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    bNF_re145798749_a_a_o: ( ( ( c > c ) > ( d > d ) > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J,type,
    bNF_re1133483099_a_b_o: ( ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re141854397_b_d_d: ( ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ) > ( ( ( a > c > c ) > a > c > c ) > ( ( b > d > d ) > b > d > d ) > $o ) > ( ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re35019871_b_d_d: ( ( ( c > c ) > a ) > ( ( d > d ) > b ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > c ) > a ) > a > c > c ) > ( ( ( d > d ) > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
    bNF_re1177671453_a_a_a: ( ( ( c > c ) > a ) > ( a > a ) > $o ) > ( ( ( c > c ) > a ) > ( a > a ) > $o ) > ( ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1238578079_d_d_d: ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ) > ( ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J_001_062_Itf__a_Mtf__c_J_001_062_Itf__b_Mtf__d_J,type,
    bNF_re1209333166_c_b_d: ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( ( a > c ) > ( b > d ) > $o ) > ( ( ( c > c ) > c ) > a > c ) > ( ( ( d > d ) > d ) > b > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_001_062_Itf__b_Mtf__b_J,type,
    bNF_re323253981_b_b_b: ( ( ( d > d ) > b ) > ( b > b ) > $o ) > ( ( ( d > d ) > b ) > ( b > b ) > $o ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    bNF_re1403739741_a_a_o: ( ( a > a > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J,type,
    bNF_re1165460699_a_b_o: ( ( a > a > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__b_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__b_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    bNF_re1310167325_a_a_o: ( ( a > a > $o ) > ( b > a > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > a ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( b > a > $o ) > ( a > b ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J_M_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_J,type,
    bNF_re2129955100_d_d_o: ( ( a > a > $o ) > ( b > b > $o ) > $o ) > ( ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ) > ( ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_Itf__b_M_062_Itf__b_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__b_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J,type,
    bNF_re1071888283_a_b_o: ( ( a > a > $o ) > ( b > b > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > b ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( b > b > $o ) > ( a > b ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_Itf__a_M_062_Itf__a_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_J,type,
    bNF_re231976415_a_a_o: ( ( a > b > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_J,type,
    bNF_re2141181021_a_b_o: ( ( a > b > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J,type,
    bNF_re880840541_a_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_J,type,
    bNF_re1311853791_b_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( b > a ) > b > c > c ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J,type,
    bNF_re978949211_a_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_J,type,
    bNF_re1409962461_b_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( b > a ) > b > c > c ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re27458217_c_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( a > c > c ) > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re1955249705_c_d_d: ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( a > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    bNF_re1684125987_a_a_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re364411746_a_b_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    bNF_re1652452067_a_a_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > d > d ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re332737826_a_b_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > d > d ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__a_J_001_Eo_001_Eo,type,
    bNF_re2074539676_a_o_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    bNF_re1256092317_b_o_o: ( ( a > c > c ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re387831090_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( ( c > c ) > a ) > a > c > c ) > ( ( ( d > d ) > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_J,type,
    bNF_re364486559_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_Eo_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_Eo_J,type,
    bNF_re1855937521_d_d_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__a_Mtf__b_J_M_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re631104669_a_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( a > b ) > a > d > d ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( a > b ) > a > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1062117919_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1160226589_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__c_Mtf__a_J_M_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__d_Mtf__b_J_M_062_Itf__d_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re2120361759_d_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > a ) > c > c > c ) > ( ( d > b ) > d > d > d ) > $o ) > ( ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( b > d > d ) > ( d > b ) > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_M_062_Itf__a_Mtf__c_J_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J_M_062_Itf__b_Mtf__d_J_J_J,type,
    bNF_re727696351_d_b_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ) > ( ( a > c > c ) > ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( b > d > d ) > ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_J_001_062_Itf__b_M_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_J,type,
    bNF_re1424479610_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > ( c > c ) > a > c > c ) > ( b > ( d > d ) > b > d > d ) > $o ) > ( ( a > c > c ) > a > ( c > c ) > a > c > c ) > ( ( b > d > d ) > b > ( d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re692482399_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > a > c > c ) > ( ( b > d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re84044842_c_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_Eo_001_Eo,type,
    bNF_re1501709470_d_o_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_Mtf__a_J_001_Eo_001_Eo,type,
    bNF_re1620723804_a_o_o: ( ( a > d > d ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > d > d ) > $o ) > ( ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    bNF_re802276445_b_o_o: ( ( a > d > d ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > d > d ) > $o ) > ( ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_M_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J,type,
    bNF_re1503602041_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > a > a ) > $o ) > ( ( a > a ) > ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J,type,
    bNF_re1258259453_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > a ) > a > a ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    bNF_re1900831913_a_a_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re581117672_a_b_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    bNF_re984549674_a_a_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > b ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re1812319081_a_b_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > b ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1691224489_a_c_c: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
    bNF_re1690311157_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J,type,
    bNF_re1698572662_a_a_b: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > a ) > a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_Eo_001_Eo,type,
    bNF_re134330537_a_o_o: ( ( a > a ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001tf__a_001tf__a,type,
    bNF_re571457705_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( a > a > $o ) > ( ( a > a ) > a ) > ( ( a > a ) > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__b_J_J,type,
    bNF_re1514436479_a_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > a ) > a > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( a > b ) > ( a > a ) > a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J,type,
    bNF_re390230442_a_a_o: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_I_062_Itf__a_Mtf__a_J_M_Eo_J_001_062_I_062_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re1217999849_a_b_o: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1787520874_a_d_d: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( a > b ) > a > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
    bNF_re857382262_a_a_a: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > b ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J,type,
    bNF_re865643767_a_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > b ) > a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    bNF_re1463366826_b_o_o: ( ( a > a ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__b_J_001tf__a_001tf__b,type,
    bNF_re473406379_b_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( a > b > $o ) > ( ( a > a ) > a ) > ( ( a > b ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__b_J_M_062_Itf__a_Mtf__a_J_J,type,
    bNF_re539937469_b_a_a: ( ( a > a ) > ( b > a ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > b ) > a > a ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > a ) > ( a > b ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1665173865_b_c_c: ( ( a > a ) > ( b > a ) > $o ) > ( ( a > c > c ) > ( b > c > c ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( b > a ) > b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__d_Mtf__d_J_J_M_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_J,type,
    bNF_re932551557_b_d_d: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ) > ( ( a > a ) > ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( b > b ) > ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J_001_062_I_062_Itf__a_Mtf__b_J_M_062_Itf__a_Mtf__b_J_J,type,
    bNF_re796114495_b_a_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > b ) > a > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > b ) > ( a > b ) > a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J,type,
    bNF_re835672381_b_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( b > b ) > b > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J,type,
    bNF_re774352699_b_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( b > a ) > b > a ) > ( ( b > b ) > b > b ) > $o ) > ( ( a > a ) > ( b > a ) > b > a ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1761470250_b_d_d: ( ( a > a ) > ( b > b ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J,type,
    bNF_re1307884917_a_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( a > a ) > ( b > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001tf__a_001tf__b,type,
    bNF_re2087760490_b_a_b: ( ( a > a ) > ( b > b ) > $o ) > ( a > b > $o ) > ( ( a > a ) > a ) > ( ( b > b ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_Eo_001_Eo,type,
    bNF_re1906994858_a_o_o: ( ( a > b ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > b ) > $o ) > ( ( a > a ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    bNF_re1088547499_b_o_o: ( ( a > b ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > b ) > $o ) > ( ( a > b ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_Mtf__c_J_001_062_Itf__b_Mtf__d_J_001_062_I_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_J_001_062_I_062_Itf__d_M_062_Itf__d_Mtf__d_J_J_M_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_J,type,
    bNF_re1606289753_b_d_d: ( ( a > c ) > ( b > d ) > $o ) > ( ( ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( d > d > d ) > ( d > d ) > b > d > d ) > $o ) > ( ( a > c ) > ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( b > d ) > ( d > d > d ) > ( d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J,type,
    bNF_re561231771_a_c_c: ( ( b > d > d ) > ( a > c > c ) > $o ) > ( ( ( b > b ) > b > d > d ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re742509149_b_d_d: ( ( b > d > d ) > ( b > d > d ) > $o ) > ( ( ( b > b ) > b > d > d ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1591514407_a_c_c: ( ( b > a ) > ( a > a ) > $o ) > ( ( b > c > c ) > ( a > c > c ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1565463783_b_c_c: ( ( b > a ) > ( b > a ) > $o ) > ( ( b > c > c ) > ( b > c > c ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( b > a ) > b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1661760168_b_d_d: ( ( b > a ) > ( b > b ) > $o ) > ( ( b > c > c ) > ( b > d > d ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__b_J,type,
    bNF_re668686835_a_b_b: ( ( b > a ) > ( b > b ) > $o ) > ( ( b > a ) > ( b > b ) > $o ) > ( ( b > a ) > b > a ) > ( ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J,type,
    bNF_re1794062813_d_d_b: ( ( b > b ) > ( ( d > d ) > b ) > $o ) > ( ( b > b ) > ( ( d > d ) > b ) > $o ) > ( ( b > b ) > b > b ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_Mtf__a_J_J,type,
    bNF_re1645058365_a_a_a: ( ( b > b ) > ( a > a ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( a > a ) > a > a ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1342462312_a_c_c: ( ( b > b ) > ( a > a ) > $o ) > ( ( b > d > d ) > ( a > c > c ) > $o ) > ( ( b > b ) > b > d > d ) > ( ( a > a ) > a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J,type,
    bNF_re310361461_b_a_a: ( ( b > b ) > ( a > a ) > $o ) > ( ( b > b ) > ( a > a ) > $o ) > ( ( b > b ) > b > b ) > ( ( a > a ) > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_M_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J,type,
    bNF_re1138812345_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > b > b ) > $o ) > ( ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_M_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J_J,type,
    bNF_re961930425_d_d_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_Mtf__b_J_J,type,
    bNF_re1222471293_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( b > b ) > b > b ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1412708073_b_d_d: ( ( b > b ) > ( b > b ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > ( ( b > b ) > b > d > d ) > ( ( b > b ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J,type,
    bNF_re2075418869_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( b > b ) > ( b > b ) > $o ) > ( ( b > b ) > b > b ) > ( ( b > b ) > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_Itf__c_M_Eo_J_J_001_062_Itf__d_M_062_Itf__d_M_Eo_J_J_001_062_I_062_Itf__c_M_062_Itf__c_M_Eo_J_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_I_062_Itf__d_M_062_Itf__d_M_Eo_J_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J,type,
    bNF_re921674337_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_Itf__c_M_Eo_J_J_001_062_Itf__d_M_062_Itf__d_M_Eo_J_J_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J,type,
    bNF_re764708765_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_Itf__c_M_Eo_J_J_001_062_Itf__d_M_062_Itf__d_M_Eo_J_J_001_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_001_062_I_062_Itf__d_Mtf__d_J_M_Eo_J,type,
    bNF_re27482973_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__d_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1507718559_b_d_d: ( ( c > c > c ) > ( d > d > d ) > $o ) > ( ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ) > ( ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( d > d > d ) > ( d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__a_J_001_062_Itf__d_Mtf__b_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_M_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J_M_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1164948833_d_d_d: ( ( c > a ) > ( d > b ) > $o ) > ( ( ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ) > ( ( c > a ) > ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( d > b ) > ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__a_J_001_062_Itf__d_Mtf__b_J_001_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__d_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1509948838_d_d_d: ( ( c > a ) > ( d > b ) > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( ( c > a ) > c > c > c ) > ( ( d > b ) > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_I_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_M_062_Itf__a_Mtf__c_J_J_001_062_I_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J_M_062_Itf__b_Mtf__d_J_J,type,
    bNF_re335372010_d_b_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( ( c > c ) > c ) > a > c ) > ( ( ( d > d ) > d ) > b > d ) > $o ) > ( ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__c_Mtf__a_J_M_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_I_062_Itf__d_Mtf__b_J_M_062_Itf__d_M_062_Itf__d_Mtf__d_J_J_J_J,type,
    bNF_re1709888353_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( b > d > d ) > ( d > b ) > d > d > d ) > $o ) > ( ( c > c ) > ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( d > d ) > ( b > d > d ) > ( d > b ) > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re888371717_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > d > d ) > $o ) > ( ( c > c ) > ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > ( d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re764096061_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ) > ( ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_001_062_I_062_Itf__d_Mtf__d_J_M_Eo_J,type,
    bNF_re781155241_d_d_o: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1145286186_b_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_Itf__c_M_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_J_001_062_Itf__d_M_062_Itf__d_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1941803873_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c > c > c ) > ( d > d > d > d ) > $o ) > ( ( c > c ) > c > c > c > c ) > ( ( d > d ) > d > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re2078100341_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_Eo_001_Eo,type,
    bNF_re857878889_d_o_o: ( ( c > c ) > ( d > d ) > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001tf__a_001tf__b,type,
    bNF_re1795127658_d_a_b: ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > ( ( c > c ) > a ) > ( ( d > d ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001tf__c_001tf__d,type,
    bNF_re1303182826_d_c_d: ( ( c > c ) > ( d > d ) > $o ) > ( c > d > $o ) > ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
    bNF_re1450278895_o_a_o: ( ( c > c ) > a > $o ) > ( ( ( c > c ) > $o ) > ( a > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_I_062_Itf__c_Mtf__c_J_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
    bNF_re2038641070_o_b_o: ( ( c > c ) > a > $o ) > ( ( ( c > c ) > $o ) > ( b > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
    bNF_re1306877487_o_a_o: ( ( c > c ) > a > $o ) > ( ( ( d > d ) > $o ) > ( a > $o ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
    bNF_re1895239662_o_b_o: ( ( c > c ) > a > $o ) > ( ( ( d > d ) > $o ) > ( b > $o ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001_Eo_001_Eo,type,
    bNF_re883196986_a_o_o: ( ( c > c ) > a > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__a_001tf__a_001tf__a,type,
    bNF_re1424579386_a_a_a: ( ( c > c ) > a > $o ) > ( a > a > $o ) > ( ( c > c ) > a ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__c_Mtf__c_J_001tf__b_001_Eo_001_Eo,type,
    bNF_re90976443_b_o_o: ( ( c > c ) > b > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_Mtf__d_J_001tf__a_001_Eo_001_Eo,type,
    bNF_re991543930_a_o_o: ( ( d > d ) > a > $o ) > ( $o > $o > $o ) > ( ( d > d ) > $o ) > ( a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_Mtf__d_J_001tf__b_001_Eo_001_Eo,type,
    bNF_re199323387_b_o_o: ( ( d > d ) > b > $o ) > ( $o > $o > $o ) > ( ( d > d ) > $o ) > ( b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__d_Mtf__d_J_001tf__b_001tf__b_001tf__b,type,
    bNF_re1703323451_b_b_b: ( ( d > d ) > b > $o ) > ( b > b > $o ) > ( ( d > d ) > b ) > ( b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_Itf__a_M_062_Itf__a_Mtf__a_J_J_001_062_Itf__a_M_062_Itf__a_Mtf__a_J_J,type,
    bNF_re1705765981_a_a_a: ( $o > $o > $o ) > ( ( a > a > a ) > ( a > a > a ) > $o ) > ( $o > a > a > a ) > ( $o > a > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_Itf__a_M_062_Itf__a_Mtf__a_J_J_001_062_Itf__b_M_062_Itf__b_Mtf__b_J_J,type,
    bNF_re588060702_b_b_b: ( $o > $o > $o ) > ( ( a > a > a ) > ( b > b > b ) > $o ) > ( $o > a > a > a ) > ( $o > b > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__d_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re647211934_d_d_d: ( $o > $o > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( $o > c > c > c ) > ( $o > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J,type,
    bNF_re1482032989_c_c_c: ( a > a > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( a > c > c ) > c > c ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( a > ( a > c > c ) > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1391160029_d_d_d: ( a > a > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( a > d > d ) > d > d ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( a > ( a > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_I_062_Itf__a_Mtf__a_J_Mtf__a_J_001_062_I_062_Itf__a_Mtf__a_J_Mtf__a_J,type,
    bNF_re865741149_a_a_a: ( a > a > $o ) > ( ( ( a > a ) > a ) > ( ( a > a ) > a ) > $o ) > ( a > ( a > a ) > a ) > ( a > ( a > a ) > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_I_062_Itf__a_Mtf__a_J_Mtf__a_J_001_062_I_062_Itf__a_Mtf__b_J_Mtf__b_J,type,
    bNF_re1093913501_a_b_b: ( a > a > $o ) > ( ( ( a > a ) > a ) > ( ( a > b ) > b ) > $o ) > ( a > ( a > a ) > a ) > ( a > ( a > b ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__a_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
    bNF_re1690123229_o_a_o: ( a > a > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > a > $o ) > ( a > a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__a_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
    bNF_re131001756_o_b_o: ( a > a > $o ) > ( ( a > $o ) > ( b > $o ) > $o ) > ( a > a > $o ) > ( a > b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
    bNF_re911029929_a_a_a: ( a > a > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( a > a > a ) > ( a > a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__b_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
    bNF_re1809376028_o_a_o: ( a > a > $o ) > ( ( b > $o ) > ( a > $o ) > $o ) > ( a > b > $o ) > ( a > a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__b_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
    bNF_re250254555_o_b_o: ( a > a > $o ) > ( ( b > $o ) > ( b > $o ) > $o ) > ( a > b > $o ) > ( a > b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re1143700905_c_c_c: ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re1979731817_c_d_d: ( a > a > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    bNF_re950444090_c_c_a: ( a > a > $o ) > ( ( c > c ) > a > $o ) > ( a > c > c ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__b,type,
    bNF_re950444091_c_c_b: ( a > a > $o ) > ( ( c > c ) > b > $o ) > ( a > c > c ) > ( a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__d_Mtf__d_J_001tf__a,type,
    bNF_re2038021754_d_d_a: ( a > a > $o ) > ( ( d > d ) > a > $o ) > ( a > d > d ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_062_Itf__d_Mtf__d_J_001tf__b,type,
    bNF_re2038021755_d_d_b: ( a > a > $o ) > ( ( d > d ) > b > $o ) > ( a > d > d ) > ( a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001_Eo_001_Eo,type,
    bNF_rel_fun_a_a_o_o: ( a > a > $o ) > ( $o > $o > $o ) > ( a > $o ) > ( a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__a_001tf__a,type,
    bNF_rel_fun_a_a_a_a: ( a > a > $o ) > ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__a_001tf__b,type,
    bNF_rel_fun_a_a_a_b: ( a > a > $o ) > ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__b_001tf__a,type,
    bNF_rel_fun_a_a_b_a: ( a > a > $o ) > ( b > a > $o ) > ( a > b ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__a_001tf__b_001tf__b,type,
    bNF_rel_fun_a_a_b_b: ( a > a > $o ) > ( b > b > $o ) > ( a > b ) > ( a > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re1327926367_d_d_d: ( a > b > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( b > ( b > d > d ) > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_I_062_Itf__a_Mtf__a_J_Mtf__a_J_001_062_I_062_Itf__b_Mtf__b_J_Mtf__b_J,type,
    bNF_re1730737055_b_b_b: ( a > b > $o ) > ( ( ( a > a ) > a ) > ( ( b > b ) > b ) > $o ) > ( a > ( a > a ) > a ) > ( b > ( b > b ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_I_062_Itf__c_Mtf__c_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__d_Mtf__d_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    bNF_re1573878111_b_d_d: ( a > b > $o ) > ( ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ) > ( a > ( c > c ) > a > c > c ) > ( b > ( d > d ) > b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_Itf__a_M_Eo_J_001_062_Itf__a_M_Eo_J,type,
    bNF_re1977372894_o_a_o: ( a > b > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > a > $o ) > ( b > a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_Itf__a_M_Eo_J_001_062_Itf__b_M_Eo_J,type,
    bNF_re418251421_o_b_o: ( a > b > $o ) > ( ( a > $o ) > ( b > $o ) > $o ) > ( a > a > $o ) > ( b > b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J,type,
    bNF_re569932906_a_b_b: ( a > b > $o ) > ( ( a > a ) > ( b > b ) > $o ) > ( a > a > a ) > ( b > b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re2114056618_c_c_c: ( a > b > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re802603882_c_d_d: ( a > b > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001_Eo_001_Eo,type,
    bNF_rel_fun_a_b_o_o: ( a > b > $o ) > ( $o > $o > $o ) > ( a > $o ) > ( b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001tf__a_001tf__a,type,
    bNF_rel_fun_a_b_a_a: ( a > b > $o ) > ( a > a > $o ) > ( a > a ) > ( b > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001tf__a_001tf__b,type,
    bNF_rel_fun_a_b_a_b: ( a > b > $o ) > ( a > b > $o ) > ( a > a ) > ( b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__a_001tf__b_001tf__c_001tf__d,type,
    bNF_rel_fun_a_b_c_d: ( a > b > $o ) > ( c > d > $o ) > ( a > c ) > ( b > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__b_001tf__b,type,
    bNF_re1573506119_d_b_b: ( b > ( d > d ) > $o ) > ( b > b > $o ) > ( b > b ) > ( ( d > d ) > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__a_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re758172648_c_c_c: ( b > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( b > c > c ) > ( a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__a_001_062_Itf__d_Mtf__d_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re38477224_d_c_c: ( b > a > $o ) > ( ( d > d ) > ( c > c ) > $o ) > ( b > d > d ) > ( a > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__a_001_Eo_001_Eo,type,
    bNF_rel_fun_b_a_o_o: ( b > a > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__a_001tf__a_001tf__a,type,
    bNF_rel_fun_b_a_a_a: ( b > a > $o ) > ( a > a > $o ) > ( b > a ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__a_001tf__b_001tf__a,type,
    bNF_rel_fun_b_a_b_a: ( b > a > $o ) > ( b > a > $o ) > ( b > b ) > ( a > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    bNF_re1728528361_c_c_c: ( b > b > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( b > c > c ) > ( b > c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re417075625_c_d_d: ( b > b > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( b > c > c ) > ( b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re1844863849_d_d_d: ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001_Eo_001_Eo,type,
    bNF_rel_fun_b_b_o_o: ( b > b > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001tf__a_001tf__a,type,
    bNF_rel_fun_b_b_a_a: ( b > b > $o ) > ( a > a > $o ) > ( b > a ) > ( b > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001tf__a_001tf__b,type,
    bNF_rel_fun_b_b_a_b: ( b > b > $o ) > ( a > b > $o ) > ( b > a ) > ( b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__b_001tf__b_001tf__b_001tf__b,type,
    bNF_rel_fun_b_b_b_b: ( b > b > $o ) > ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__c_001tf__c_001tf__c,type,
    bNF_rel_fun_c_c_c_c: ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001_062_I_062_Itf__c_Mtf__c_J_Mtf__c_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__d_J,type,
    bNF_re1313098655_d_d_d: ( c > d > $o ) > ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( c > ( c > c ) > c ) > ( d > ( d > d ) > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001_062_Itf__c_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__d_M_062_Itf__d_Mtf__d_J_J,type,
    bNF_re822780063_d_d_d: ( c > d > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( c > c > c > c ) > ( d > d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001_062_Itf__c_M_Eo_J_001_062_Itf__d_M_Eo_J,type,
    bNF_re391428377_o_d_o: ( c > d > $o ) > ( ( c > $o ) > ( d > $o ) > $o ) > ( c > c > $o ) > ( d > d > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bNF_re1972258794_c_d_d: ( c > d > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( c > c > c ) > ( d > d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001_Eo_001_Eo,type,
    bNF_rel_fun_c_d_o_o: ( c > d > $o ) > ( $o > $o > $o ) > ( c > $o ) > ( d > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001tf__a_001tf__b,type,
    bNF_rel_fun_c_d_a_b: ( c > d > $o ) > ( a > b > $o ) > ( c > a ) > ( d > b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__c_001tf__d_001tf__c_001tf__d,type,
    bNF_rel_fun_c_d_c_d: ( c > d > $o ) > ( c > d > $o ) > ( c > c ) > ( d > d ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001tf__d_001tf__d_001tf__d_001tf__d,type,
    bNF_rel_fun_d_d_d_d: ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ).

thf(sy_c_Complete__Partial__Order_Omonotone_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    comple1702356924_a_c_c: ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ).

thf(sy_c_Complete__Partial__Order_Omonotone_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    comple61207421_b_d_d: ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ).

thf(sy_c_Complete__Partial__Order_Omonotone_001tf__c_001tf__c,type,
    comple787379047ne_c_c: ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > $o ).

thf(sy_c_Complete__Partial__Order_Omonotone_001tf__d_001tf__d,type,
    comple1615148455ne_d_d: ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > $o ).

thf(sy_c_FSet_Offold_001tf__a_001tf__c,type,
    ffold_a_c: ( a > c > c ) > c > fset_a > c ).

thf(sy_c_FSet_Offold_001tf__b_001tf__d,type,
    ffold_b_d: ( b > d > d ) > d > fset_b > d ).

thf(sy_c_Finite__Set_Ocomp__fun__commute_001tf__a_001tf__c,type,
    finite746615251te_a_c: ( a > c > c ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__commute_001tf__b_001tf__c,type,
    finite1574384658te_b_c: ( b > c > c ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__commute_001tf__b_001tf__d,type,
    finite1574384659te_b_d: ( b > d > d ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__a_001tf__c,type,
    finite40241358em_a_c: ( a > c > c ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__b_001tf__c,type,
    finite868010765em_b_c: ( b > c > c ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem_001tf__b_001tf__d,type,
    finite868010766em_b_d: ( b > d > d ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem__axioms_001tf__a_001tf__c,type,
    finite19304177ms_a_c: ( a > c > c ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem__axioms_001tf__b_001tf__d,type,
    finite847073585ms_b_d: ( b > d > d ) > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__a_001tf__a,type,
    finite1511629766ph_a_a: ( a > a > a ) > a > set_a > a > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__a_001tf__b,type,
    finite1511629767ph_a_b: ( a > b > b ) > b > set_a > b > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__a_001tf__c,type,
    finite1511629768ph_a_c: ( a > c > c ) > c > set_a > c > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__a_001tf__d,type,
    finite1511629769ph_a_d: ( a > d > d ) > d > set_a > d > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__b_001tf__a,type,
    finite191915525ph_b_a: ( b > a > a ) > a > set_b > a > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__b_001tf__d,type,
    finite191915528ph_b_d: ( b > d > d ) > d > set_b > d > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__c_001tf__a,type,
    finite1019684932ph_c_a: ( c > a > a ) > a > set_c > a > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__c_001tf__b,type,
    finite1019684933ph_c_b: ( c > b > b ) > b > set_c > b > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__c_001tf__c,type,
    finite1019684934ph_c_c: ( c > c > c ) > c > set_c > c > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001tf__c_001tf__d,type,
    finite1019684935ph_c_d: ( c > d > d ) > d > set_c > d > $o ).

thf(sy_c_Fun_Ocomp_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__c_Mtf__c_J_Mtf__a_J,type,
    comp_a_a_a_c_c_c_c_a: ( ( a > a ) > a > c > c ) > ( ( ( c > c ) > a ) > a > a ) > ( ( c > c ) > a ) > a > c > c ).

thf(sy_c_Fun_Ocomp_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__c_Mtf__c_J_Mtf__b_J,type,
    comp_a_b_a_d_d_c_c_b: ( ( a > b ) > a > d > d ) > ( ( ( c > c ) > b ) > a > b ) > ( ( c > c ) > b ) > a > d > d ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__a_J,type,
    comp_b_a_b_c_c_d_d_a: ( ( b > a ) > b > c > c ) > ( ( ( d > d ) > a ) > b > a ) > ( ( d > d ) > a ) > b > c > c ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__d_Mtf__d_J_Mtf__b_J,type,
    comp_b_b_b_d_d_d_d_b: ( ( b > b ) > b > d > d ) > ( ( ( d > d ) > b ) > b > b ) > ( ( d > d ) > b ) > b > d > d ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    comp_c_c_c_c_a: ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    comp_c_c_a_c_c: ( ( c > c ) > a ) > ( ( c > c ) > c > c ) > ( c > c ) > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c_Mtf__c_J_001tf__a_001tf__a,type,
    comp_c_c_a_a: ( ( c > c ) > a ) > ( a > c > c ) > a > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c_Mtf__c_J_001tf__b_001tf__a,type,
    comp_c_c_b_a: ( ( c > c ) > b ) > ( a > c > c ) > a > b ).

thf(sy_c_Fun_Ocomp_001_062_Itf__c_Mtf__c_J_001tf__b_001tf__b,type,
    comp_c_c_b_b: ( ( c > c ) > b ) > ( b > c > c ) > b > b ).

thf(sy_c_Fun_Ocomp_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J_001tf__b,type,
    comp_d_d_d_d_b: ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ).

thf(sy_c_Fun_Ocomp_001_062_Itf__d_Mtf__d_J_001tf__b_001tf__b,type,
    comp_d_d_b_b: ( ( d > d ) > b ) > ( b > d > d ) > b > b ).

thf(sy_c_Fun_Ocomp_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    comp_a_c_c_a: ( a > c > c ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Ocomp_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__b,type,
    comp_a_c_c_b: ( a > c > c ) > ( b > a ) > b > c > c ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    comp_a_a_c_c: ( a > a ) > ( ( c > c ) > a ) > ( c > c ) > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__a,type,
    comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__b,type,
    comp_a_a_b: ( a > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001tf__a,type,
    comp_a_b_a: ( a > b ) > ( a > a ) > a > b ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__b_001tf__b,type,
    comp_a_b_b: ( a > b ) > ( b > a ) > b > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    comp_b_c_c_a: ( b > c > c ) > ( a > b ) > a > c > c ).

thf(sy_c_Fun_Ocomp_001tf__b_001_062_Itf__c_Mtf__c_J_001tf__b,type,
    comp_b_c_c_b: ( b > c > c ) > ( b > b ) > b > c > c ).

thf(sy_c_Fun_Ocomp_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__a,type,
    comp_b_d_d_a: ( b > d > d ) > ( a > b ) > a > d > d ).

thf(sy_c_Fun_Ocomp_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__b,type,
    comp_b_d_d_b: ( b > d > d ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__a_001tf__a,type,
    comp_b_a_a: ( b > a ) > ( a > b ) > a > a ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__a_001tf__b,type,
    comp_b_a_b: ( b > a ) > ( b > b ) > b > a ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    comp_b_b_d_d: ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__a,type,
    comp_b_b_a: ( b > b ) > ( a > b ) > a > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__b,type,
    comp_b_b_b: ( b > b ) > ( b > b ) > b > b ).

thf(sy_c_Fun_Ocomp_001tf__c_001tf__c_001tf__c,type,
    comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).

thf(sy_c_Fun_Ocomp_001tf__d_001tf__d_001tf__d,type,
    comp_d_d_d: ( d > d ) > ( d > d ) > d > d ).

thf(sy_c_Fun_Ofun__upd_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    fun_upd_a_c_c: ( a > c > c ) > a > ( c > c ) > a > c > c ).

thf(sy_c_Fun_Ofun__upd_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    fun_upd_b_d_d: ( b > d > d ) > b > ( d > d ) > b > d > d ).

thf(sy_c_Fun_Ofun__upd_001tf__c_001tf__c,type,
    fun_upd_c_c: ( c > c ) > c > c > c > c ).

thf(sy_c_Fun_Ofun__upd_001tf__d_001tf__d,type,
    fun_upd_d_d: ( d > d ) > d > d > d > d ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J,type,
    map_fu676564502_a_c_c: ( ( a > c > c ) > a > c > c ) > ( ( ( a > a ) > a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( a > c > c ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J,type,
    map_fu232832790_a_c_c: ( ( a > c > c ) > b > d > d ) > ( ( ( b > b ) > b > d > d ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( a > c > c ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J,type,
    map_fu961723106_a_c_c: ( ( a > a ) > a > a ) > ( ( a > c > c ) > a > c > c ) > ( ( a > a ) > a > c > c ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__a_Mtf__a_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J,type,
    map_fu75729569_a_c_c: ( ( a > a ) > b > b ) > ( ( b > d > d ) > a > c > c ) > ( ( b > b ) > b > d > d ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_I_062_Itf__a_Mtf__a_J_M_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    map_fu981964822_b_d_d: ( ( b > d > d ) > a > c > c ) > ( ( ( a > a ) > a > c > c ) > ( b > b ) > b > d > d ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( b > d > d ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J_001_062_I_062_Itf__b_Mtf__b_J_M_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_J,type,
    map_fu538233110_b_d_d: ( ( b > d > d ) > b > d > d ) > ( ( ( b > b ) > b > d > d ) > ( b > b ) > b > d > d ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( b > d > d ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    map_fu1569200227_b_d_d: ( ( b > b ) > a > a ) > ( ( a > c > c ) > b > d > d ) > ( ( a > a ) > a > c > c ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    map_fu683206690_b_d_d: ( ( b > b ) > b > b ) > ( ( b > d > d ) > b > d > d ) > ( ( b > b ) > b > d > d ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    map_fun_a_c_c_a_c_c: ( a > c > c ) > ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__a_001tf__a,type,
    map_fun_a_c_c_a_a: ( a > c > c ) > ( a > a ) > ( ( c > c ) > a ) > a > a ).

thf(sy_c_Fun_Omap__fun_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    map_fun_a_c_c_b_d_d: ( a > c > c ) > ( b > d > d ) > ( ( c > c ) > b ) > a > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__b_001tf__b,type,
    map_fun_a_c_c_b_b: ( a > c > c ) > ( b > b ) > ( ( c > c ) > b ) > a > b ).

thf(sy_c_Fun_Omap__fun_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__c_001tf__c,type,
    map_fun_a_c_c_c_c: ( a > c > c ) > ( c > c ) > ( ( c > c ) > c ) > a > c ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    map_fun_a_a_c_c_c_c: ( a > a ) > ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    map_fun_a_a_a_c_c: ( a > a ) > ( a > c > c ) > ( a > a ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001tf__a_001tf__a,type,
    map_fun_a_a_a_a: ( a > a ) > ( a > a ) > ( a > a ) > a > a ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    map_fun_a_a_b_d_d: ( a > a ) > ( b > d > d ) > ( a > b ) > a > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__b_001_062_Itf__d_Mtf__d_J_001_062_Itf__c_Mtf__c_J,type,
    map_fun_a_b_d_d_c_c: ( a > b ) > ( ( d > d ) > c > c ) > ( b > d > d ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__b_001tf__b_001tf__a,type,
    map_fun_a_b_b_a: ( a > b ) > ( b > a ) > ( b > b ) > a > a ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__c_001tf__c_001_062_Itf__c_Mtf__c_J,type,
    map_fun_a_c_c_c_c2: ( a > c ) > ( c > c > c ) > ( c > c ) > a > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    map_fun_b_d_d_a_c_c: ( b > d > d ) > ( a > c > c ) > ( ( d > d ) > a ) > b > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__a_001tf__a,type,
    map_fun_b_d_d_a_a: ( b > d > d ) > ( a > a ) > ( ( d > d ) > a ) > b > a ).

thf(sy_c_Fun_Omap__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    map_fun_b_d_d_b_d_d: ( b > d > d ) > ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__b_001tf__b,type,
    map_fun_b_d_d_b_b: ( b > d > d ) > ( b > b ) > ( ( d > d ) > b ) > b > b ).

thf(sy_c_Fun_Omap__fun_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__d_001tf__d,type,
    map_fun_b_d_d_d_d: ( b > d > d ) > ( d > d ) > ( ( d > d ) > d ) > b > d ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__a_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    map_fun_b_a_c_c_d_d: ( b > a ) > ( ( c > c ) > d > d ) > ( a > c > c ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__a_001tf__a_001tf__b,type,
    map_fun_b_a_a_b: ( b > a ) > ( a > b ) > ( a > a ) > b > b ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    map_fun_b_b_d_d_d_d: ( b > b ) > ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    map_fun_b_b_a_c_c: ( b > b ) > ( a > c > c ) > ( b > a ) > b > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    map_fun_b_b_b_d_d: ( b > b ) > ( b > d > d ) > ( b > b ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001tf__b_001tf__b,type,
    map_fun_b_b_b_b: ( b > b ) > ( b > b ) > ( b > b ) > b > b ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__d_001tf__d_001_062_Itf__d_Mtf__d_J,type,
    map_fun_b_d_d_d_d2: ( b > d ) > ( d > d > d ) > ( d > d ) > b > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__c_001tf__a_001_062_Itf__c_Mtf__c_J_001tf__c,type,
    map_fun_c_a_c_c_c: ( c > a ) > ( ( c > c ) > c ) > ( a > c > c ) > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__c_001tf__c_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    map_fun_c_c_a_c_c: ( c > c ) > ( a > c > c ) > ( c > a ) > c > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__c_001tf__c_001tf__c_001tf__c,type,
    map_fun_c_c_c_c: ( c > c ) > ( c > c ) > ( c > c ) > c > c ).

thf(sy_c_Fun_Omap__fun_001tf__d_001tf__b_001_062_Itf__d_Mtf__d_J_001tf__d,type,
    map_fun_d_b_d_d_d: ( d > b ) > ( ( d > d ) > d ) > ( b > d > d ) > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__d_001tf__d_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    map_fun_d_d_b_d_d: ( d > d ) > ( b > d > d ) > ( d > b ) > d > d > d ).

thf(sy_c_Fun_Omap__fun_001tf__d_001tf__d_001tf__d_001tf__d,type,
    map_fun_d_d_d_d: ( d > d ) > ( d > d ) > ( d > d ) > d > d ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__a_J,type,
    plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_Itf__b_J,type,
    plus_plus_multiset_b: multiset_b > multiset_b > multiset_b ).

thf(sy_c_If_001tf__a,type,
    if_a: $o > a > a > a ).

thf(sy_c_If_001tf__b,type,
    if_b: $o > b > b > b ).

thf(sy_c_If_001tf__c,type,
    if_c: $o > c > c > c ).

thf(sy_c_If_001tf__d,type,
    if_d: $o > d > d > d ).

thf(sy_c_Multiset_Ofold__mset_001tf__a_001tf__c,type,
    fold_mset_a_c: ( a > c > c ) > c > multiset_a > c ).

thf(sy_c_Multiset_Ofold__mset_001tf__b_001tf__d,type,
    fold_mset_b_d: ( b > d > d ) > d > multiset_b > d ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_M_062_I_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_M_Eo_J_J,type,
    ord_le469275661_d_d_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_Itf__c_Mtf__c_J_M_062_I_062_Itf__d_Mtf__d_J_M_Eo_J_J,type,
    ord_le1338099484_d_d_o: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_062_Itf__b_M_Eo_J_J,type,
    ord_less_eq_a_b_o: ( a > b > $o ) > ( a > b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__c_M_062_Itf__d_M_Eo_J_J,type,
    ord_less_eq_c_d_o: ( c > d > $o ) > ( c > d > $o ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    partia186872226_c_c_a: ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J_001tf__b,type,
    partia1709452835_d_d_b: ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001tf__c_001tf__c_001tf__c,type,
    partia1494029680_c_c_c: ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001tf__d_001tf__d_001tf__d,type,
    partia1041982257_d_d_d: ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    quotient3_c_c_c_c: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > c > c ) > ( ( c > c ) > c > c ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    quotient3_c_c_d_d: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > d > d ) > ( ( d > d ) > c > c ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__c_Mtf__c_J_001tf__a,type,
    quotient3_c_c_a: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > a ) > ( a > c > c ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__d_Mtf__d_J_001_062_Itf__c_Mtf__c_J,type,
    quotient3_d_d_c_c: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > c > c ) > ( ( c > c ) > d > d ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    quotient3_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > d > d ) > ( ( d > d ) > d > d ) > $o ).

thf(sy_c_Quotient_OQuotient3_001_062_Itf__d_Mtf__d_J_001tf__b,type,
    quotient3_d_d_b: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > b ) > ( b > d > d ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__a_001_062_Itf__c_Mtf__c_J,type,
    quotient3_a_c_c: ( a > a > $o ) > ( a > c > c ) > ( ( c > c ) > a ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__a_001tf__a,type,
    quotient3_a_a: ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__a_001tf__b,type,
    quotient3_a_b: ( a > a > $o ) > ( a > b ) > ( b > a ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__b_001_062_Itf__d_Mtf__d_J,type,
    quotient3_b_d_d: ( b > b > $o ) > ( b > d > d ) > ( ( d > d ) > b ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__b_001tf__a,type,
    quotient3_b_a: ( b > b > $o ) > ( b > a ) > ( a > b ) > $o ).

thf(sy_c_Quotient_OQuotient3_001tf__b_001tf__b,type,
    quotient3_b_b: ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    relcom1813708708_b_d_d: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    relcom1887247779_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J,type,
    relcompp_c_c_c_c_c_c: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( c > c ) > ( c > c ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__c_Mtf__c_J_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    relcompp_c_c_c_c_d_d: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( c > c ) > ( d > d ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    relcompp_c_c_d_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( c > c ) > ( d > d ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    relcompp_d_d_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( d > d ) > ( d > d ) > $o ).

thf(sy_c_Relation_Orelcompp_001tf__a_001tf__a_001tf__a,type,
    relcompp_a_a_a: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).

thf(sy_c_Relation_Orelcompp_001tf__a_001tf__a_001tf__b,type,
    relcompp_a_a_b: ( a > a > $o ) > ( a > b > $o ) > a > b > $o ).

thf(sy_c_Relation_Orelcompp_001tf__a_001tf__b_001tf__b,type,
    relcompp_a_b_b: ( a > b > $o ) > ( b > b > $o ) > a > b > $o ).

thf(sy_c_Relation_Orelcompp_001tf__b_001tf__b_001tf__b,type,
    relcompp_b_b_b: ( b > b > $o ) > ( b > b > $o ) > b > b > $o ).

thf(sy_c_Relation_Orelcompp_001tf__c_001tf__c_001tf__d,type,
    relcompp_c_c_d: ( c > c > $o ) > ( c > d > $o ) > c > d > $o ).

thf(sy_c_Relation_Orelcompp_001tf__c_001tf__d_001tf__d,type,
    relcompp_c_d_d: ( c > d > $o ) > ( d > d > $o ) > c > d > $o ).

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_OCollect_001tf__c,type,
    collect_c: ( c > $o ) > set_c ).

thf(sy_c_Set_OCollect_001tf__d,type,
    collect_d: ( d > $o ) > set_d ).

thf(sy_c_Transfer_Obi__total_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bi_total_a_c_c_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bi_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001tf__a_001tf__b,type,
    bi_total_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001tf__c_001tf__d,type,
    bi_total_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    bi_uni844770768_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    bi_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001tf__a_001tf__b,type,
    bi_unique_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001tf__c_001tf__d,type,
    bi_unique_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    left_t1993719015_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    left_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001tf__a_001tf__b,type,
    left_total_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001tf__b_001tf__b,type,
    left_total_b_b: ( b > b > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001tf__c_001tf__d,type,
    left_total_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001tf__d_001tf__d,type,
    left_total_d_d: ( d > d > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    left_u1654071760_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    left_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    left_unique_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001tf__a_001tf__a,type,
    left_unique_a_a: ( a > a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001tf__a_001tf__b,type,
    left_unique_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001tf__c_001tf__c,type,
    left_unique_c_c: ( c > c > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001tf__c_001tf__d,type,
    left_unique_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001tf__d_001tf__d,type,
    left_unique_d_d: ( d > d > $o ) > $o ).

thf(sy_c_Transfer_Orev__implies,type,
    rev_implies: $o > $o > $o ).

thf(sy_c_Transfer_Oright__total_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    right_386984928_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    right_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_Itf__d_Mtf__d_J_001_062_Itf__d_Mtf__d_J,type,
    right_total_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001tf__a_001tf__a,type,
    right_total_a_a: ( a > a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001tf__a_001tf__b,type,
    right_total_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001tf__c_001tf__c,type,
    right_total_c_c: ( c > c > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001tf__c_001tf__d,type,
    right_total_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001tf__d_001tf__d,type,
    right_total_d_d: ( d > d > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_Itf__a_M_062_Itf__c_Mtf__c_J_J_001_062_Itf__b_M_062_Itf__d_Mtf__d_J_J,type,
    right_2142487_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_Itf__c_Mtf__c_J_001_062_Itf__d_Mtf__d_J,type,
    right_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001tf__a_001tf__b,type,
    right_unique_a_b: ( a > b > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001tf__b_001tf__b,type,
    right_unique_b_b: ( b > b > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001tf__c_001tf__d,type,
    right_unique_c_d: ( c > d > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001tf__d_001tf__d,type,
    right_unique_d_d: ( d > d > $o ) > $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_c_member_001tf__c,type,
    member_c: c > set_c > $o ).

thf(sy_c_member_001tf__d,type,
    member_d: d > set_d > $o ).

thf(sy_v_A,type,
    a2: a > b > $o ).

thf(sy_v_B,type,
    b2: c > d > $o ).

thf(sy_v_f1,type,
    f1: a > c > c ).

thf(sy_v_f2,type,
    f2: b > d > d ).

% Relevant facts (354)
thf(fact_0_assms_I2_J,axiom,
    finite746615251te_a_c @ f1 ).

% assms(2)
thf(fact_1_comp__fun__commute_Ofun__left__comm,axiom,
    ! [F: a > c > c,Y: a,X: a,Z: c] :
      ( ( finite746615251te_a_c @ F )
     => ( ( F @ Y @ ( F @ X @ Z ) )
        = ( F @ X @ ( F @ Y @ Z ) ) ) ) ).

% comp_fun_commute.fun_left_comm
thf(fact_2_comp__fun__commute_Ofun__left__comm,axiom,
    ! [F: b > d > d,Y: b,X: b,Z: d] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( F @ Y @ ( F @ X @ Z ) )
        = ( F @ X @ ( F @ Y @ Z ) ) ) ) ).

% comp_fun_commute.fun_left_comm
thf(fact_3_assms_I3_J,axiom,
    finite1574384659te_b_d @ f2 ).

% assms(3)
thf(fact_4__C12_C,axiom,
    bNF_re802603882_c_d_d @ a2 @ ( bNF_rel_fun_c_d_c_d @ b2 @ b2 ) @ f1 @ f2 ).

% "12"
thf(fact_5_comp__fun__commute_Ofold__mset__fusion,axiom,
    ! [F: a > c > c,G: a > c > c,H: c > c,W: c,A: multiset_a] :
      ( ( finite746615251te_a_c @ F )
     => ( ( finite746615251te_a_c @ G )
       => ( ! [X2: a,Y2: c] :
              ( ( H @ ( G @ X2 @ Y2 ) )
              = ( F @ X2 @ ( H @ Y2 ) ) )
         => ( ( H @ ( fold_mset_a_c @ G @ W @ A ) )
            = ( fold_mset_a_c @ F @ ( H @ W ) @ A ) ) ) ) ) ).

% comp_fun_commute.fold_mset_fusion
thf(fact_6_comp__fun__commute_Ofold__mset__fusion,axiom,
    ! [F: b > d > d,G: b > d > d,H: d > d,W: d,A: multiset_b] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( finite1574384659te_b_d @ G )
       => ( ! [X2: b,Y2: d] :
              ( ( H @ ( G @ X2 @ Y2 ) )
              = ( F @ X2 @ ( H @ Y2 ) ) )
         => ( ( H @ ( fold_mset_b_d @ G @ W @ A ) )
            = ( fold_mset_b_d @ F @ ( H @ W ) @ A ) ) ) ) ) ).

% comp_fun_commute.fold_mset_fusion
thf(fact_7_comp__fun__commute_Ofold__mset__fun__left__comm,axiom,
    ! [F: a > c > c,X: a,S: c,M: multiset_a] :
      ( ( finite746615251te_a_c @ F )
     => ( ( F @ X @ ( fold_mset_a_c @ F @ S @ M ) )
        = ( fold_mset_a_c @ F @ ( F @ X @ S ) @ M ) ) ) ).

% comp_fun_commute.fold_mset_fun_left_comm
thf(fact_8_comp__fun__commute_Ofold__mset__fun__left__comm,axiom,
    ! [F: b > d > d,X: b,S: d,M: multiset_b] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( F @ X @ ( fold_mset_b_d @ F @ S @ M ) )
        = ( fold_mset_b_d @ F @ ( F @ X @ S ) @ M ) ) ) ).

% comp_fun_commute.fold_mset_fun_left_comm
thf(fact_9_comp__fun__idem_Oaxioms_I1_J,axiom,
    ! [F: a > c > c] :
      ( ( finite40241358em_a_c @ F )
     => ( finite746615251te_a_c @ F ) ) ).

% comp_fun_idem.axioms(1)
thf(fact_10_comp__fun__idem_Oaxioms_I1_J,axiom,
    ! [F: b > d > d] :
      ( ( finite868010766em_b_d @ F )
     => ( finite1574384659te_b_d @ F ) ) ).

% comp_fun_idem.axioms(1)
thf(fact_11_comp__fun__commute_Ofold__graph__determ,axiom,
    ! [F: a > c > c,Z: c,A: set_a,X: c,Y: c] :
      ( ( finite746615251te_a_c @ F )
     => ( ( finite1511629768ph_a_c @ F @ Z @ A @ X )
       => ( ( finite1511629768ph_a_c @ F @ Z @ A @ Y )
         => ( Y = X ) ) ) ) ).

% comp_fun_commute.fold_graph_determ
thf(fact_12_comp__fun__commute_Ofold__graph__determ,axiom,
    ! [F: b > d > d,Z: d,A: set_b,X: d,Y: d] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( finite191915528ph_b_d @ F @ Z @ A @ X )
       => ( ( finite191915528ph_b_d @ F @ Z @ A @ Y )
         => ( Y = X ) ) ) ) ).

% comp_fun_commute.fold_graph_determ
thf(fact_13_comp__fun__commute_Offold__fun__left__comm,axiom,
    ! [F: a > c > c,X: a,Z: c,A: fset_a] :
      ( ( finite746615251te_a_c @ F )
     => ( ( F @ X @ ( ffold_a_c @ F @ Z @ A ) )
        = ( ffold_a_c @ F @ ( F @ X @ Z ) @ A ) ) ) ).

% comp_fun_commute.ffold_fun_left_comm
thf(fact_14_comp__fun__commute_Offold__fun__left__comm,axiom,
    ! [F: b > d > d,X: b,Z: d,A: fset_b] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( F @ X @ ( ffold_b_d @ F @ Z @ A ) )
        = ( ffold_b_d @ F @ ( F @ X @ Z ) @ A ) ) ) ).

% comp_fun_commute.ffold_fun_left_comm
thf(fact_15_comp__fun__commute_Ocomp__comp__fun__commute,axiom,
    ! [F: a > c > c,G: b > a] :
      ( ( finite746615251te_a_c @ F )
     => ( finite1574384658te_b_c @ ( comp_a_c_c_b @ F @ G ) ) ) ).

% comp_fun_commute.comp_comp_fun_commute
thf(fact_16_comp__fun__commute_Ocomp__comp__fun__commute,axiom,
    ! [F: a > c > c,G: a > a] :
      ( ( finite746615251te_a_c @ F )
     => ( finite746615251te_a_c @ ( comp_a_c_c_a @ F @ G ) ) ) ).

% comp_fun_commute.comp_comp_fun_commute
thf(fact_17_comp__fun__commute_Ocomp__comp__fun__commute,axiom,
    ! [F: b > d > d,G: b > b] :
      ( ( finite1574384659te_b_d @ F )
     => ( finite1574384659te_b_d @ ( comp_b_d_d_b @ F @ G ) ) ) ).

% comp_fun_commute.comp_comp_fun_commute
thf(fact_18_comp__fun__commute__def,axiom,
    ( finite746615251te_a_c
    = ( ^ [F2: a > c > c] :
        ! [Y3: a,X3: a] :
          ( ( comp_c_c_c @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
          = ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ) ).

% comp_fun_commute_def
thf(fact_19_comp__fun__commute__def,axiom,
    ( finite1574384659te_b_d
    = ( ^ [F2: b > d > d] :
        ! [Y3: b,X3: b] :
          ( ( comp_d_d_d @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
          = ( comp_d_d_d @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ) ).

% comp_fun_commute_def
thf(fact_20_comp__fun__commute_Ointro,axiom,
    ! [F: a > c > c] :
      ( ! [Y2: a,X2: a] :
          ( ( comp_c_c_c @ ( F @ Y2 ) @ ( F @ X2 ) )
          = ( comp_c_c_c @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( finite746615251te_a_c @ F ) ) ).

% comp_fun_commute.intro
thf(fact_21_comp__fun__commute_Ointro,axiom,
    ! [F: b > d > d] :
      ( ! [Y2: b,X2: b] :
          ( ( comp_d_d_d @ ( F @ Y2 ) @ ( F @ X2 ) )
          = ( comp_d_d_d @ ( F @ X2 ) @ ( F @ Y2 ) ) )
     => ( finite1574384659te_b_d @ F ) ) ).

% comp_fun_commute.intro
thf(fact_22_comp__fun__commute_Ocomp__fun__commute,axiom,
    ! [F: a > c > c,Y: a,X: a] :
      ( ( finite746615251te_a_c @ F )
     => ( ( comp_c_c_c @ ( F @ Y ) @ ( F @ X ) )
        = ( comp_c_c_c @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% comp_fun_commute.comp_fun_commute
thf(fact_23_comp__fun__commute_Ocomp__fun__commute,axiom,
    ! [F: b > d > d,Y: b,X: b] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( comp_d_d_d @ ( F @ Y ) @ ( F @ X ) )
        = ( comp_d_d_d @ ( F @ X ) @ ( F @ Y ) ) ) ) ).

% comp_fun_commute.comp_fun_commute
thf(fact_24_fold__graph__closed__eq,axiom,
    ! [A: set_b,B: set_d,F: b > d > d,G: b > d > d,Z: d] :
      ( ! [A2: b,B2: d] :
          ( ( member_b @ A2 @ A )
         => ( ( member_d @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: b,B2: d] :
            ( ( member_b @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_d @ Z @ B )
         => ( ( finite191915528ph_b_d @ F @ Z @ A )
            = ( finite191915528ph_b_d @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_25_fold__graph__closed__eq,axiom,
    ! [A: set_a,B: set_c,F: a > c > c,G: a > c > c,Z: c] :
      ( ! [A2: a,B2: c] :
          ( ( member_a @ A2 @ A )
         => ( ( member_c @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: a,B2: c] :
            ( ( member_a @ A2 @ A )
           => ( ( member_c @ B2 @ B )
             => ( member_c @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_c @ Z @ B )
         => ( ( finite1511629768ph_a_c @ F @ Z @ A )
            = ( finite1511629768ph_a_c @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_26_fold__graph__closed__eq,axiom,
    ! [A: set_a,B: set_a,F: a > a > a,G: a > a > a,Z: a] :
      ( ! [A2: a,B2: a] :
          ( ( member_a @ A2 @ A )
         => ( ( member_a @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: a,B2: a] :
            ( ( member_a @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_a @ Z @ B )
         => ( ( finite1511629766ph_a_a @ F @ Z @ A )
            = ( finite1511629766ph_a_a @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_27_fold__graph__closed__eq,axiom,
    ! [A: set_a,B: set_b,F: a > b > b,G: a > b > b,Z: b] :
      ( ! [A2: a,B2: b] :
          ( ( member_a @ A2 @ A )
         => ( ( member_b @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: a,B2: b] :
            ( ( member_a @ A2 @ A )
           => ( ( member_b @ B2 @ B )
             => ( member_b @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_b @ Z @ B )
         => ( ( finite1511629767ph_a_b @ F @ Z @ A )
            = ( finite1511629767ph_a_b @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_28_fold__graph__closed__eq,axiom,
    ! [A: set_a,B: set_d,F: a > d > d,G: a > d > d,Z: d] :
      ( ! [A2: a,B2: d] :
          ( ( member_a @ A2 @ A )
         => ( ( member_d @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: a,B2: d] :
            ( ( member_a @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_d @ Z @ B )
         => ( ( finite1511629769ph_a_d @ F @ Z @ A )
            = ( finite1511629769ph_a_d @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_29_fold__graph__closed__eq,axiom,
    ! [A: set_c,B: set_a,F: c > a > a,G: c > a > a,Z: a] :
      ( ! [A2: c,B2: a] :
          ( ( member_c @ A2 @ A )
         => ( ( member_a @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: c,B2: a] :
            ( ( member_c @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_a @ Z @ B )
         => ( ( finite1019684932ph_c_a @ F @ Z @ A )
            = ( finite1019684932ph_c_a @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_30_fold__graph__closed__eq,axiom,
    ! [A: set_c,B: set_c,F: c > c > c,G: c > c > c,Z: c] :
      ( ! [A2: c,B2: c] :
          ( ( member_c @ A2 @ A )
         => ( ( member_c @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: c,B2: c] :
            ( ( member_c @ A2 @ A )
           => ( ( member_c @ B2 @ B )
             => ( member_c @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_c @ Z @ B )
         => ( ( finite1019684934ph_c_c @ F @ Z @ A )
            = ( finite1019684934ph_c_c @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_31_fold__graph__closed__eq,axiom,
    ! [A: set_c,B: set_b,F: c > b > b,G: c > b > b,Z: b] :
      ( ! [A2: c,B2: b] :
          ( ( member_c @ A2 @ A )
         => ( ( member_b @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: c,B2: b] :
            ( ( member_c @ A2 @ A )
           => ( ( member_b @ B2 @ B )
             => ( member_b @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_b @ Z @ B )
         => ( ( finite1019684933ph_c_b @ F @ Z @ A )
            = ( finite1019684933ph_c_b @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_32_fold__graph__closed__eq,axiom,
    ! [A: set_c,B: set_d,F: c > d > d,G: c > d > d,Z: d] :
      ( ! [A2: c,B2: d] :
          ( ( member_c @ A2 @ A )
         => ( ( member_d @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: c,B2: d] :
            ( ( member_c @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_d @ Z @ B )
         => ( ( finite1019684935ph_c_d @ F @ Z @ A )
            = ( finite1019684935ph_c_d @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_33_fold__graph__closed__eq,axiom,
    ! [A: set_b,B: set_a,F: b > a > a,G: b > a > a,Z: a] :
      ( ! [A2: b,B2: a] :
          ( ( member_b @ A2 @ A )
         => ( ( member_a @ B2 @ B )
           => ( ( F @ A2 @ B2 )
              = ( G @ A2 @ B2 ) ) ) )
     => ( ! [A2: b,B2: a] :
            ( ( member_b @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
       => ( ( member_a @ Z @ B )
         => ( ( finite191915525ph_b_a @ F @ Z @ A )
            = ( finite191915525ph_b_a @ G @ Z @ A ) ) ) ) ) ).

% fold_graph_closed_eq
thf(fact_34_fold__graph__closed__lemma,axiom,
    ! [G: b > d > d,Z: d,A: set_b,X: d,B: set_d,F: b > d > d] :
      ( ( finite191915528ph_b_d @ G @ Z @ A @ X )
     => ( ! [A2: b,B2: d] :
            ( ( member_b @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: b,B2: d] :
              ( ( member_b @ A2 @ A )
             => ( ( member_d @ B2 @ B )
               => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_d @ Z @ B )
           => ( ( finite191915528ph_b_d @ F @ Z @ A @ X )
              & ( member_d @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_35_fold__graph__closed__lemma,axiom,
    ! [G: a > c > c,Z: c,A: set_a,X: c,B: set_c,F: a > c > c] :
      ( ( finite1511629768ph_a_c @ G @ Z @ A @ X )
     => ( ! [A2: a,B2: c] :
            ( ( member_a @ A2 @ A )
           => ( ( member_c @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: a,B2: c] :
              ( ( member_a @ A2 @ A )
             => ( ( member_c @ B2 @ B )
               => ( member_c @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_c @ Z @ B )
           => ( ( finite1511629768ph_a_c @ F @ Z @ A @ X )
              & ( member_c @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_36_fold__graph__closed__lemma,axiom,
    ! [G: a > a > a,Z: a,A: set_a,X: a,B: set_a,F: a > a > a] :
      ( ( finite1511629766ph_a_a @ G @ Z @ A @ X )
     => ( ! [A2: a,B2: a] :
            ( ( member_a @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: a,B2: a] :
              ( ( member_a @ A2 @ A )
             => ( ( member_a @ B2 @ B )
               => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_a @ Z @ B )
           => ( ( finite1511629766ph_a_a @ F @ Z @ A @ X )
              & ( member_a @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_37_fold__graph__closed__lemma,axiom,
    ! [G: a > b > b,Z: b,A: set_a,X: b,B: set_b,F: a > b > b] :
      ( ( finite1511629767ph_a_b @ G @ Z @ A @ X )
     => ( ! [A2: a,B2: b] :
            ( ( member_a @ A2 @ A )
           => ( ( member_b @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: a,B2: b] :
              ( ( member_a @ A2 @ A )
             => ( ( member_b @ B2 @ B )
               => ( member_b @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_b @ Z @ B )
           => ( ( finite1511629767ph_a_b @ F @ Z @ A @ X )
              & ( member_b @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_38_fold__graph__closed__lemma,axiom,
    ! [G: a > d > d,Z: d,A: set_a,X: d,B: set_d,F: a > d > d] :
      ( ( finite1511629769ph_a_d @ G @ Z @ A @ X )
     => ( ! [A2: a,B2: d] :
            ( ( member_a @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: a,B2: d] :
              ( ( member_a @ A2 @ A )
             => ( ( member_d @ B2 @ B )
               => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_d @ Z @ B )
           => ( ( finite1511629769ph_a_d @ F @ Z @ A @ X )
              & ( member_d @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_39_fold__graph__closed__lemma,axiom,
    ! [G: c > a > a,Z: a,A: set_c,X: a,B: set_a,F: c > a > a] :
      ( ( finite1019684932ph_c_a @ G @ Z @ A @ X )
     => ( ! [A2: c,B2: a] :
            ( ( member_c @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: c,B2: a] :
              ( ( member_c @ A2 @ A )
             => ( ( member_a @ B2 @ B )
               => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_a @ Z @ B )
           => ( ( finite1019684932ph_c_a @ F @ Z @ A @ X )
              & ( member_a @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_40_fold__graph__closed__lemma,axiom,
    ! [G: c > c > c,Z: c,A: set_c,X: c,B: set_c,F: c > c > c] :
      ( ( finite1019684934ph_c_c @ G @ Z @ A @ X )
     => ( ! [A2: c,B2: c] :
            ( ( member_c @ A2 @ A )
           => ( ( member_c @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: c,B2: c] :
              ( ( member_c @ A2 @ A )
             => ( ( member_c @ B2 @ B )
               => ( member_c @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_c @ Z @ B )
           => ( ( finite1019684934ph_c_c @ F @ Z @ A @ X )
              & ( member_c @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_41_fold__graph__closed__lemma,axiom,
    ! [G: c > b > b,Z: b,A: set_c,X: b,B: set_b,F: c > b > b] :
      ( ( finite1019684933ph_c_b @ G @ Z @ A @ X )
     => ( ! [A2: c,B2: b] :
            ( ( member_c @ A2 @ A )
           => ( ( member_b @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: c,B2: b] :
              ( ( member_c @ A2 @ A )
             => ( ( member_b @ B2 @ B )
               => ( member_b @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_b @ Z @ B )
           => ( ( finite1019684933ph_c_b @ F @ Z @ A @ X )
              & ( member_b @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_42_fold__graph__closed__lemma,axiom,
    ! [G: c > d > d,Z: d,A: set_c,X: d,B: set_d,F: c > d > d] :
      ( ( finite1019684935ph_c_d @ G @ Z @ A @ X )
     => ( ! [A2: c,B2: d] :
            ( ( member_c @ A2 @ A )
           => ( ( member_d @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: c,B2: d] :
              ( ( member_c @ A2 @ A )
             => ( ( member_d @ B2 @ B )
               => ( member_d @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_d @ Z @ B )
           => ( ( finite1019684935ph_c_d @ F @ Z @ A @ X )
              & ( member_d @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_43_fold__graph__closed__lemma,axiom,
    ! [G: b > a > a,Z: a,A: set_b,X: a,B: set_a,F: b > a > a] :
      ( ( finite191915525ph_b_a @ G @ Z @ A @ X )
     => ( ! [A2: b,B2: a] :
            ( ( member_b @ A2 @ A )
           => ( ( member_a @ B2 @ B )
             => ( ( F @ A2 @ B2 )
                = ( G @ A2 @ B2 ) ) ) )
       => ( ! [A2: b,B2: a] :
              ( ( member_b @ A2 @ A )
             => ( ( member_a @ B2 @ B )
               => ( member_a @ ( G @ A2 @ B2 ) @ B ) ) )
         => ( ( member_a @ Z @ B )
           => ( ( finite191915525ph_b_a @ F @ Z @ A @ X )
              & ( member_a @ X @ B ) ) ) ) ) ) ).

% fold_graph_closed_lemma
thf(fact_44_comp__fun__idem_Ocomp__fun__idem,axiom,
    ! [F: b > d > d,X: b] :
      ( ( finite868010766em_b_d @ F )
     => ( ( comp_d_d_d @ ( F @ X ) @ ( F @ X ) )
        = ( F @ X ) ) ) ).

% comp_fun_idem.comp_fun_idem
thf(fact_45_comp__fun__idem_Ocomp__fun__idem,axiom,
    ! [F: a > c > c,X: a] :
      ( ( finite40241358em_a_c @ F )
     => ( ( comp_c_c_c @ ( F @ X ) @ ( F @ X ) )
        = ( F @ X ) ) ) ).

% comp_fun_idem.comp_fun_idem
thf(fact_46_comp__fun__idem_Ofun__left__idem,axiom,
    ! [F: b > d > d,X: b,Z: d] :
      ( ( finite868010766em_b_d @ F )
     => ( ( F @ X @ ( F @ X @ Z ) )
        = ( F @ X @ Z ) ) ) ).

% comp_fun_idem.fun_left_idem
thf(fact_47_comp__fun__idem_Ofun__left__idem,axiom,
    ! [F: a > c > c,X: a,Z: c] :
      ( ( finite40241358em_a_c @ F )
     => ( ( F @ X @ ( F @ X @ Z ) )
        = ( F @ X @ Z ) ) ) ).

% comp_fun_idem.fun_left_idem
thf(fact_48_comp__fun__idem_Ocomp__comp__fun__idem,axiom,
    ! [F: a > c > c,G: b > a] :
      ( ( finite40241358em_a_c @ F )
     => ( finite868010765em_b_c @ ( comp_a_c_c_b @ F @ G ) ) ) ).

% comp_fun_idem.comp_comp_fun_idem
thf(fact_49_comp__fun__idem_Ocomp__comp__fun__idem,axiom,
    ! [F: b > d > d,G: b > b] :
      ( ( finite868010766em_b_d @ F )
     => ( finite868010766em_b_d @ ( comp_b_d_d_b @ F @ G ) ) ) ).

% comp_fun_idem.comp_comp_fun_idem
thf(fact_50_comp__fun__idem_Ocomp__comp__fun__idem,axiom,
    ! [F: a > c > c,G: a > a] :
      ( ( finite40241358em_a_c @ F )
     => ( finite40241358em_a_c @ ( comp_a_c_c_a @ F @ G ) ) ) ).

% comp_fun_idem.comp_comp_fun_idem
thf(fact_51_comp__apply,axiom,
    ( comp_b_b_d_d
    = ( ^ [F2: b > b,G2: ( d > d ) > b,X3: d > d] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_52_comp__apply,axiom,
    ( comp_b_b_b
    = ( ^ [F2: b > b,G2: b > b,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_53_comp__apply,axiom,
    ( comp_a_c_c_b
    = ( ^ [F2: a > c > c,G2: b > a,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_54_comp__apply,axiom,
    ( comp_a_a_c_c
    = ( ^ [F2: a > a,G2: ( c > c ) > a,X3: c > c] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_55_comp__apply,axiom,
    ( comp_a_a_a
    = ( ^ [F2: a > a,G2: a > a,X3: a] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_56_comp__apply,axiom,
    ( comp_b_d_d_b
    = ( ^ [F2: b > d > d,G2: b > b,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_57_comp__apply,axiom,
    ( comp_a_c_c_a
    = ( ^ [F2: a > c > c,G2: a > a,X3: a] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_58_rel__funI,axiom,
    ! [A: a > b > $o,B: a > b > $o,F: a > a,G: b > b] :
      ( ! [X2: a,Y2: b] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_rel_fun_a_b_a_b @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_59_rel__funI,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: a > d > d] :
      ( ! [X2: a,Y2: a] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_re1979731817_c_d_d @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_60_rel__funI,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( c > c ) > $o,F: a > c > c,G: a > c > c] :
      ( ! [X2: a,Y2: a] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_re1143700905_c_c_c @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_61_rel__funI,axiom,
    ! [A: a > a > $o,B: a > b > $o,F: a > a,G: a > b] :
      ( ! [X2: a,Y2: a] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_rel_fun_a_a_a_b @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_62_rel__funI,axiom,
    ! [A: a > a > $o,B: a > a > $o,F: a > a,G: a > a] :
      ( ! [X2: a,Y2: a] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_rel_fun_a_a_a_a @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_63_rel__funI,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d] :
      ( ! [X2: a,Y2: b] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_re802603882_c_d_d @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_64_rel__funI,axiom,
    ! [A: c > d > $o,B: c > d > $o,F: c > c,G: d > d] :
      ( ! [X2: c,Y2: d] :
          ( ( A @ X2 @ Y2 )
         => ( B @ ( F @ X2 ) @ ( G @ Y2 ) ) )
     => ( bNF_rel_fun_c_d_c_d @ A @ B @ F @ G ) ) ).

% rel_funI
thf(fact_65_If__transfer,axiom,
    ! [A: a > b > $o] :
      ( bNF_re588060702_b_b_b
      @ ^ [Y4: $o,Z2: $o] : Y4 = Z2
      @ ( bNF_re569932906_a_b_b @ A @ ( bNF_rel_fun_a_b_a_b @ A @ A ) )
      @ if_a
      @ if_b ) ).

% If_transfer
thf(fact_66_If__transfer,axiom,
    ! [A: a > a > $o] :
      ( bNF_re1705765981_a_a_a
      @ ^ [Y4: $o,Z2: $o] : Y4 = Z2
      @ ( bNF_re911029929_a_a_a @ A @ ( bNF_rel_fun_a_a_a_a @ A @ A ) )
      @ if_a
      @ if_a ) ).

% If_transfer
thf(fact_67_If__transfer,axiom,
    ! [A: c > d > $o] :
      ( bNF_re647211934_d_d_d
      @ ^ [Y4: $o,Z2: $o] : Y4 = Z2
      @ ( bNF_re1972258794_c_d_d @ A @ ( bNF_rel_fun_c_d_c_d @ A @ A ) )
      @ if_c
      @ if_d ) ).

% If_transfer
thf(fact_68_rel__fun__def__butlast,axiom,
    ! [R: a > a > $o,S2: c > d > $o,T: c > d > $o,F: a > c > c,G: a > d > d] :
      ( ( bNF_re1979731817_c_d_d @ R @ ( bNF_rel_fun_c_d_c_d @ S2 @ T ) @ F @ G )
      = ( ! [X3: a,Y3: a] :
            ( ( R @ X3 @ Y3 )
           => ( bNF_rel_fun_c_d_c_d @ S2 @ T @ ( F @ X3 ) @ ( G @ Y3 ) ) ) ) ) ).

% rel_fun_def_butlast
thf(fact_69_rel__fun__def__butlast,axiom,
    ! [R: a > a > $o,S2: c > c > $o,T: c > c > $o,F: a > c > c,G: a > c > c] :
      ( ( bNF_re1143700905_c_c_c @ R @ ( bNF_rel_fun_c_c_c_c @ S2 @ T ) @ F @ G )
      = ( ! [X3: a,Y3: a] :
            ( ( R @ X3 @ Y3 )
           => ( bNF_rel_fun_c_c_c_c @ S2 @ T @ ( F @ X3 ) @ ( G @ Y3 ) ) ) ) ) ).

% rel_fun_def_butlast
thf(fact_70_rel__fun__def__butlast,axiom,
    ! [R: a > b > $o,S2: c > d > $o,T: c > d > $o,F: a > c > c,G: b > d > d] :
      ( ( bNF_re802603882_c_d_d @ R @ ( bNF_rel_fun_c_d_c_d @ S2 @ T ) @ F @ G )
      = ( ! [X3: a,Y3: b] :
            ( ( R @ X3 @ Y3 )
           => ( bNF_rel_fun_c_d_c_d @ S2 @ T @ ( F @ X3 ) @ ( G @ Y3 ) ) ) ) ) ).

% rel_fun_def_butlast
thf(fact_71_o__rsp_I2_J,axiom,
    ! [R1: b > b > $o] :
      ( bNF_re742509149_b_d_d
      @ ^ [Y4: b > d > d,Z2: b > d > d] : Y4 = Z2
      @ ( bNF_re1412708073_b_d_d
        @ ( bNF_rel_fun_b_b_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 )
        @ ( bNF_re1844863849_d_d_d @ R1
          @ ^ [Y4: d > d,Z2: d > d] : Y4 = Z2 ) )
      @ comp_b_d_d_b
      @ comp_b_d_d_b ) ).

% o_rsp(2)
thf(fact_72_o__rsp_I2_J,axiom,
    ! [R1: a > a > $o] :
      ( bNF_re880840541_a_c_c
      @ ^ [Y4: a > c > c,Z2: a > c > c] : Y4 = Z2
      @ ( bNF_re1691224489_a_c_c
        @ ( bNF_rel_fun_a_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_re1143700905_c_c_c @ R1
          @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2 ) )
      @ comp_a_c_c_a
      @ comp_a_c_c_a ) ).

% o_rsp(2)
thf(fact_73_o__rsp_I2_J,axiom,
    ! [R1: b > b > $o] :
      ( bNF_re1222471293_b_b_b
      @ ^ [Y4: b > b,Z2: b > b] : Y4 = Z2
      @ ( bNF_re2075418869_b_b_b
        @ ( bNF_rel_fun_b_b_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 )
        @ ( bNF_rel_fun_b_b_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 ) )
      @ comp_b_b_b
      @ comp_b_b_b ) ).

% o_rsp(2)
thf(fact_74_o__rsp_I2_J,axiom,
    ! [R1: a > a > $o] :
      ( bNF_re1258259453_a_a_a
      @ ^ [Y4: a > a,Z2: a > a] : Y4 = Z2
      @ ( bNF_re1690311157_a_a_a
        @ ( bNF_rel_fun_a_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_rel_fun_a_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) )
      @ comp_a_a_a
      @ comp_a_a_a ) ).

% o_rsp(2)
thf(fact_75_o__rsp_I2_J,axiom,
    ! [R1: a > b > $o] :
      ( bNF_re1311853791_b_c_c
      @ ^ [Y4: a > c > c,Z2: a > c > c] : Y4 = Z2
      @ ( bNF_re1665173865_b_c_c
        @ ( bNF_rel_fun_a_b_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_re2114056618_c_c_c @ R1
          @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2 ) )
      @ comp_a_c_c_a
      @ comp_a_c_c_b ) ).

% o_rsp(2)
thf(fact_76_o__rsp_I2_J,axiom,
    ! [R1: ( d > d ) > b > $o] :
      ( bNF_re1138812345_b_b_b
      @ ^ [Y4: b > b,Z2: b > b] : Y4 = Z2
      @ ( bNF_re323253981_b_b_b
        @ ( bNF_re1703323451_b_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 )
        @ ( bNF_re1703323451_b_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 ) )
      @ comp_b_b_d_d
      @ comp_b_b_b ) ).

% o_rsp(2)
thf(fact_77_o__rsp_I2_J,axiom,
    ! [R1: b > ( d > d ) > $o] :
      ( bNF_re961930425_d_d_b
      @ ^ [Y4: b > b,Z2: b > b] : Y4 = Z2
      @ ( bNF_re1794062813_d_d_b
        @ ( bNF_re1573506119_d_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 )
        @ ( bNF_re1573506119_d_b_b @ R1
          @ ^ [Y4: b,Z2: b] : Y4 = Z2 ) )
      @ comp_b_b_b
      @ comp_b_b_d_d ) ).

% o_rsp(2)
thf(fact_78_o__rsp_I2_J,axiom,
    ! [R1: b > a > $o] :
      ( bNF_re978949211_a_c_c
      @ ^ [Y4: a > c > c,Z2: a > c > c] : Y4 = Z2
      @ ( bNF_re1591514407_a_c_c
        @ ( bNF_rel_fun_b_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_re758172648_c_c_c @ R1
          @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2 ) )
      @ comp_a_c_c_b
      @ comp_a_c_c_a ) ).

% o_rsp(2)
thf(fact_79_o__rsp_I2_J,axiom,
    ! [R1: b > b > $o] :
      ( bNF_re1409962461_b_c_c
      @ ^ [Y4: a > c > c,Z2: a > c > c] : Y4 = Z2
      @ ( bNF_re1565463783_b_c_c
        @ ( bNF_rel_fun_b_b_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_re1728528361_c_c_c @ R1
          @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2 ) )
      @ comp_a_c_c_b
      @ comp_a_c_c_b ) ).

% o_rsp(2)
thf(fact_80_o__rsp_I2_J,axiom,
    ! [R1: ( c > c ) > a > $o] :
      ( bNF_re1503602041_a_a_a
      @ ^ [Y4: a > a,Z2: a > a] : Y4 = Z2
      @ ( bNF_re1177671453_a_a_a
        @ ( bNF_re1424579386_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
        @ ( bNF_re1424579386_a_a_a @ R1
          @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) )
      @ comp_a_a_c_c
      @ comp_a_a_a ) ).

% o_rsp(2)
thf(fact_81_o__rsp_I1_J,axiom,
    ! [R2: c > d > $o,R3: c > d > $o,R1: c > d > $o] : ( bNF_re764096061_d_d_d @ ( bNF_rel_fun_c_d_c_d @ R2 @ R3 ) @ ( bNF_re2078100341_c_d_d @ ( bNF_rel_fun_c_d_c_d @ R1 @ R2 ) @ ( bNF_rel_fun_c_d_c_d @ R1 @ R3 ) ) @ comp_c_c_c @ comp_d_d_d ) ).

% o_rsp(1)
thf(fact_82_o__rsp_I1_J,axiom,
    ! [R2: b > b > $o,R3: ( d > d ) > ( d > d ) > $o,R1: b > b > $o] : ( bNF_re742509149_b_d_d @ ( bNF_re1844863849_d_d_d @ R2 @ R3 ) @ ( bNF_re1412708073_b_d_d @ ( bNF_rel_fun_b_b_b_b @ R1 @ R2 ) @ ( bNF_re1844863849_d_d_d @ R1 @ R3 ) ) @ comp_b_d_d_b @ comp_b_d_d_b ) ).

% o_rsp(1)
thf(fact_83_o__rsp_I1_J,axiom,
    ! [R2: b > a > $o,R3: ( d > d ) > ( c > c ) > $o,R1: b > a > $o] : ( bNF_re561231771_a_c_c @ ( bNF_re38477224_d_c_c @ R2 @ R3 ) @ ( bNF_re1342462312_a_c_c @ ( bNF_rel_fun_b_a_b_a @ R1 @ R2 ) @ ( bNF_re38477224_d_c_c @ R1 @ R3 ) ) @ comp_b_d_d_b @ comp_a_c_c_a ) ).

% o_rsp(1)
thf(fact_84_o__rsp_I1_J,axiom,
    ! [R2: a > a > $o,R3: ( c > c ) > ( c > c ) > $o,R1: a > a > $o] : ( bNF_re880840541_a_c_c @ ( bNF_re1143700905_c_c_c @ R2 @ R3 ) @ ( bNF_re1691224489_a_c_c @ ( bNF_rel_fun_a_a_a_a @ R1 @ R2 ) @ ( bNF_re1143700905_c_c_c @ R1 @ R3 ) ) @ comp_a_c_c_a @ comp_a_c_c_a ) ).

% o_rsp(1)
thf(fact_85_o__rsp_I1_J,axiom,
    ! [R2: a > b > $o,R3: ( c > c ) > ( d > d ) > $o,R1: a > b > $o] : ( bNF_re1062117919_b_d_d @ ( bNF_re802603882_c_d_d @ R2 @ R3 ) @ ( bNF_re1761470250_b_d_d @ ( bNF_rel_fun_a_b_a_b @ R1 @ R2 ) @ ( bNF_re802603882_c_d_d @ R1 @ R3 ) ) @ comp_a_c_c_a @ comp_b_d_d_b ) ).

% o_rsp(1)
thf(fact_86_o__rsp_I1_J,axiom,
    ! [R2: ( c > c ) > ( d > d ) > $o,R3: ( c > c ) > ( d > d ) > $o,R1: a > b > $o] : ( bNF_re141854397_b_d_d @ ( bNF_re2078100341_c_d_d @ R2 @ R3 ) @ ( bNF_re692482399_b_d_d @ ( bNF_re802603882_c_d_d @ R1 @ R2 ) @ ( bNF_re802603882_c_d_d @ R1 @ R3 ) ) @ comp_c_c_c_c_a @ comp_d_d_d_d_b ) ).

% o_rsp(1)
thf(fact_87_o__rsp_I1_J,axiom,
    ! [R2: b > b > $o,R3: b > b > $o,R1: b > b > $o] : ( bNF_re1222471293_b_b_b @ ( bNF_rel_fun_b_b_b_b @ R2 @ R3 ) @ ( bNF_re2075418869_b_b_b @ ( bNF_rel_fun_b_b_b_b @ R1 @ R2 ) @ ( bNF_rel_fun_b_b_b_b @ R1 @ R3 ) ) @ comp_b_b_b @ comp_b_b_b ) ).

% o_rsp(1)
thf(fact_88_o__rsp_I1_J,axiom,
    ! [R2: b > a > $o,R3: b > a > $o,R1: b > a > $o] : ( bNF_re1645058365_a_a_a @ ( bNF_rel_fun_b_a_b_a @ R2 @ R3 ) @ ( bNF_re310361461_b_a_a @ ( bNF_rel_fun_b_a_b_a @ R1 @ R2 ) @ ( bNF_rel_fun_b_a_b_a @ R1 @ R3 ) ) @ comp_b_b_b @ comp_a_a_a ) ).

% o_rsp(1)
thf(fact_89_o__rsp_I1_J,axiom,
    ! [R2: a > b > $o,R3: a > a > $o,R1: a > a > $o] : ( bNF_re539937469_b_a_a @ ( bNF_rel_fun_a_b_a_a @ R2 @ R3 ) @ ( bNF_re857382262_a_a_a @ ( bNF_rel_fun_a_a_a_b @ R1 @ R2 ) @ ( bNF_rel_fun_a_a_a_a @ R1 @ R3 ) ) @ comp_a_a_a @ comp_b_a_a ) ).

% o_rsp(1)
thf(fact_90_o__rsp_I1_J,axiom,
    ! [R2: a > b > $o,R3: a > b > $o,R1: a > b > $o] : ( bNF_re835672381_b_b_b @ ( bNF_rel_fun_a_b_a_b @ R2 @ R3 ) @ ( bNF_re1307884917_a_b_b @ ( bNF_rel_fun_a_b_a_b @ R1 @ R2 ) @ ( bNF_rel_fun_a_b_a_b @ R1 @ R3 ) ) @ comp_a_a_a @ comp_b_b_b ) ).

% o_rsp(1)
thf(fact_91_fun_Omap__transfer,axiom,
    ! [Rb: b > b > $o,Sd: ( d > d ) > ( d > d ) > $o] :
      ( bNF_re742509149_b_d_d @ ( bNF_re1844863849_d_d_d @ Rb @ Sd )
      @ ( bNF_re1412708073_b_d_d
        @ ( bNF_rel_fun_b_b_b_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Rb )
        @ ( bNF_re1844863849_d_d_d
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Sd ) )
      @ comp_b_d_d_b
      @ comp_b_d_d_b ) ).

% fun.map_transfer
thf(fact_92_fun_Omap__transfer,axiom,
    ! [Rb: a > a > $o,Sd: ( c > c ) > ( c > c ) > $o] :
      ( bNF_re880840541_a_c_c @ ( bNF_re1143700905_c_c_c @ Rb @ Sd )
      @ ( bNF_re1691224489_a_c_c
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_re1143700905_c_c_c
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_c_c_a
      @ comp_a_c_c_a ) ).

% fun.map_transfer
thf(fact_93_fun_Omap__transfer,axiom,
    ! [Rb: a > b > $o,Sd: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re1160226589_b_d_d @ ( bNF_re802603882_c_d_d @ Rb @ Sd )
      @ ( bNF_re1661760168_b_d_d
        @ ( bNF_rel_fun_b_b_a_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Rb )
        @ ( bNF_re417075625_c_d_d
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Sd ) )
      @ comp_a_c_c_b
      @ comp_b_d_d_b ) ).

% fun.map_transfer
thf(fact_94_fun_Omap__transfer,axiom,
    ! [Rb: a > b > $o,Sd: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re631104669_a_d_d @ ( bNF_re802603882_c_d_d @ Rb @ Sd )
      @ ( bNF_re1787520874_a_d_d
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_re1979731817_c_d_d
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_c_c_a
      @ comp_b_d_d_a ) ).

% fun.map_transfer
thf(fact_95_fun_Omap__transfer,axiom,
    ! [Rb: b > b > $o,Sd: b > b > $o] :
      ( bNF_re1222471293_b_b_b @ ( bNF_rel_fun_b_b_b_b @ Rb @ Sd )
      @ ( bNF_re2075418869_b_b_b
        @ ( bNF_rel_fun_b_b_b_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_b_b_b_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Sd ) )
      @ comp_b_b_b
      @ comp_b_b_b ) ).

% fun.map_transfer
thf(fact_96_fun_Omap__transfer,axiom,
    ! [Rb: a > b > $o,Sd: a > a > $o] :
      ( bNF_re539937469_b_a_a @ ( bNF_rel_fun_a_b_a_a @ Rb @ Sd )
      @ ( bNF_re857382262_a_a_a
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_a_a
      @ comp_b_a_a ) ).

% fun.map_transfer
thf(fact_97_fun_Omap__transfer,axiom,
    ! [Rb: a > b > $o,Sd: a > b > $o] :
      ( bNF_re774352699_b_b_b @ ( bNF_rel_fun_a_b_a_b @ Rb @ Sd )
      @ ( bNF_re668686835_a_b_b
        @ ( bNF_rel_fun_b_b_a_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_b_b_a_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Sd ) )
      @ comp_a_a_b
      @ comp_b_b_b ) ).

% fun.map_transfer
thf(fact_98_fun_Omap__transfer,axiom,
    ! [Rb: a > b > $o,Sd: a > b > $o] :
      ( bNF_re796114495_b_a_b @ ( bNF_rel_fun_a_b_a_b @ Rb @ Sd )
      @ ( bNF_re865643767_a_a_b
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_a_a
      @ comp_b_b_a ) ).

% fun.map_transfer
thf(fact_99_fun_Omap__transfer,axiom,
    ! [Rb: a > a > $o,Sd: a > b > $o] :
      ( bNF_re1514436479_a_a_b @ ( bNF_rel_fun_a_a_a_b @ Rb @ Sd )
      @ ( bNF_re1698572662_a_a_b
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_a_a
      @ comp_a_b_a ) ).

% fun.map_transfer
thf(fact_100_fun_Omap__transfer,axiom,
    ! [Rb: a > a > $o,Sd: a > a > $o] :
      ( bNF_re1258259453_a_a_a @ ( bNF_rel_fun_a_a_a_a @ Rb @ Sd )
      @ ( bNF_re1690311157_a_a_a
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Rb )
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sd ) )
      @ comp_a_a_a
      @ comp_a_a_a ) ).

% fun.map_transfer
thf(fact_101_comp__transfer,axiom,
    ! [B: c > d > $o,C: c > d > $o,A: c > d > $o] : ( bNF_re764096061_d_d_d @ ( bNF_rel_fun_c_d_c_d @ B @ C ) @ ( bNF_re2078100341_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ ( bNF_rel_fun_c_d_c_d @ A @ C ) ) @ comp_c_c_c @ comp_d_d_d ) ).

% comp_transfer
thf(fact_102_comp__transfer,axiom,
    ! [B: b > b > $o,C: ( d > d ) > ( d > d ) > $o,A: b > b > $o] : ( bNF_re742509149_b_d_d @ ( bNF_re1844863849_d_d_d @ B @ C ) @ ( bNF_re1412708073_b_d_d @ ( bNF_rel_fun_b_b_b_b @ A @ B ) @ ( bNF_re1844863849_d_d_d @ A @ C ) ) @ comp_b_d_d_b @ comp_b_d_d_b ) ).

% comp_transfer
thf(fact_103_comp__transfer,axiom,
    ! [B: b > a > $o,C: ( d > d ) > ( c > c ) > $o,A: b > a > $o] : ( bNF_re561231771_a_c_c @ ( bNF_re38477224_d_c_c @ B @ C ) @ ( bNF_re1342462312_a_c_c @ ( bNF_rel_fun_b_a_b_a @ A @ B ) @ ( bNF_re38477224_d_c_c @ A @ C ) ) @ comp_b_d_d_b @ comp_a_c_c_a ) ).

% comp_transfer
thf(fact_104_comp__transfer,axiom,
    ! [B: a > a > $o,C: ( c > c ) > ( c > c ) > $o,A: a > a > $o] : ( bNF_re880840541_a_c_c @ ( bNF_re1143700905_c_c_c @ B @ C ) @ ( bNF_re1691224489_a_c_c @ ( bNF_rel_fun_a_a_a_a @ A @ B ) @ ( bNF_re1143700905_c_c_c @ A @ C ) ) @ comp_a_c_c_a @ comp_a_c_c_a ) ).

% comp_transfer
thf(fact_105_comp__transfer,axiom,
    ! [B: a > b > $o,C: ( c > c ) > ( d > d ) > $o,A: a > b > $o] : ( bNF_re1062117919_b_d_d @ ( bNF_re802603882_c_d_d @ B @ C ) @ ( bNF_re1761470250_b_d_d @ ( bNF_rel_fun_a_b_a_b @ A @ B ) @ ( bNF_re802603882_c_d_d @ A @ C ) ) @ comp_a_c_c_a @ comp_b_d_d_b ) ).

% comp_transfer
thf(fact_106_comp__transfer,axiom,
    ! [B: ( c > c ) > ( d > d ) > $o,C: ( c > c ) > ( d > d ) > $o,A: a > b > $o] : ( bNF_re141854397_b_d_d @ ( bNF_re2078100341_c_d_d @ B @ C ) @ ( bNF_re692482399_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) @ ( bNF_re802603882_c_d_d @ A @ C ) ) @ comp_c_c_c_c_a @ comp_d_d_d_d_b ) ).

% comp_transfer
thf(fact_107_comp__transfer,axiom,
    ! [B: b > b > $o,C: b > b > $o,A: b > b > $o] : ( bNF_re1222471293_b_b_b @ ( bNF_rel_fun_b_b_b_b @ B @ C ) @ ( bNF_re2075418869_b_b_b @ ( bNF_rel_fun_b_b_b_b @ A @ B ) @ ( bNF_rel_fun_b_b_b_b @ A @ C ) ) @ comp_b_b_b @ comp_b_b_b ) ).

% comp_transfer
thf(fact_108_comp__transfer,axiom,
    ! [B: b > a > $o,C: b > a > $o,A: b > a > $o] : ( bNF_re1645058365_a_a_a @ ( bNF_rel_fun_b_a_b_a @ B @ C ) @ ( bNF_re310361461_b_a_a @ ( bNF_rel_fun_b_a_b_a @ A @ B ) @ ( bNF_rel_fun_b_a_b_a @ A @ C ) ) @ comp_b_b_b @ comp_a_a_a ) ).

% comp_transfer
thf(fact_109_comp__transfer,axiom,
    ! [B: a > b > $o,C: a > a > $o,A: a > a > $o] : ( bNF_re539937469_b_a_a @ ( bNF_rel_fun_a_b_a_a @ B @ C ) @ ( bNF_re857382262_a_a_a @ ( bNF_rel_fun_a_a_a_b @ A @ B ) @ ( bNF_rel_fun_a_a_a_a @ A @ C ) ) @ comp_a_a_a @ comp_b_a_a ) ).

% comp_transfer
thf(fact_110_comp__transfer,axiom,
    ! [B: a > b > $o,C: a > b > $o,A: a > b > $o] : ( bNF_re835672381_b_b_b @ ( bNF_rel_fun_a_b_a_b @ B @ C ) @ ( bNF_re1307884917_a_b_b @ ( bNF_rel_fun_a_b_a_b @ A @ B ) @ ( bNF_rel_fun_a_b_a_b @ A @ C ) ) @ comp_a_a_a @ comp_b_b_b ) ).

% comp_transfer
thf(fact_111_comp__fun__idem_Ointro,axiom,
    ! [F: a > c > c] :
      ( ( finite746615251te_a_c @ F )
     => ( ( finite19304177ms_a_c @ F )
       => ( finite40241358em_a_c @ F ) ) ) ).

% comp_fun_idem.intro
thf(fact_112_comp__fun__idem_Ointro,axiom,
    ! [F: b > d > d] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( finite847073585ms_b_d @ F )
       => ( finite868010766em_b_d @ F ) ) ) ).

% comp_fun_idem.intro
thf(fact_113_comp__fun__idem__def,axiom,
    ( finite40241358em_a_c
    = ( ^ [F2: a > c > c] :
          ( ( finite746615251te_a_c @ F2 )
          & ( finite19304177ms_a_c @ F2 ) ) ) ) ).

% comp_fun_idem_def
thf(fact_114_comp__fun__idem__def,axiom,
    ( finite868010766em_b_d
    = ( ^ [F2: b > d > d] :
          ( ( finite1574384659te_b_d @ F2 )
          & ( finite847073585ms_b_d @ F2 ) ) ) ) ).

% comp_fun_idem_def
thf(fact_115_comp__fun__idem_Oaxioms_I2_J,axiom,
    ! [F: b > d > d] :
      ( ( finite868010766em_b_d @ F )
     => ( finite847073585ms_b_d @ F ) ) ).

% comp_fun_idem.axioms(2)
thf(fact_116_comp__fun__idem_Oaxioms_I2_J,axiom,
    ! [F: a > c > c] :
      ( ( finite40241358em_a_c @ F )
     => ( finite19304177ms_a_c @ F ) ) ).

% comp_fun_idem.axioms(2)
thf(fact_117_comp__fun__idem__axioms_Ointro,axiom,
    ! [F: b > d > d] :
      ( ! [X2: b] :
          ( ( comp_d_d_d @ ( F @ X2 ) @ ( F @ X2 ) )
          = ( F @ X2 ) )
     => ( finite847073585ms_b_d @ F ) ) ).

% comp_fun_idem_axioms.intro
thf(fact_118_comp__fun__idem__axioms_Ointro,axiom,
    ! [F: a > c > c] :
      ( ! [X2: a] :
          ( ( comp_c_c_c @ ( F @ X2 ) @ ( F @ X2 ) )
          = ( F @ X2 ) )
     => ( finite19304177ms_a_c @ F ) ) ).

% comp_fun_idem_axioms.intro
thf(fact_119_comp__fun__idem__axioms__def,axiom,
    ( finite847073585ms_b_d
    = ( ^ [F2: b > d > d] :
        ! [X3: b] :
          ( ( comp_d_d_d @ ( F2 @ X3 ) @ ( F2 @ X3 ) )
          = ( F2 @ X3 ) ) ) ) ).

% comp_fun_idem_axioms_def
thf(fact_120_comp__fun__idem__axioms__def,axiom,
    ( finite19304177ms_a_c
    = ( ^ [F2: a > c > c] :
        ! [X3: a] :
          ( ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ X3 ) )
          = ( F2 @ X3 ) ) ) ) ).

% comp_fun_idem_axioms_def
thf(fact_121_fun_Orel__transfer,axiom,
    ! [Sa: a > b > $o,Sc: a > b > $o] :
      ( bNF_re1071888283_a_b_o
      @ ( bNF_re418251421_o_b_o @ Sa
        @ ( bNF_rel_fun_a_b_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1217999849_a_b_o
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1463366826_b_o_o
          @ ( bNF_rel_fun_a_a_a_b
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_b_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_122_fun_Orel__transfer,axiom,
    ! [Sa: a > b > $o,Sc: a > a > $o] :
      ( bNF_re1310167325_a_a_o
      @ ( bNF_re1977372894_o_a_o @ Sa
        @ ( bNF_rel_fun_a_a_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re390230442_a_a_o
        @ ( bNF_rel_fun_a_a_a_b
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re134330537_a_o_o
          @ ( bNF_rel_fun_a_a_a_a
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_b_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_123_fun_Orel__transfer,axiom,
    ! [Sa: a > a > $o,Sc: b > b > $o] :
      ( bNF_re2141181021_a_b_o
      @ ( bNF_re250254555_o_b_o @ Sa
        @ ( bNF_rel_fun_b_b_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1812319081_a_b_o
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1088547499_b_o_o
          @ ( bNF_rel_fun_a_a_b_b
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_124_fun_Orel__transfer,axiom,
    ! [Sa: a > a > $o,Sc: b > a > $o] :
      ( bNF_re231976415_a_a_o
      @ ( bNF_re1809376028_o_a_o @ Sa
        @ ( bNF_rel_fun_b_a_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re984549674_a_a_o
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1906994858_a_o_o
          @ ( bNF_rel_fun_a_a_b_a
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_125_fun_Orel__transfer,axiom,
    ! [Sa: a > a > $o,Sc: a > b > $o] :
      ( bNF_re1165460699_a_b_o
      @ ( bNF_re131001756_o_b_o @ Sa
        @ ( bNF_rel_fun_a_b_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re581117672_a_b_o
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1463366826_b_o_o
          @ ( bNF_rel_fun_a_a_a_b
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_126_fun_Orel__transfer,axiom,
    ! [Sa: a > a > $o,Sc: a > a > $o] :
      ( bNF_re1403739741_a_a_o
      @ ( bNF_re1690123229_o_a_o @ Sa
        @ ( bNF_rel_fun_a_a_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1900831913_a_a_o
        @ ( bNF_rel_fun_a_a_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re134330537_a_o_o
          @ ( bNF_rel_fun_a_a_a_a
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_127_fun_Orel__transfer,axiom,
    ! [Sa: ( c > c ) > a > $o,Sc: ( d > d ) > b > $o] :
      ( bNF_re1133483099_a_b_o
      @ ( bNF_re1895239662_o_b_o @ Sa
        @ ( bNF_re199323387_b_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re332737826_a_b_o
        @ ( bNF_re950444090_c_c_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re802276445_b_o_o
          @ ( bNF_re2038021755_d_d_b
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1979731817_c_d_d
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_128_fun_Orel__transfer,axiom,
    ! [Sa: ( c > c ) > a > $o,Sc: ( d > d ) > a > $o] :
      ( bNF_re145798749_a_a_o
      @ ( bNF_re1306877487_o_a_o @ Sa
        @ ( bNF_re991543930_a_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1652452067_a_a_o
        @ ( bNF_re950444090_c_c_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1620723804_a_o_o
          @ ( bNF_re2038021754_d_d_a
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1979731817_c_d_d
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_129_fun_Orel__transfer,axiom,
    ! [Sa: ( c > c ) > a > $o,Sc: ( c > c ) > b > $o] :
      ( bNF_re708047067_a_b_o
      @ ( bNF_re2038641070_o_b_o @ Sa
        @ ( bNF_re90976443_b_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re364411746_a_b_o
        @ ( bNF_re950444090_c_c_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re1256092317_b_o_o
          @ ( bNF_re950444091_c_c_b
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1143700905_c_c_c
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_b
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_130_fun_Orel__transfer,axiom,
    ! [Sa: ( c > c ) > a > $o,Sc: ( c > c ) > a > $o] :
      ( bNF_re1867846365_a_a_o
      @ ( bNF_re1450278895_o_a_o @ Sa
        @ ( bNF_re883196986_a_o_o @ Sc
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1684125987_a_a_o
        @ ( bNF_re950444090_c_c_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Sa )
        @ ( bNF_re2074539676_a_o_o
          @ ( bNF_re950444090_c_c_a
            @ ^ [Y4: a,Z2: a] : Y4 = Z2
            @ Sc )
          @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
      @ ( bNF_re1143700905_c_c_c
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
      @ ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2 ) ) ).

% fun.rel_transfer
thf(fact_131_fun_Orel__refl,axiom,
    ! [Ra: ( c > c ) > ( c > c ) > $o,X: a > c > c] :
      ( ! [X2: c > c] : ( Ra @ X2 @ X2 )
     => ( bNF_re1143700905_c_c_c
        @ ^ [Y4: a,Z2: a] : Y4 = Z2
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_132_fun_Orel__refl,axiom,
    ! [Ra: a > a > $o,X: a > a] :
      ( ! [X2: a] : ( Ra @ X2 @ X2 )
     => ( bNF_rel_fun_a_a_a_a
        @ ^ [Y4: a,Z2: a] : Y4 = Z2
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_133_fun_Orel__eq,axiom,
    ( ( bNF_re1143700905_c_c_c
      @ ^ [Y4: a,Z2: a] : Y4 = Z2
      @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2 )
    = ( ^ [Y4: a > c > c,Z2: a > c > c] : Y4 = Z2 ) ) ).

% fun.rel_eq
thf(fact_134_fun_Orel__eq,axiom,
    ( ( bNF_rel_fun_a_a_a_a
      @ ^ [Y4: a,Z2: a] : Y4 = Z2
      @ ^ [Y4: a,Z2: a] : Y4 = Z2 )
    = ( ^ [Y4: a > a,Z2: a > a] : Y4 = Z2 ) ) ).

% fun.rel_eq
thf(fact_135_rel__fun__mono_H,axiom,
    ! [Y5: a > b > $o,X4: a > b > $o,A: a > b > $o,B: a > b > $o,F: a > a,G: b > b] :
      ( ! [X2: a,Y2: b] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: a,Y2: b] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_rel_fun_a_b_a_b @ X4 @ A @ F @ G )
         => ( bNF_rel_fun_a_b_a_b @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_136_rel__fun__mono_H,axiom,
    ! [Y5: a > a > $o,X4: a > a > $o,A: ( c > c ) > ( d > d ) > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: a > d > d] :
      ( ! [X2: a,Y2: a] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: c > c,Y2: d > d] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_re1979731817_c_d_d @ X4 @ A @ F @ G )
         => ( bNF_re1979731817_c_d_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_137_rel__fun__mono_H,axiom,
    ! [Y5: a > a > $o,X4: a > a > $o,A: ( c > c ) > ( c > c ) > $o,B: ( c > c ) > ( c > c ) > $o,F: a > c > c,G: a > c > c] :
      ( ! [X2: a,Y2: a] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: c > c,Y2: c > c] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_re1143700905_c_c_c @ X4 @ A @ F @ G )
         => ( bNF_re1143700905_c_c_c @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_138_rel__fun__mono_H,axiom,
    ! [Y5: a > a > $o,X4: a > a > $o,A: a > b > $o,B: a > b > $o,F: a > a,G: a > b] :
      ( ! [X2: a,Y2: a] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: a,Y2: b] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_rel_fun_a_a_a_b @ X4 @ A @ F @ G )
         => ( bNF_rel_fun_a_a_a_b @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_139_rel__fun__mono_H,axiom,
    ! [Y5: a > a > $o,X4: a > a > $o,A: a > a > $o,B: a > a > $o,F: a > a,G: a > a] :
      ( ! [X2: a,Y2: a] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: a,Y2: a] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_rel_fun_a_a_a_a @ X4 @ A @ F @ G )
         => ( bNF_rel_fun_a_a_a_a @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_140_rel__fun__mono_H,axiom,
    ! [Y5: a > b > $o,X4: a > b > $o,A: ( c > c ) > ( d > d ) > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d] :
      ( ! [X2: a,Y2: b] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: c > c,Y2: d > d] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_re802603882_c_d_d @ X4 @ A @ F @ G )
         => ( bNF_re802603882_c_d_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_141_rel__fun__mono_H,axiom,
    ! [Y5: c > d > $o,X4: c > d > $o,A: c > d > $o,B: c > d > $o,F: c > c,G: d > d] :
      ( ! [X2: c,Y2: d] :
          ( ( Y5 @ X2 @ Y2 )
         => ( X4 @ X2 @ Y2 ) )
     => ( ! [X2: c,Y2: d] :
            ( ( A @ X2 @ Y2 )
           => ( B @ X2 @ Y2 ) )
       => ( ( bNF_rel_fun_c_d_c_d @ X4 @ A @ F @ G )
         => ( bNF_rel_fun_c_d_c_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_142_rel__fun__mono,axiom,
    ! [X4: a > b > $o,A: a > b > $o,F: a > a,G: b > b,Y5: a > b > $o,B: a > b > $o] :
      ( ( bNF_rel_fun_a_b_a_b @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: b] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: a,Y2: b] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_rel_fun_a_b_a_b @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_143_rel__fun__mono,axiom,
    ! [X4: a > a > $o,A: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: a > d > d,Y5: a > a > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bNF_re1979731817_c_d_d @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: a] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: c > c,Y2: d > d] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_re1979731817_c_d_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_144_rel__fun__mono,axiom,
    ! [X4: a > a > $o,A: ( c > c ) > ( c > c ) > $o,F: a > c > c,G: a > c > c,Y5: a > a > $o,B: ( c > c ) > ( c > c ) > $o] :
      ( ( bNF_re1143700905_c_c_c @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: a] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: c > c,Y2: c > c] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_re1143700905_c_c_c @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_145_rel__fun__mono,axiom,
    ! [X4: a > a > $o,A: a > b > $o,F: a > a,G: a > b,Y5: a > a > $o,B: a > b > $o] :
      ( ( bNF_rel_fun_a_a_a_b @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: a] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: a,Y2: b] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_rel_fun_a_a_a_b @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_146_rel__fun__mono,axiom,
    ! [X4: a > a > $o,A: a > a > $o,F: a > a,G: a > a,Y5: a > a > $o,B: a > a > $o] :
      ( ( bNF_rel_fun_a_a_a_a @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: a] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: a,Y2: a] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_rel_fun_a_a_a_a @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_147_rel__fun__mono,axiom,
    ! [X4: a > b > $o,A: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d,Y5: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bNF_re802603882_c_d_d @ X4 @ A @ F @ G )
     => ( ! [X2: a,Y2: b] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: c > c,Y2: d > d] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_re802603882_c_d_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_148_rel__fun__mono,axiom,
    ! [X4: c > d > $o,A: c > d > $o,F: c > c,G: d > d,Y5: c > d > $o,B: c > d > $o] :
      ( ( bNF_rel_fun_c_d_c_d @ X4 @ A @ F @ G )
     => ( ! [X2: c,Y2: d] :
            ( ( Y5 @ X2 @ Y2 )
           => ( X4 @ X2 @ Y2 ) )
       => ( ! [X2: c,Y2: d] :
              ( ( A @ X2 @ Y2 )
             => ( B @ X2 @ Y2 ) )
         => ( bNF_rel_fun_c_d_c_d @ Y5 @ B @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_149_let__rsp,axiom,
    ! [R1: a > b > $o,R2: a > b > $o] :
      ( bNF_re1730737055_b_b_b @ R1 @ ( bNF_re2087760490_b_a_b @ ( bNF_rel_fun_a_b_a_b @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: b,F2: b > b] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_150_let__rsp,axiom,
    ! [R1: a > a > $o,R2: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re1391160029_d_d_d @ R1 @ ( bNF_re1955249705_c_d_d @ ( bNF_re1979731817_c_d_d @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > d > d] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_151_let__rsp,axiom,
    ! [R1: a > a > $o,R2: ( c > c ) > ( c > c ) > $o] :
      ( bNF_re1482032989_c_c_c @ R1 @ ( bNF_re27458217_c_c_c @ ( bNF_re1143700905_c_c_c @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_152_let__rsp,axiom,
    ! [R1: a > a > $o,R2: a > b > $o] :
      ( bNF_re1093913501_a_b_b @ R1 @ ( bNF_re473406379_b_a_b @ ( bNF_rel_fun_a_a_a_b @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > b] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_153_let__rsp,axiom,
    ! [R1: a > a > $o,R2: a > a > $o] :
      ( bNF_re865741149_a_a_a @ R1 @ ( bNF_re571457705_a_a_a @ ( bNF_rel_fun_a_a_a_a @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_154_let__rsp,axiom,
    ! [R1: a > b > $o,R2: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re1327926367_d_d_d @ R1 @ ( bNF_re84044842_c_d_d @ ( bNF_re802603882_c_d_d @ R1 @ R2 ) @ R2 )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: b,F2: b > d > d] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_155_let__rsp,axiom,
    ! [R1: c > d > $o,R2: c > d > $o] :
      ( bNF_re1313098655_d_d_d @ R1 @ ( bNF_re1303182826_d_c_d @ ( bNF_rel_fun_c_d_c_d @ R1 @ R2 ) @ R2 )
      @ ^ [S3: c,F2: c > c] : ( F2 @ S3 )
      @ ^ [S3: d,F2: d > d] : ( F2 @ S3 ) ) ).

% let_rsp
thf(fact_156_rel__funD,axiom,
    ! [A: a > b > $o,B: a > b > $o,F: a > a,G: b > b,X: a,Y: b] :
      ( ( bNF_rel_fun_a_b_a_b @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_157_rel__funD,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: a > d > d,X: a,Y: a] :
      ( ( bNF_re1979731817_c_d_d @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_158_rel__funD,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( c > c ) > $o,F: a > c > c,G: a > c > c,X: a,Y: a] :
      ( ( bNF_re1143700905_c_c_c @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_159_rel__funD,axiom,
    ! [A: a > a > $o,B: a > b > $o,F: a > a,G: a > b,X: a,Y: a] :
      ( ( bNF_rel_fun_a_a_a_b @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_160_rel__funD,axiom,
    ! [A: a > a > $o,B: a > a > $o,F: a > a,G: a > a,X: a,Y: a] :
      ( ( bNF_rel_fun_a_a_a_a @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_161_rel__funD,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d,X: a,Y: b] :
      ( ( bNF_re802603882_c_d_d @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_162_rel__funD,axiom,
    ! [A: c > d > $o,B: c > d > $o,F: c > c,G: d > d,X: c,Y: d] :
      ( ( bNF_rel_fun_c_d_c_d @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_163_rewriteR__comp__comp2,axiom,
    ! [G: b > b,H: b > b,R12: b > b,R22: b > b,F: b > d > d,L: b > d > d] :
      ( ( ( comp_b_b_b @ G @ H )
        = ( comp_b_b_b @ R12 @ R22 ) )
     => ( ( ( comp_b_d_d_b @ F @ R12 )
          = L )
       => ( ( comp_b_d_d_b @ ( comp_b_d_d_b @ F @ G ) @ H )
          = ( comp_b_d_d_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_164_rewriteR__comp__comp2,axiom,
    ! [G: a > a,H: a > a,R12: a > a,R22: a > a,F: a > c > c,L: a > c > c] :
      ( ( ( comp_a_a_a @ G @ H )
        = ( comp_a_a_a @ R12 @ R22 ) )
     => ( ( ( comp_a_c_c_a @ F @ R12 )
          = L )
       => ( ( comp_a_c_c_a @ ( comp_a_c_c_a @ F @ G ) @ H )
          = ( comp_a_c_c_a @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_165_rewriteR__comp__comp2,axiom,
    ! [G: b > d > d,H: b > b,R12: b > d > d,R22: b > b,F: ( d > d ) > d > d,L: b > d > d] :
      ( ( ( comp_b_d_d_b @ G @ H )
        = ( comp_b_d_d_b @ R12 @ R22 ) )
     => ( ( ( comp_d_d_d_d_b @ F @ R12 )
          = L )
       => ( ( comp_b_d_d_b @ ( comp_d_d_d_d_b @ F @ G ) @ H )
          = ( comp_b_d_d_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_166_rewriteR__comp__comp2,axiom,
    ! [G: a > c > c,H: a > a,R12: a > c > c,R22: a > a,F: ( c > c ) > c > c,L: a > c > c] :
      ( ( ( comp_a_c_c_a @ G @ H )
        = ( comp_a_c_c_a @ R12 @ R22 ) )
     => ( ( ( comp_c_c_c_c_a @ F @ R12 )
          = L )
       => ( ( comp_a_c_c_a @ ( comp_c_c_c_c_a @ F @ G ) @ H )
          = ( comp_a_c_c_a @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_167_rewriteR__comp__comp2,axiom,
    ! [G: b > b,H: b > b,R12: b > b,R22: b > b,F: b > b,L: b > b] :
      ( ( ( comp_b_b_b @ G @ H )
        = ( comp_b_b_b @ R12 @ R22 ) )
     => ( ( ( comp_b_b_b @ F @ R12 )
          = L )
       => ( ( comp_b_b_b @ ( comp_b_b_b @ F @ G ) @ H )
          = ( comp_b_b_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_168_rewriteR__comp__comp2,axiom,
    ! [G: a > a,H: a > a,R12: a > a,R22: a > a,F: a > a,L: a > a] :
      ( ( ( comp_a_a_a @ G @ H )
        = ( comp_a_a_a @ R12 @ R22 ) )
     => ( ( ( comp_a_a_a @ F @ R12 )
          = L )
       => ( ( comp_a_a_a @ ( comp_a_a_a @ F @ G ) @ H )
          = ( comp_a_a_a @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_169_rewriteR__comp__comp2,axiom,
    ! [G: b > a,H: b > b,R12: a > a,R22: b > a,F: a > c > c,L: a > c > c] :
      ( ( ( comp_b_a_b @ G @ H )
        = ( comp_a_a_b @ R12 @ R22 ) )
     => ( ( ( comp_a_c_c_a @ F @ R12 )
          = L )
       => ( ( comp_b_c_c_b @ ( comp_a_c_c_b @ F @ G ) @ H )
          = ( comp_a_c_c_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_170_rewriteR__comp__comp2,axiom,
    ! [G: a > a,H: b > a,R12: a > a,R22: b > a,F: a > c > c,L: a > c > c] :
      ( ( ( comp_a_a_b @ G @ H )
        = ( comp_a_a_b @ R12 @ R22 ) )
     => ( ( ( comp_a_c_c_a @ F @ R12 )
          = L )
       => ( ( comp_a_c_c_b @ ( comp_a_c_c_a @ F @ G ) @ H )
          = ( comp_a_c_c_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_171_rewriteR__comp__comp2,axiom,
    ! [G: a > a,H: b > a,R12: b > a,R22: b > b,F: a > c > c,L: b > c > c] :
      ( ( ( comp_a_a_b @ G @ H )
        = ( comp_b_a_b @ R12 @ R22 ) )
     => ( ( ( comp_a_c_c_b @ F @ R12 )
          = L )
       => ( ( comp_a_c_c_b @ ( comp_a_c_c_a @ F @ G ) @ H )
          = ( comp_b_c_c_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_172_rewriteR__comp__comp2,axiom,
    ! [G: a > b,H: b > a,R12: b > b,R22: b > b,F: b > c > c,L: b > c > c] :
      ( ( ( comp_a_b_b @ G @ H )
        = ( comp_b_b_b @ R12 @ R22 ) )
     => ( ( ( comp_b_c_c_b @ F @ R12 )
          = L )
       => ( ( comp_a_c_c_b @ ( comp_b_c_c_a @ F @ G ) @ H )
          = ( comp_b_c_c_b @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_173_rewriteL__comp__comp2,axiom,
    ! [F: b > d > d,G: b > b,L1: b > d > d,L2: b > b,H: b > b,R4: b > b] :
      ( ( ( comp_b_d_d_b @ F @ G )
        = ( comp_b_d_d_b @ L1 @ L2 ) )
     => ( ( ( comp_b_b_b @ L2 @ H )
          = R4 )
       => ( ( comp_b_d_d_b @ F @ ( comp_b_b_b @ G @ H ) )
          = ( comp_b_d_d_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_174_rewriteL__comp__comp2,axiom,
    ! [F: a > c > c,G: a > a,L1: a > c > c,L2: a > a,H: a > a,R4: a > a] :
      ( ( ( comp_a_c_c_a @ F @ G )
        = ( comp_a_c_c_a @ L1 @ L2 ) )
     => ( ( ( comp_a_a_a @ L2 @ H )
          = R4 )
       => ( ( comp_a_c_c_a @ F @ ( comp_a_a_a @ G @ H ) )
          = ( comp_a_c_c_a @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_175_rewriteL__comp__comp2,axiom,
    ! [F: ( d > d ) > d > d,G: b > d > d,L1: b > d > d,L2: b > b,H: b > b,R4: b > b] :
      ( ( ( comp_d_d_d_d_b @ F @ G )
        = ( comp_b_d_d_b @ L1 @ L2 ) )
     => ( ( ( comp_b_b_b @ L2 @ H )
          = R4 )
       => ( ( comp_d_d_d_d_b @ F @ ( comp_b_d_d_b @ G @ H ) )
          = ( comp_b_d_d_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_176_rewriteL__comp__comp2,axiom,
    ! [F: ( c > c ) > c > c,G: a > c > c,L1: a > c > c,L2: a > a,H: a > a,R4: a > a] :
      ( ( ( comp_c_c_c_c_a @ F @ G )
        = ( comp_a_c_c_a @ L1 @ L2 ) )
     => ( ( ( comp_a_a_a @ L2 @ H )
          = R4 )
       => ( ( comp_c_c_c_c_a @ F @ ( comp_a_c_c_a @ G @ H ) )
          = ( comp_a_c_c_a @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_177_rewriteL__comp__comp2,axiom,
    ! [F: b > d > d,G: b > b,L1: ( d > d ) > d > d,L2: b > d > d,H: b > b,R4: b > d > d] :
      ( ( ( comp_b_d_d_b @ F @ G )
        = ( comp_d_d_d_d_b @ L1 @ L2 ) )
     => ( ( ( comp_b_d_d_b @ L2 @ H )
          = R4 )
       => ( ( comp_b_d_d_b @ F @ ( comp_b_b_b @ G @ H ) )
          = ( comp_d_d_d_d_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_178_rewriteL__comp__comp2,axiom,
    ! [F: a > c > c,G: a > a,L1: ( c > c ) > c > c,L2: a > c > c,H: a > a,R4: a > c > c] :
      ( ( ( comp_a_c_c_a @ F @ G )
        = ( comp_c_c_c_c_a @ L1 @ L2 ) )
     => ( ( ( comp_a_c_c_a @ L2 @ H )
          = R4 )
       => ( ( comp_a_c_c_a @ F @ ( comp_a_a_a @ G @ H ) )
          = ( comp_c_c_c_c_a @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_179_rewriteL__comp__comp2,axiom,
    ! [F: b > b,G: b > b,L1: b > b,L2: b > b,H: b > b,R4: b > b] :
      ( ( ( comp_b_b_b @ F @ G )
        = ( comp_b_b_b @ L1 @ L2 ) )
     => ( ( ( comp_b_b_b @ L2 @ H )
          = R4 )
       => ( ( comp_b_b_b @ F @ ( comp_b_b_b @ G @ H ) )
          = ( comp_b_b_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_180_rewriteL__comp__comp2,axiom,
    ! [F: a > a,G: a > a,L1: a > a,L2: a > a,H: a > a,R4: a > a] :
      ( ( ( comp_a_a_a @ F @ G )
        = ( comp_a_a_a @ L1 @ L2 ) )
     => ( ( ( comp_a_a_a @ L2 @ H )
          = R4 )
       => ( ( comp_a_a_a @ F @ ( comp_a_a_a @ G @ H ) )
          = ( comp_a_a_a @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_181_rewriteL__comp__comp2,axiom,
    ! [F: ( c > c ) > b,G: a > c > c,L1: b > b,L2: a > b,H: b > a,R4: b > b] :
      ( ( ( comp_c_c_b_a @ F @ G )
        = ( comp_b_b_a @ L1 @ L2 ) )
     => ( ( ( comp_a_b_b @ L2 @ H )
          = R4 )
       => ( ( comp_c_c_b_b @ F @ ( comp_a_c_c_b @ G @ H ) )
          = ( comp_b_b_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_182_rewriteL__comp__comp2,axiom,
    ! [F: b > b,G: a > b,L1: ( c > c ) > b,L2: a > c > c,H: b > a,R4: b > c > c] :
      ( ( ( comp_b_b_a @ F @ G )
        = ( comp_c_c_b_a @ L1 @ L2 ) )
     => ( ( ( comp_a_c_c_b @ L2 @ H )
          = R4 )
       => ( ( comp_b_b_b @ F @ ( comp_a_b_b @ G @ H ) )
          = ( comp_c_c_b_b @ L1 @ R4 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_183_rewriteR__comp__comp,axiom,
    ! [G: b > b,H: b > b,R4: b > b,F: b > d > d] :
      ( ( ( comp_b_b_b @ G @ H )
        = R4 )
     => ( ( comp_b_d_d_b @ ( comp_b_d_d_b @ F @ G ) @ H )
        = ( comp_b_d_d_b @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_184_rewriteR__comp__comp,axiom,
    ! [G: a > a,H: a > a,R4: a > a,F: a > c > c] :
      ( ( ( comp_a_a_a @ G @ H )
        = R4 )
     => ( ( comp_a_c_c_a @ ( comp_a_c_c_a @ F @ G ) @ H )
        = ( comp_a_c_c_a @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_185_rewriteR__comp__comp,axiom,
    ! [G: b > d > d,H: b > b,R4: b > d > d,F: ( d > d ) > d > d] :
      ( ( ( comp_b_d_d_b @ G @ H )
        = R4 )
     => ( ( comp_b_d_d_b @ ( comp_d_d_d_d_b @ F @ G ) @ H )
        = ( comp_d_d_d_d_b @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_186_rewriteR__comp__comp,axiom,
    ! [G: a > c > c,H: a > a,R4: a > c > c,F: ( c > c ) > c > c] :
      ( ( ( comp_a_c_c_a @ G @ H )
        = R4 )
     => ( ( comp_a_c_c_a @ ( comp_c_c_c_c_a @ F @ G ) @ H )
        = ( comp_c_c_c_c_a @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_187_rewriteR__comp__comp,axiom,
    ! [G: b > b,H: b > b,R4: b > b,F: b > b] :
      ( ( ( comp_b_b_b @ G @ H )
        = R4 )
     => ( ( comp_b_b_b @ ( comp_b_b_b @ F @ G ) @ H )
        = ( comp_b_b_b @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_188_rewriteR__comp__comp,axiom,
    ! [G: a > a,H: a > a,R4: a > a,F: a > a] :
      ( ( ( comp_a_a_a @ G @ H )
        = R4 )
     => ( ( comp_a_a_a @ ( comp_a_a_a @ F @ G ) @ H )
        = ( comp_a_a_a @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_189_rewriteR__comp__comp,axiom,
    ! [G: ( d > d ) > b,H: b > d > d,R4: b > b,F: b > b] :
      ( ( ( comp_d_d_b_b @ G @ H )
        = R4 )
     => ( ( comp_d_d_b_b @ ( comp_b_b_d_d @ F @ G ) @ H )
        = ( comp_b_b_b @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_190_rewriteR__comp__comp,axiom,
    ! [G: b > a,H: a > b,R4: a > a,F: a > c > c] :
      ( ( ( comp_b_a_a @ G @ H )
        = R4 )
     => ( ( comp_b_c_c_a @ ( comp_a_c_c_b @ F @ G ) @ H )
        = ( comp_a_c_c_a @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_191_rewriteR__comp__comp,axiom,
    ! [G: b > a,H: b > b,R4: b > a,F: a > c > c] :
      ( ( ( comp_b_a_b @ G @ H )
        = R4 )
     => ( ( comp_b_c_c_b @ ( comp_a_c_c_b @ F @ G ) @ H )
        = ( comp_a_c_c_b @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_192_rewriteR__comp__comp,axiom,
    ! [G: ( c > c ) > a,H: a > c > c,R4: a > a,F: a > a] :
      ( ( ( comp_c_c_a_a @ G @ H )
        = R4 )
     => ( ( comp_c_c_a_a @ ( comp_a_a_c_c @ F @ G ) @ H )
        = ( comp_a_a_a @ F @ R4 ) ) ) ).

% rewriteR_comp_comp
thf(fact_193_rewriteL__comp__comp,axiom,
    ! [F: b > d > d,G: b > b,L: b > d > d,H: b > b] :
      ( ( ( comp_b_d_d_b @ F @ G )
        = L )
     => ( ( comp_b_d_d_b @ F @ ( comp_b_b_b @ G @ H ) )
        = ( comp_b_d_d_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_194_rewriteL__comp__comp,axiom,
    ! [F: a > c > c,G: a > a,L: a > c > c,H: a > a] :
      ( ( ( comp_a_c_c_a @ F @ G )
        = L )
     => ( ( comp_a_c_c_a @ F @ ( comp_a_a_a @ G @ H ) )
        = ( comp_a_c_c_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_195_rewriteL__comp__comp,axiom,
    ! [F: ( d > d ) > d > d,G: b > d > d,L: b > d > d,H: b > b] :
      ( ( ( comp_d_d_d_d_b @ F @ G )
        = L )
     => ( ( comp_d_d_d_d_b @ F @ ( comp_b_d_d_b @ G @ H ) )
        = ( comp_b_d_d_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_196_rewriteL__comp__comp,axiom,
    ! [F: ( c > c ) > c > c,G: a > c > c,L: a > c > c,H: a > a] :
      ( ( ( comp_c_c_c_c_a @ F @ G )
        = L )
     => ( ( comp_c_c_c_c_a @ F @ ( comp_a_c_c_a @ G @ H ) )
        = ( comp_a_c_c_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_197_rewriteL__comp__comp,axiom,
    ! [F: b > b,G: b > b,L: b > b,H: b > b] :
      ( ( ( comp_b_b_b @ F @ G )
        = L )
     => ( ( comp_b_b_b @ F @ ( comp_b_b_b @ G @ H ) )
        = ( comp_b_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_198_rewriteL__comp__comp,axiom,
    ! [F: a > a,G: a > a,L: a > a,H: a > a] :
      ( ( ( comp_a_a_a @ F @ G )
        = L )
     => ( ( comp_a_a_a @ F @ ( comp_a_a_a @ G @ H ) )
        = ( comp_a_a_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_199_rewriteL__comp__comp,axiom,
    ! [F: ( d > d ) > b,G: b > d > d,L: b > b,H: b > b] :
      ( ( ( comp_d_d_b_b @ F @ G )
        = L )
     => ( ( comp_d_d_b_b @ F @ ( comp_b_d_d_b @ G @ H ) )
        = ( comp_b_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_200_rewriteL__comp__comp,axiom,
    ! [F: ( c > c ) > a,G: a > c > c,L: a > a,H: a > a] :
      ( ( ( comp_c_c_a_a @ F @ G )
        = L )
     => ( ( comp_c_c_a_a @ F @ ( comp_a_c_c_a @ G @ H ) )
        = ( comp_a_a_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_201_rewriteL__comp__comp,axiom,
    ! [F: a > c > c,G: a > a,L: a > c > c,H: b > a] :
      ( ( ( comp_a_c_c_a @ F @ G )
        = L )
     => ( ( comp_a_c_c_b @ F @ ( comp_a_a_b @ G @ H ) )
        = ( comp_a_c_c_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_202_rewriteL__comp__comp,axiom,
    ! [F: b > b,G: ( d > d ) > b,L: ( d > d ) > b,H: b > d > d] :
      ( ( ( comp_b_b_d_d @ F @ G )
        = L )
     => ( ( comp_b_b_b @ F @ ( comp_d_d_b_b @ G @ H ) )
        = ( comp_d_d_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_203_fun_Omap__comp,axiom,
    ! [G: b > d > d,F: b > b,V: b > b] :
      ( ( comp_b_d_d_b @ G @ ( comp_b_b_b @ F @ V ) )
      = ( comp_b_d_d_b @ ( comp_b_d_d_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_204_fun_Omap__comp,axiom,
    ! [G: a > c > c,F: a > a,V: a > a] :
      ( ( comp_a_c_c_a @ G @ ( comp_a_a_a @ F @ V ) )
      = ( comp_a_c_c_a @ ( comp_a_c_c_a @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_205_fun_Omap__comp,axiom,
    ! [G: ( d > d ) > d > d,F: b > d > d,V: b > b] :
      ( ( comp_d_d_d_d_b @ G @ ( comp_b_d_d_b @ F @ V ) )
      = ( comp_b_d_d_b @ ( comp_d_d_d_d_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_206_fun_Omap__comp,axiom,
    ! [G: ( c > c ) > c > c,F: a > c > c,V: a > a] :
      ( ( comp_c_c_c_c_a @ G @ ( comp_a_c_c_a @ F @ V ) )
      = ( comp_a_c_c_a @ ( comp_c_c_c_c_a @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_207_fun_Omap__comp,axiom,
    ! [G: b > b,F: b > b,V: b > b] :
      ( ( comp_b_b_b @ G @ ( comp_b_b_b @ F @ V ) )
      = ( comp_b_b_b @ ( comp_b_b_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_208_fun_Omap__comp,axiom,
    ! [G: a > a,F: a > a,V: a > a] :
      ( ( comp_a_a_a @ G @ ( comp_a_a_a @ F @ V ) )
      = ( comp_a_a_a @ ( comp_a_a_a @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_209_fun_Omap__comp,axiom,
    ! [G: ( d > d ) > b,F: b > d > d,V: b > b] :
      ( ( comp_d_d_b_b @ G @ ( comp_b_d_d_b @ F @ V ) )
      = ( comp_b_b_b @ ( comp_d_d_b_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_210_fun_Omap__comp,axiom,
    ! [G: ( c > c ) > a,F: a > c > c,V: a > a] :
      ( ( comp_c_c_a_a @ G @ ( comp_a_c_c_a @ F @ V ) )
      = ( comp_a_a_a @ ( comp_c_c_a_a @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_211_fun_Omap__comp,axiom,
    ! [G: a > c > c,F: b > a,V: a > b] :
      ( ( comp_a_c_c_a @ G @ ( comp_b_a_a @ F @ V ) )
      = ( comp_b_c_c_a @ ( comp_a_c_c_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_212_fun_Omap__comp,axiom,
    ! [G: b > b,F: b > b,V: ( d > d ) > b] :
      ( ( comp_b_b_d_d @ G @ ( comp_b_b_d_d @ F @ V ) )
      = ( comp_b_b_d_d @ ( comp_b_b_b @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_213_comp__apply__eq,axiom,
    ! [F: b > b,G: ( d > d ) > b,X: d > d,H: b > b,K: ( d > d ) > b] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_b_b_d_d @ F @ G @ X )
        = ( comp_b_b_d_d @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_214_comp__apply__eq,axiom,
    ! [F: b > b,G: b > b,X: b,H: b > b,K: b > b] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_b_b_b @ F @ G @ X )
        = ( comp_b_b_b @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_215_comp__apply__eq,axiom,
    ! [F: a > c > c,G: b > a,X: b,H: a > c > c,K: b > a] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_a_c_c_b @ F @ G @ X )
        = ( comp_a_c_c_b @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_216_comp__apply__eq,axiom,
    ! [F: a > a,G: ( c > c ) > a,X: c > c,H: a > a,K: ( c > c ) > a] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_a_a_c_c @ F @ G @ X )
        = ( comp_a_a_c_c @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_217_comp__apply__eq,axiom,
    ! [F: a > a,G: a > a,X: a,H: a > a,K: a > a] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_a_a_a @ F @ G @ X )
        = ( comp_a_a_a @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_218_comp__apply__eq,axiom,
    ! [F: b > d > d,G: b > b,X: b,H: b > d > d,K: b > b] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_b_d_d_b @ F @ G @ X )
        = ( comp_b_d_d_b @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_219_comp__apply__eq,axiom,
    ! [F: a > c > c,G: a > a,X: a,H: a > c > c,K: a > a] :
      ( ( ( F @ ( G @ X ) )
        = ( H @ ( K @ X ) ) )
     => ( ( comp_a_c_c_a @ F @ G @ X )
        = ( comp_a_c_c_a @ H @ K @ X ) ) ) ).

% comp_apply_eq
thf(fact_220_mem__Collect__eq,axiom,
    ! [A3: a,P: a > $o] :
      ( ( member_a @ A3 @ ( collect_a @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_221_mem__Collect__eq,axiom,
    ! [A3: c,P: c > $o] :
      ( ( member_c @ A3 @ ( collect_c @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_222_mem__Collect__eq,axiom,
    ! [A3: b,P: b > $o] :
      ( ( member_b @ A3 @ ( collect_b @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_223_mem__Collect__eq,axiom,
    ! [A3: d,P: d > $o] :
      ( ( member_d @ A3 @ ( collect_d @ P ) )
      = ( P @ A3 ) ) ).

% mem_Collect_eq
thf(fact_224_Collect__mem__eq,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [X3: a] : ( member_a @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_225_Collect__mem__eq,axiom,
    ! [A: set_c] :
      ( ( collect_c
        @ ^ [X3: c] : ( member_c @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_226_Collect__mem__eq,axiom,
    ! [A: set_b] :
      ( ( collect_b
        @ ^ [X3: b] : ( member_b @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_227_Collect__mem__eq,axiom,
    ! [A: set_d] :
      ( ( collect_d
        @ ^ [X3: d] : ( member_d @ X3 @ A ) )
      = A ) ).

% Collect_mem_eq
thf(fact_228_comp__eq__dest__lhs,axiom,
    ! [A3: b > b,B3: ( d > d ) > b,C2: ( d > d ) > b,V: d > d] :
      ( ( ( comp_b_b_d_d @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_229_comp__eq__dest__lhs,axiom,
    ! [A3: b > b,B3: b > b,C2: b > b,V: b] :
      ( ( ( comp_b_b_b @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_230_comp__eq__dest__lhs,axiom,
    ! [A3: a > c > c,B3: b > a,C2: b > c > c,V: b] :
      ( ( ( comp_a_c_c_b @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_231_comp__eq__dest__lhs,axiom,
    ! [A3: a > a,B3: ( c > c ) > a,C2: ( c > c ) > a,V: c > c] :
      ( ( ( comp_a_a_c_c @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_232_comp__eq__dest__lhs,axiom,
    ! [A3: a > a,B3: a > a,C2: a > a,V: a] :
      ( ( ( comp_a_a_a @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_233_comp__eq__dest__lhs,axiom,
    ! [A3: b > d > d,B3: b > b,C2: b > d > d,V: b] :
      ( ( ( comp_b_d_d_b @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_234_comp__eq__dest__lhs,axiom,
    ! [A3: a > c > c,B3: a > a,C2: a > c > c,V: a] :
      ( ( ( comp_a_c_c_a @ A3 @ B3 )
        = C2 )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_235_comp__eq__elim,axiom,
    ! [A3: b > b,B3: ( d > d ) > b,C2: b > b,D: ( d > d ) > b] :
      ( ( ( comp_b_b_d_d @ A3 @ B3 )
        = ( comp_b_b_d_d @ C2 @ D ) )
     => ! [V2: d > d] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_236_comp__eq__elim,axiom,
    ! [A3: b > b,B3: b > b,C2: b > b,D: b > b] :
      ( ( ( comp_b_b_b @ A3 @ B3 )
        = ( comp_b_b_b @ C2 @ D ) )
     => ! [V2: b] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_237_comp__eq__elim,axiom,
    ! [A3: a > c > c,B3: b > a,C2: a > c > c,D: b > a] :
      ( ( ( comp_a_c_c_b @ A3 @ B3 )
        = ( comp_a_c_c_b @ C2 @ D ) )
     => ! [V2: b] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_238_comp__eq__elim,axiom,
    ! [A3: a > a,B3: ( c > c ) > a,C2: a > a,D: ( c > c ) > a] :
      ( ( ( comp_a_a_c_c @ A3 @ B3 )
        = ( comp_a_a_c_c @ C2 @ D ) )
     => ! [V2: c > c] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_239_comp__eq__elim,axiom,
    ! [A3: a > a,B3: a > a,C2: a > a,D: a > a] :
      ( ( ( comp_a_a_a @ A3 @ B3 )
        = ( comp_a_a_a @ C2 @ D ) )
     => ! [V2: a] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_240_comp__eq__elim,axiom,
    ! [A3: b > d > d,B3: b > b,C2: b > d > d,D: b > b] :
      ( ( ( comp_b_d_d_b @ A3 @ B3 )
        = ( comp_b_d_d_b @ C2 @ D ) )
     => ! [V2: b] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_241_comp__eq__elim,axiom,
    ! [A3: a > c > c,B3: a > a,C2: a > c > c,D: a > a] :
      ( ( ( comp_a_c_c_a @ A3 @ B3 )
        = ( comp_a_c_c_a @ C2 @ D ) )
     => ! [V2: a] :
          ( ( A3 @ ( B3 @ V2 ) )
          = ( C2 @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_242_comp__eq__dest,axiom,
    ! [A3: b > b,B3: ( d > d ) > b,C2: b > b,D: ( d > d ) > b,V: d > d] :
      ( ( ( comp_b_b_d_d @ A3 @ B3 )
        = ( comp_b_b_d_d @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_243_comp__eq__dest,axiom,
    ! [A3: b > b,B3: b > b,C2: b > b,D: b > b,V: b] :
      ( ( ( comp_b_b_b @ A3 @ B3 )
        = ( comp_b_b_b @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_244_comp__eq__dest,axiom,
    ! [A3: a > c > c,B3: b > a,C2: a > c > c,D: b > a,V: b] :
      ( ( ( comp_a_c_c_b @ A3 @ B3 )
        = ( comp_a_c_c_b @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_245_comp__eq__dest,axiom,
    ! [A3: a > a,B3: ( c > c ) > a,C2: a > a,D: ( c > c ) > a,V: c > c] :
      ( ( ( comp_a_a_c_c @ A3 @ B3 )
        = ( comp_a_a_c_c @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_246_comp__eq__dest,axiom,
    ! [A3: a > a,B3: a > a,C2: a > a,D: a > a,V: a] :
      ( ( ( comp_a_a_a @ A3 @ B3 )
        = ( comp_a_a_a @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_247_comp__eq__dest,axiom,
    ! [A3: b > d > d,B3: b > b,C2: b > d > d,D: b > b,V: b] :
      ( ( ( comp_b_d_d_b @ A3 @ B3 )
        = ( comp_b_d_d_b @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_248_comp__eq__dest,axiom,
    ! [A3: a > c > c,B3: a > a,C2: a > c > c,D: a > a,V: a] :
      ( ( ( comp_a_c_c_a @ A3 @ B3 )
        = ( comp_a_c_c_a @ C2 @ D ) )
     => ( ( A3 @ ( B3 @ V ) )
        = ( C2 @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_249_comp__assoc,axiom,
    ! [F: b > d > d,G: b > b,H: b > b] :
      ( ( comp_b_d_d_b @ ( comp_b_d_d_b @ F @ G ) @ H )
      = ( comp_b_d_d_b @ F @ ( comp_b_b_b @ G @ H ) ) ) ).

% comp_assoc
thf(fact_250_comp__assoc,axiom,
    ! [F: a > c > c,G: a > a,H: a > a] :
      ( ( comp_a_c_c_a @ ( comp_a_c_c_a @ F @ G ) @ H )
      = ( comp_a_c_c_a @ F @ ( comp_a_a_a @ G @ H ) ) ) ).

% comp_assoc
thf(fact_251_comp__assoc,axiom,
    ! [F: ( d > d ) > d > d,G: b > d > d,H: b > b] :
      ( ( comp_b_d_d_b @ ( comp_d_d_d_d_b @ F @ G ) @ H )
      = ( comp_d_d_d_d_b @ F @ ( comp_b_d_d_b @ G @ H ) ) ) ).

% comp_assoc
thf(fact_252_comp__assoc,axiom,
    ! [F: ( c > c ) > c > c,G: a > c > c,H: a > a] :
      ( ( comp_a_c_c_a @ ( comp_c_c_c_c_a @ F @ G ) @ H )
      = ( comp_c_c_c_c_a @ F @ ( comp_a_c_c_a @ G @ H ) ) ) ).

% comp_assoc
thf(fact_253_comp__assoc,axiom,
    ! [F: b > b,G: b > b,H: b > b] :
      ( ( comp_b_b_b @ ( comp_b_b_b @ F @ G ) @ H )
      = ( comp_b_b_b @ F @ ( comp_b_b_b @ G @ H ) ) ) ).

% comp_assoc
thf(fact_254_comp__assoc,axiom,
    ! [F: a > a,G: a > a,H: a > a] :
      ( ( comp_a_a_a @ ( comp_a_a_a @ F @ G ) @ H )
      = ( comp_a_a_a @ F @ ( comp_a_a_a @ G @ H ) ) ) ).

% comp_assoc
thf(fact_255_comp__assoc,axiom,
    ! [F: b > b,G: ( d > d ) > b,H: b > d > d] :
      ( ( comp_d_d_b_b @ ( comp_b_b_d_d @ F @ G ) @ H )
      = ( comp_b_b_b @ F @ ( comp_d_d_b_b @ G @ H ) ) ) ).

% comp_assoc
thf(fact_256_comp__assoc,axiom,
    ! [F: a > c > c,G: b > a,H: a > b] :
      ( ( comp_b_c_c_a @ ( comp_a_c_c_b @ F @ G ) @ H )
      = ( comp_a_c_c_a @ F @ ( comp_b_a_a @ G @ H ) ) ) ).

% comp_assoc
thf(fact_257_comp__assoc,axiom,
    ! [F: a > c > c,G: b > a,H: b > b] :
      ( ( comp_b_c_c_b @ ( comp_a_c_c_b @ F @ G ) @ H )
      = ( comp_a_c_c_b @ F @ ( comp_b_a_b @ G @ H ) ) ) ).

% comp_assoc
thf(fact_258_comp__assoc,axiom,
    ! [F: a > a,G: ( c > c ) > a,H: a > c > c] :
      ( ( comp_c_c_a_a @ ( comp_a_a_c_c @ F @ G ) @ H )
      = ( comp_a_a_a @ F @ ( comp_c_c_a_a @ G @ H ) ) ) ).

% comp_assoc
thf(fact_259_comp__def,axiom,
    ( comp_b_b_d_d
    = ( ^ [F2: b > b,G2: ( d > d ) > b,X3: d > d] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_260_comp__def,axiom,
    ( comp_b_b_b
    = ( ^ [F2: b > b,G2: b > b,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_261_comp__def,axiom,
    ( comp_a_c_c_b
    = ( ^ [F2: a > c > c,G2: b > a,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_262_comp__def,axiom,
    ( comp_a_a_c_c
    = ( ^ [F2: a > a,G2: ( c > c ) > a,X3: c > c] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_263_comp__def,axiom,
    ( comp_a_a_a
    = ( ^ [F2: a > a,G2: a > a,X3: a] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_264_comp__def,axiom,
    ( comp_b_d_d_b
    = ( ^ [F2: b > d > d,G2: b > b,X3: b] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_265_comp__def,axiom,
    ( comp_a_c_c_a
    = ( ^ [F2: a > c > c,G2: a > a,X3: a] : ( F2 @ ( G2 @ X3 ) ) ) ) ).

% comp_def
thf(fact_266_Let__transfer,axiom,
    ! [A: a > b > $o,B: a > b > $o] :
      ( bNF_re1730737055_b_b_b @ A @ ( bNF_re2087760490_b_a_b @ ( bNF_rel_fun_a_b_a_b @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: b,F2: b > b] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_267_Let__transfer,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re1391160029_d_d_d @ A @ ( bNF_re1955249705_c_d_d @ ( bNF_re1979731817_c_d_d @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > d > d] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_268_Let__transfer,axiom,
    ! [A: a > a > $o,B: ( c > c ) > ( c > c ) > $o] :
      ( bNF_re1482032989_c_c_c @ A @ ( bNF_re27458217_c_c_c @ ( bNF_re1143700905_c_c_c @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_269_Let__transfer,axiom,
    ! [A: a > a > $o,B: a > b > $o] :
      ( bNF_re1093913501_a_b_b @ A @ ( bNF_re473406379_b_a_b @ ( bNF_rel_fun_a_a_a_b @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > b] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_270_Let__transfer,axiom,
    ! [A: a > a > $o,B: a > a > $o] :
      ( bNF_re865741149_a_a_a @ A @ ( bNF_re571457705_a_a_a @ ( bNF_rel_fun_a_a_a_a @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 )
      @ ^ [S3: a,F2: a > a] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_271_Let__transfer,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( bNF_re1327926367_d_d_d @ A @ ( bNF_re84044842_c_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) @ B )
      @ ^ [S3: a,F2: a > c > c] : ( F2 @ S3 )
      @ ^ [S3: b,F2: b > d > d] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_272_Let__transfer,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( bNF_re1313098655_d_d_d @ A @ ( bNF_re1303182826_d_c_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ B )
      @ ^ [S3: c,F2: c > c] : ( F2 @ S3 )
      @ ^ [S3: d,F2: d > d] : ( F2 @ S3 ) ) ).

% Let_transfer
thf(fact_273_type__copy__map__cong0,axiom,
    ! [M: a > a,G: b > a,X: b,N: a > a,H: b > a,F: a > c > c] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_c_c_b @ ( comp_a_c_c_a @ F @ M ) @ G @ X )
        = ( comp_a_c_c_b @ ( comp_a_c_c_a @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_274_type__copy__map__cong0,axiom,
    ! [M: a > a,G: ( c > c ) > a,X: c > c,N: ( c > c ) > a,H: ( c > c ) > c > c,F: a > a] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_a_c_c @ ( comp_a_a_a @ F @ M ) @ G @ X )
        = ( comp_c_c_a_c_c @ ( comp_a_a_c_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_275_type__copy__map__cong0,axiom,
    ! [M: a > a,G: ( c > c ) > a,X: c > c,N: a > a,H: ( c > c ) > a,F: a > a] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_a_c_c @ ( comp_a_a_a @ F @ M ) @ G @ X )
        = ( comp_a_a_c_c @ ( comp_a_a_a @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_276_type__copy__map__cong0,axiom,
    ! [M: a > a,G: a > a,X: a,N: ( c > c ) > a,H: a > c > c,F: a > a] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_a_a @ ( comp_a_a_a @ F @ M ) @ G @ X )
        = ( comp_c_c_a_a @ ( comp_a_a_c_c @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_277_type__copy__map__cong0,axiom,
    ! [M: a > a,G: a > a,X: a,N: a > a,H: a > a,F: a > a] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_a_a @ ( comp_a_a_a @ F @ M ) @ G @ X )
        = ( comp_a_a_a @ ( comp_a_a_a @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_278_type__copy__map__cong0,axiom,
    ! [M: b > b,G: b > b,X: b,N: b > b,H: b > b,F: b > d > d] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_b_d_d_b @ ( comp_b_d_d_b @ F @ M ) @ G @ X )
        = ( comp_b_d_d_b @ ( comp_b_d_d_b @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_279_type__copy__map__cong0,axiom,
    ! [M: a > a,G: a > a,X: a,N: a > a,H: a > a,F: a > c > c] :
      ( ( ( M @ ( G @ X ) )
        = ( N @ ( H @ X ) ) )
     => ( ( comp_a_c_c_a @ ( comp_a_c_c_a @ F @ M ) @ G @ X )
        = ( comp_a_c_c_a @ ( comp_a_c_c_a @ F @ N ) @ H @ X ) ) ) ).

% type_copy_map_cong0
thf(fact_280_function__factors__right,axiom,
    ! [G: b > d > d,F: b > d > d] :
      ( ( ! [X3: b] :
          ? [Y3: b] :
            ( ( G @ Y3 )
            = ( F @ X3 ) ) )
      = ( ? [H2: b > b] :
            ( F
            = ( comp_b_d_d_b @ G @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_281_function__factors__right,axiom,
    ! [G: a > c > c,F: a > c > c] :
      ( ( ! [X3: a] :
          ? [Y3: a] :
            ( ( G @ Y3 )
            = ( F @ X3 ) ) )
      = ( ? [H2: a > a] :
            ( F
            = ( comp_a_c_c_a @ G @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_282_function__factors__left,axiom,
    ! [G: b > b,F: b > d > d] :
      ( ( ! [X3: b,Y3: b] :
            ( ( ( G @ X3 )
              = ( G @ Y3 ) )
           => ( ( F @ X3 )
              = ( F @ Y3 ) ) ) )
      = ( ? [H2: b > d > d] :
            ( F
            = ( comp_b_d_d_b @ H2 @ G ) ) ) ) ).

% function_factors_left
thf(fact_283_function__factors__left,axiom,
    ! [G: a > a,F: a > c > c] :
      ( ( ! [X3: a,Y3: a] :
            ( ( ( G @ X3 )
              = ( G @ Y3 ) )
           => ( ( F @ X3 )
              = ( F @ Y3 ) ) ) )
      = ( ? [H2: a > c > c] :
            ( F
            = ( comp_a_c_c_a @ H2 @ G ) ) ) ) ).

% function_factors_left
thf(fact_284_comp__cong,axiom,
    ! [F: b > d > d,G: b > b,X: b,F3: b > d > d,G3: b > b,X5: b] :
      ( ( ( F @ ( G @ X ) )
        = ( F3 @ ( G3 @ X5 ) ) )
     => ( ( comp_b_d_d_b @ F @ G @ X )
        = ( comp_b_d_d_b @ F3 @ G3 @ X5 ) ) ) ).

% comp_cong
thf(fact_285_comp__cong,axiom,
    ! [F: a > c > c,G: a > a,X: a,F3: a > c > c,G3: a > a,X5: a] :
      ( ( ( F @ ( G @ X ) )
        = ( F3 @ ( G3 @ X5 ) ) )
     => ( ( comp_a_c_c_a @ F @ G @ X )
        = ( comp_a_c_c_a @ F3 @ G3 @ X5 ) ) ) ).

% comp_cong
thf(fact_286_apply__rsp_H,axiom,
    ! [R1: a > b > $o,R2: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d,X: a,Y: b] :
      ( ( bNF_re802603882_c_d_d @ R1 @ R2 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_287_apply__rsp_H,axiom,
    ! [R1: c > d > $o,R2: c > d > $o,F: c > c,G: d > d,X: c,Y: d] :
      ( ( bNF_rel_fun_c_d_c_d @ R1 @ R2 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_288_rel__funE,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,F: a > c > c,G: b > d > d,X: a,Y: b] :
      ( ( bNF_re802603882_c_d_d @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_289_rel__funE,axiom,
    ! [A: c > d > $o,B: c > d > $o,F: c > c,G: d > d,X: c,Y: d] :
      ( ( bNF_rel_fun_c_d_c_d @ A @ B @ F @ G )
     => ( ( A @ X @ Y )
       => ( B @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_290_map__fun__parametric,axiom,
    ! [A: a > b > $o,B: a > b > $o,C: ( c > c ) > ( d > d ) > $o,D2: ( c > c ) > ( d > d ) > $o] : ( bNF_re932551557_b_d_d @ ( bNF_rel_fun_a_b_a_b @ A @ B ) @ ( bNF_re141854397_b_d_d @ ( bNF_re2078100341_c_d_d @ C @ D2 ) @ ( bNF_re692482399_b_d_d @ ( bNF_re802603882_c_d_d @ B @ C ) @ ( bNF_re802603882_c_d_d @ A @ D2 ) ) ) @ map_fun_a_a_c_c_c_c @ map_fun_b_b_d_d_d_d ) ).

% map_fun_parametric
thf(fact_291_map__fun__parametric,axiom,
    ! [A: c > d > $o,B: a > b > $o,C: ( c > c ) > ( d > d ) > $o,D2: c > d > $o] : ( bNF_re1164948833_d_d_d @ ( bNF_rel_fun_c_d_a_b @ A @ B ) @ ( bNF_re1238578079_d_d_d @ ( bNF_re1303182826_d_c_d @ C @ D2 ) @ ( bNF_re84044842_c_d_d @ ( bNF_re802603882_c_d_d @ B @ C ) @ ( bNF_rel_fun_c_d_c_d @ A @ D2 ) ) ) @ map_fun_c_a_c_c_c @ map_fun_d_b_d_d_d ) ).

% map_fun_parametric
thf(fact_292_map__fun__parametric,axiom,
    ! [A: a > b > $o,B: c > d > $o,C: c > d > $o,D2: ( c > c ) > ( d > d ) > $o] : ( bNF_re1606289753_b_d_d @ ( bNF_rel_fun_a_b_c_d @ A @ B ) @ ( bNF_re1507718559_b_d_d @ ( bNF_re1972258794_c_d_d @ C @ D2 ) @ ( bNF_re1145286186_b_d_d @ ( bNF_rel_fun_c_d_c_d @ B @ C ) @ ( bNF_re802603882_c_d_d @ A @ D2 ) ) ) @ map_fun_a_c_c_c_c2 @ map_fun_b_d_d_d_d2 ) ).

% map_fun_parametric
thf(fact_293_map__fun__parametric,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,C: a > b > $o,D2: ( c > c ) > ( d > d ) > $o] : ( bNF_re364486559_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) @ ( bNF_re387831090_b_d_d @ ( bNF_re802603882_c_d_d @ C @ D2 ) @ ( bNF_re35019871_b_d_d @ ( bNF_re1795127658_d_a_b @ B @ C ) @ ( bNF_re802603882_c_d_d @ A @ D2 ) ) ) @ map_fun_a_c_c_a_c_c @ map_fun_b_d_d_b_d_d ) ).

% map_fun_parametric
thf(fact_294_map__fun__parametric,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,C: c > d > $o,D2: c > d > $o] : ( bNF_re727696351_d_b_d @ ( bNF_re802603882_c_d_d @ A @ B ) @ ( bNF_re335372010_d_b_d @ ( bNF_rel_fun_c_d_c_d @ C @ D2 ) @ ( bNF_re1209333166_c_b_d @ ( bNF_re1303182826_d_c_d @ B @ C ) @ ( bNF_rel_fun_a_b_c_d @ A @ D2 ) ) ) @ map_fun_a_c_c_c_c @ map_fun_b_d_d_d_d ) ).

% map_fun_parametric
thf(fact_295_map__fun__parametric,axiom,
    ! [A: c > d > $o,B: c > d > $o,C: a > b > $o,D2: ( c > c ) > ( d > d ) > $o] : ( bNF_re1709888353_d_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ ( bNF_re2120361759_d_d_d @ ( bNF_re802603882_c_d_d @ C @ D2 ) @ ( bNF_re1509948838_d_d_d @ ( bNF_rel_fun_c_d_a_b @ B @ C ) @ ( bNF_re1972258794_c_d_d @ A @ D2 ) ) ) @ map_fun_c_c_a_c_c @ map_fun_d_d_b_d_d ) ).

% map_fun_parametric
thf(fact_296_map__fun__parametric,axiom,
    ! [A: c > d > $o,B: c > d > $o,C: c > d > $o,D2: c > d > $o] : ( bNF_re888371717_d_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ ( bNF_re764096061_d_d_d @ ( bNF_rel_fun_c_d_c_d @ C @ D2 ) @ ( bNF_re2078100341_c_d_d @ ( bNF_rel_fun_c_d_c_d @ B @ C ) @ ( bNF_rel_fun_c_d_c_d @ A @ D2 ) ) ) @ map_fun_c_c_c_c @ map_fun_d_d_d_d ) ).

% map_fun_parametric
thf(fact_297_fun__ord__parametric,axiom,
    ! [C: a > b > $o,A: ( c > c ) > ( d > d ) > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bi_total_a_b @ C )
     => ( bNF_re19414301_d_d_o
        @ ( bNF_re781155241_d_d_o @ A
          @ ( bNF_re857878889_d_o_o @ B
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ ( bNF_re1855937521_d_d_o @ ( bNF_re802603882_c_d_d @ C @ A )
          @ ( bNF_re1501709470_d_o_o @ ( bNF_re802603882_c_d_d @ C @ B )
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ partia186872226_c_c_a
        @ partia1709452835_d_d_b ) ) ).

% fun_ord_parametric
thf(fact_298_fun__ord__parametric,axiom,
    ! [C: c > d > $o,A: c > d > $o,B: c > d > $o] :
      ( ( bi_total_c_d @ C )
     => ( bNF_re764708765_d_d_o
        @ ( bNF_re391428377_o_d_o @ A
          @ ( bNF_rel_fun_c_d_o_o @ B
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ ( bNF_re781155241_d_d_o @ ( bNF_rel_fun_c_d_c_d @ C @ A )
          @ ( bNF_re857878889_d_o_o @ ( bNF_rel_fun_c_d_c_d @ C @ B )
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ partia1494029680_c_c_c
        @ partia1041982257_d_d_d ) ) ).

% fun_ord_parametric
thf(fact_299_comp__fun__commute_Ofold__mset__union,axiom,
    ! [F: a > c > c,S: c,M: multiset_a,N: multiset_a] :
      ( ( finite746615251te_a_c @ F )
     => ( ( fold_mset_a_c @ F @ S @ ( plus_plus_multiset_a @ M @ N ) )
        = ( fold_mset_a_c @ F @ ( fold_mset_a_c @ F @ S @ M ) @ N ) ) ) ).

% comp_fun_commute.fold_mset_union
thf(fact_300_comp__fun__commute_Ofold__mset__union,axiom,
    ! [F: b > d > d,S: d,M: multiset_b,N: multiset_b] :
      ( ( finite1574384659te_b_d @ F )
     => ( ( fold_mset_b_d @ F @ S @ ( plus_plus_multiset_b @ M @ N ) )
        = ( fold_mset_b_d @ F @ ( fold_mset_b_d @ F @ S @ M ) @ N ) ) ) ).

% comp_fun_commute.fold_mset_union
thf(fact_301_o__prs_I1_J,axiom,
    ! [R1: b > b > $o,Abs1: b > b,Rep1: b > b,R2: b > b > $o,Abs2: b > b,Rep2: b > b,R3: ( d > d ) > ( d > d ) > $o,Abs3: ( d > d ) > d > d,Rep3: ( d > d ) > d > d] :
      ( ( quotient3_b_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_b @ R2 @ Abs2 @ Rep2 )
       => ( ( quotient3_d_d_d_d @ R3 @ Abs3 @ Rep3 )
         => ( ( map_fu538233110_b_d_d @ ( map_fun_b_b_d_d_d_d @ Abs2 @ Rep3 ) @ ( map_fu683206690_b_d_d @ ( map_fun_b_b_b_b @ Abs1 @ Rep2 ) @ ( map_fun_b_b_d_d_d_d @ Rep1 @ Abs3 ) ) @ comp_b_d_d_b )
            = comp_b_d_d_b ) ) ) ) ).

% o_prs(1)
thf(fact_302_o__prs_I1_J,axiom,
    ! [R1: b > b > $o,Abs1: b > a,Rep1: a > b,R2: b > b > $o,Abs2: b > a,Rep2: a > b,R3: ( d > d ) > ( d > d ) > $o,Abs3: ( d > d ) > c > c,Rep3: ( c > c ) > d > d] :
      ( ( quotient3_b_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_a @ R2 @ Abs2 @ Rep2 )
       => ( ( quotient3_d_d_c_c @ R3 @ Abs3 @ Rep3 )
         => ( ( map_fu232832790_a_c_c @ ( map_fun_b_a_c_c_d_d @ Abs2 @ Rep3 ) @ ( map_fu75729569_a_c_c @ ( map_fun_b_a_a_b @ Abs1 @ Rep2 ) @ ( map_fun_a_b_d_d_c_c @ Rep1 @ Abs3 ) ) @ comp_b_d_d_b )
            = comp_a_c_c_a ) ) ) ) ).

% o_prs(1)
thf(fact_303_o__prs_I1_J,axiom,
    ! [R1: a > a > $o,Abs1: a > b,Rep1: b > a,R2: a > a > $o,Abs2: a > b,Rep2: b > a,R3: ( c > c ) > ( c > c ) > $o,Abs3: ( c > c ) > d > d,Rep3: ( d > d ) > c > c] :
      ( ( quotient3_a_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_b @ R2 @ Abs2 @ Rep2 )
       => ( ( quotient3_c_c_d_d @ R3 @ Abs3 @ Rep3 )
         => ( ( map_fu981964822_b_d_d @ ( map_fun_a_b_d_d_c_c @ Abs2 @ Rep3 ) @ ( map_fu1569200227_b_d_d @ ( map_fun_a_b_b_a @ Abs1 @ Rep2 ) @ ( map_fun_b_a_c_c_d_d @ Rep1 @ Abs3 ) ) @ comp_a_c_c_a )
            = comp_b_d_d_b ) ) ) ) ).

% o_prs(1)
thf(fact_304_o__prs_I1_J,axiom,
    ! [R1: a > a > $o,Abs1: a > a,Rep1: a > a,R2: a > a > $o,Abs2: a > a,Rep2: a > a,R3: ( c > c ) > ( c > c ) > $o,Abs3: ( c > c ) > c > c,Rep3: ( c > c ) > c > c] :
      ( ( quotient3_a_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_a @ R2 @ Abs2 @ Rep2 )
       => ( ( quotient3_c_c_c_c @ R3 @ Abs3 @ Rep3 )
         => ( ( map_fu676564502_a_c_c @ ( map_fun_a_a_c_c_c_c @ Abs2 @ Rep3 ) @ ( map_fu961723106_a_c_c @ ( map_fun_a_a_a_a @ Abs1 @ Rep2 ) @ ( map_fun_a_a_c_c_c_c @ Rep1 @ Abs3 ) ) @ comp_a_c_c_a )
            = comp_a_c_c_a ) ) ) ) ).

% o_prs(1)
thf(fact_305_map__fun_Ocompositionality,axiom,
    ! [F: b > b,G: b > d > d,H: b > d > d,I: b > b,Fun: ( d > d ) > b] :
      ( ( map_fun_b_b_b_d_d @ F @ G @ ( map_fun_b_d_d_b_b @ H @ I @ Fun ) )
      = ( map_fun_b_d_d_b_d_d @ ( comp_b_d_d_b @ H @ F ) @ ( comp_b_d_d_b @ G @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_306_map__fun_Ocompositionality,axiom,
    ! [F: b > b,G: a > c > c,H: b > d > d,I: a > a,Fun: ( d > d ) > a] :
      ( ( map_fun_b_b_a_c_c @ F @ G @ ( map_fun_b_d_d_a_a @ H @ I @ Fun ) )
      = ( map_fun_b_d_d_a_c_c @ ( comp_b_d_d_b @ H @ F ) @ ( comp_a_c_c_a @ G @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_307_map__fun_Ocompositionality,axiom,
    ! [F: a > a,G: b > d > d,H: a > c > c,I: b > b,Fun: ( c > c ) > b] :
      ( ( map_fun_a_a_b_d_d @ F @ G @ ( map_fun_a_c_c_b_b @ H @ I @ Fun ) )
      = ( map_fun_a_c_c_b_d_d @ ( comp_a_c_c_a @ H @ F ) @ ( comp_b_d_d_b @ G @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_308_map__fun_Ocompositionality,axiom,
    ! [F: a > a,G: a > c > c,H: a > c > c,I: a > a,Fun: ( c > c ) > a] :
      ( ( map_fun_a_a_a_c_c @ F @ G @ ( map_fun_a_c_c_a_a @ H @ I @ Fun ) )
      = ( map_fun_a_c_c_a_c_c @ ( comp_a_c_c_a @ H @ F ) @ ( comp_a_c_c_a @ G @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_309_map__fun_Ocomp,axiom,
    ! [F: b > b,G: b > d > d,H: b > d > d,I: b > b] :
      ( ( comp_b_b_b_d_d_d_d_b @ ( map_fun_b_b_b_d_d @ F @ G ) @ ( map_fun_b_d_d_b_b @ H @ I ) )
      = ( map_fun_b_d_d_b_d_d @ ( comp_b_d_d_b @ H @ F ) @ ( comp_b_d_d_b @ G @ I ) ) ) ).

% map_fun.comp
thf(fact_310_map__fun_Ocomp,axiom,
    ! [F: b > b,G: a > c > c,H: b > d > d,I: a > a] :
      ( ( comp_b_a_b_c_c_d_d_a @ ( map_fun_b_b_a_c_c @ F @ G ) @ ( map_fun_b_d_d_a_a @ H @ I ) )
      = ( map_fun_b_d_d_a_c_c @ ( comp_b_d_d_b @ H @ F ) @ ( comp_a_c_c_a @ G @ I ) ) ) ).

% map_fun.comp
thf(fact_311_map__fun_Ocomp,axiom,
    ! [F: a > a,G: b > d > d,H: a > c > c,I: b > b] :
      ( ( comp_a_b_a_d_d_c_c_b @ ( map_fun_a_a_b_d_d @ F @ G ) @ ( map_fun_a_c_c_b_b @ H @ I ) )
      = ( map_fun_a_c_c_b_d_d @ ( comp_a_c_c_a @ H @ F ) @ ( comp_b_d_d_b @ G @ I ) ) ) ).

% map_fun.comp
thf(fact_312_map__fun_Ocomp,axiom,
    ! [F: a > a,G: a > c > c,H: a > c > c,I: a > a] :
      ( ( comp_a_a_a_c_c_c_c_a @ ( map_fun_a_a_a_c_c @ F @ G ) @ ( map_fun_a_c_c_a_a @ H @ I ) )
      = ( map_fun_a_c_c_a_c_c @ ( comp_a_c_c_a @ H @ F ) @ ( comp_a_c_c_a @ G @ I ) ) ) ).

% map_fun.comp
thf(fact_313_map__fun__def,axiom,
    ( map_fun_b_b_b_d_d
    = ( ^ [F2: b > b,G2: b > d > d,H2: b > b] : ( comp_b_d_d_b @ ( comp_b_d_d_b @ G2 @ H2 ) @ F2 ) ) ) ).

% map_fun_def
thf(fact_314_map__fun__def,axiom,
    ( map_fun_a_a_a_c_c
    = ( ^ [F2: a > a,G2: a > c > c,H2: a > a] : ( comp_a_c_c_a @ ( comp_a_c_c_a @ G2 @ H2 ) @ F2 ) ) ) ).

% map_fun_def
thf(fact_315_monotone__parametric,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bi_total_a_b @ A )
     => ( bNF_re2129955100_d_d_o
        @ ( bNF_re418251421_o_b_o @ A
          @ ( bNF_rel_fun_a_b_o_o @ A
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ ( bNF_re674980784_d_d_o
          @ ( bNF_re781155241_d_d_o @ B
            @ ( bNF_re857878889_d_o_o @ B
              @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
          @ ( bNF_re1501709470_d_o_o @ ( bNF_re802603882_c_d_d @ A @ B )
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ comple1702356924_a_c_c
        @ comple61207421_b_d_d ) ) ).

% monotone_parametric
thf(fact_316_monotone__parametric,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( bi_total_c_d @ A )
     => ( bNF_re921674337_d_d_o
        @ ( bNF_re391428377_o_d_o @ A
          @ ( bNF_rel_fun_c_d_o_o @ A
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ ( bNF_re27482973_d_d_o
          @ ( bNF_re391428377_o_d_o @ B
            @ ( bNF_rel_fun_c_d_o_o @ B
              @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
          @ ( bNF_re857878889_d_o_o @ ( bNF_rel_fun_c_d_c_d @ A @ B )
            @ ^ [Y4: $o,Z2: $o] : Y4 = Z2 ) )
        @ comple787379047ne_c_c
        @ comple1615148455ne_d_d ) ) ).

% monotone_parametric
thf(fact_317_OOO__quotient3,axiom,
    ! [R1: ( d > d ) > ( d > d ) > $o,Abs1: ( d > d ) > b,Rep1: b > d > d,R2: b > b > $o,Abs2: b > b,Rep2: b > b,R23: ( d > d ) > ( d > d ) > $o] :
      ( ( quotient3_d_d_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_b @ R2 @ Abs2 @ Rep2 )
       => ( ! [X2: d > d,Y2: d > d] :
              ( ( R23 @ X2 @ Y2 )
             => ( ( R1 @ X2 @ X2 )
               => ( ( R1 @ Y2 @ Y2 )
                 => ( R2 @ ( Abs1 @ X2 ) @ ( Abs1 @ Y2 ) ) ) ) )
         => ( ! [X2: b,Y2: b] :
                ( ( R2 @ X2 @ Y2 )
               => ( R23 @ ( Rep1 @ X2 ) @ ( Rep1 @ Y2 ) ) )
           => ( quotient3_d_d_b @ ( relcompp_d_d_d_d_d_d @ R1 @ ( relcompp_d_d_d_d_d_d @ R23 @ R1 ) ) @ ( comp_b_b_d_d @ Abs2 @ Abs1 ) @ ( comp_b_d_d_b @ Rep1 @ Rep2 ) ) ) ) ) ) ).

% OOO_quotient3
thf(fact_318_OOO__quotient3,axiom,
    ! [R1: ( c > c ) > ( c > c ) > $o,Abs1: ( c > c ) > a,Rep1: a > c > c,R2: a > a > $o,Abs2: a > a,Rep2: a > a,R23: ( c > c ) > ( c > c ) > $o] :
      ( ( quotient3_c_c_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_a @ R2 @ Abs2 @ Rep2 )
       => ( ! [X2: c > c,Y2: c > c] :
              ( ( R23 @ X2 @ Y2 )
             => ( ( R1 @ X2 @ X2 )
               => ( ( R1 @ Y2 @ Y2 )
                 => ( R2 @ ( Abs1 @ X2 ) @ ( Abs1 @ Y2 ) ) ) ) )
         => ( ! [X2: a,Y2: a] :
                ( ( R2 @ X2 @ Y2 )
               => ( R23 @ ( Rep1 @ X2 ) @ ( Rep1 @ Y2 ) ) )
           => ( quotient3_c_c_a @ ( relcompp_c_c_c_c_c_c @ R1 @ ( relcompp_c_c_c_c_c_c @ R23 @ R1 ) ) @ ( comp_a_a_c_c @ Abs2 @ Abs1 ) @ ( comp_a_c_c_a @ Rep1 @ Rep2 ) ) ) ) ) ) ).

% OOO_quotient3
thf(fact_319_OOO__quotient3,axiom,
    ! [R1: b > b > $o,Abs1: b > b,Rep1: b > b,R2: b > b > $o,Abs2: b > d > d,Rep2: ( d > d ) > b,R23: b > b > $o] :
      ( ( quotient3_b_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_d_d @ R2 @ Abs2 @ Rep2 )
       => ( ! [X2: b,Y2: b] :
              ( ( R23 @ X2 @ Y2 )
             => ( ( R1 @ X2 @ X2 )
               => ( ( R1 @ Y2 @ Y2 )
                 => ( R2 @ ( Abs1 @ X2 ) @ ( Abs1 @ Y2 ) ) ) ) )
         => ( ! [X2: b,Y2: b] :
                ( ( R2 @ X2 @ Y2 )
               => ( R23 @ ( Rep1 @ X2 ) @ ( Rep1 @ Y2 ) ) )
           => ( quotient3_b_d_d @ ( relcompp_b_b_b @ R1 @ ( relcompp_b_b_b @ R23 @ R1 ) ) @ ( comp_b_d_d_b @ Abs2 @ Abs1 ) @ ( comp_b_b_d_d @ Rep1 @ Rep2 ) ) ) ) ) ) ).

% OOO_quotient3
thf(fact_320_OOO__quotient3,axiom,
    ! [R1: a > a > $o,Abs1: a > a,Rep1: a > a,R2: a > a > $o,Abs2: a > c > c,Rep2: ( c > c ) > a,R23: a > a > $o] :
      ( ( quotient3_a_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_c_c @ R2 @ Abs2 @ Rep2 )
       => ( ! [X2: a,Y2: a] :
              ( ( R23 @ X2 @ Y2 )
             => ( ( R1 @ X2 @ X2 )
               => ( ( R1 @ Y2 @ Y2 )
                 => ( R2 @ ( Abs1 @ X2 ) @ ( Abs1 @ Y2 ) ) ) ) )
         => ( ! [X2: a,Y2: a] :
                ( ( R2 @ X2 @ Y2 )
               => ( R23 @ ( Rep1 @ X2 ) @ ( Rep1 @ Y2 ) ) )
           => ( quotient3_a_c_c @ ( relcompp_a_a_a @ R1 @ ( relcompp_a_a_a @ R23 @ R1 ) ) @ ( comp_a_c_c_a @ Abs2 @ Abs1 ) @ ( comp_a_a_c_c @ Rep1 @ Rep2 ) ) ) ) ) ) ).

% OOO_quotient3
thf(fact_321_OOO__eq__quotient3,axiom,
    ! [R1: ( d > d ) > ( d > d ) > $o,Abs1: ( d > d ) > b,Rep1: b > d > d,Abs2: b > b,Rep2: b > b] :
      ( ( quotient3_d_d_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_b
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Abs2
          @ Rep2 )
       => ( quotient3_d_d_b
          @ ( relcompp_d_d_d_d_d_d @ R1
            @ ( relcompp_d_d_d_d_d_d
              @ ^ [Y4: d > d,Z2: d > d] : Y4 = Z2
              @ R1 ) )
          @ ( comp_b_b_d_d @ Abs2 @ Abs1 )
          @ ( comp_b_d_d_b @ Rep1 @ Rep2 ) ) ) ) ).

% OOO_eq_quotient3
thf(fact_322_OOO__eq__quotient3,axiom,
    ! [R1: ( c > c ) > ( c > c ) > $o,Abs1: ( c > c ) > a,Rep1: a > c > c,Abs2: a > a,Rep2: a > a] :
      ( ( quotient3_c_c_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_a
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Abs2
          @ Rep2 )
       => ( quotient3_c_c_a
          @ ( relcompp_c_c_c_c_c_c @ R1
            @ ( relcompp_c_c_c_c_c_c
              @ ^ [Y4: c > c,Z2: c > c] : Y4 = Z2
              @ R1 ) )
          @ ( comp_a_a_c_c @ Abs2 @ Abs1 )
          @ ( comp_a_c_c_a @ Rep1 @ Rep2 ) ) ) ) ).

% OOO_eq_quotient3
thf(fact_323_OOO__eq__quotient3,axiom,
    ! [R1: b > b > $o,Abs1: b > b,Rep1: b > b,Abs2: b > d > d,Rep2: ( d > d ) > b] :
      ( ( quotient3_b_b @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_b_d_d
          @ ^ [Y4: b,Z2: b] : Y4 = Z2
          @ Abs2
          @ Rep2 )
       => ( quotient3_b_d_d
          @ ( relcompp_b_b_b @ R1
            @ ( relcompp_b_b_b
              @ ^ [Y4: b,Z2: b] : Y4 = Z2
              @ R1 ) )
          @ ( comp_b_d_d_b @ Abs2 @ Abs1 )
          @ ( comp_b_b_d_d @ Rep1 @ Rep2 ) ) ) ) ).

% OOO_eq_quotient3
thf(fact_324_OOO__eq__quotient3,axiom,
    ! [R1: a > a > $o,Abs1: a > a,Rep1: a > a,Abs2: a > c > c,Rep2: ( c > c ) > a] :
      ( ( quotient3_a_a @ R1 @ Abs1 @ Rep1 )
     => ( ( quotient3_a_c_c
          @ ^ [Y4: a,Z2: a] : Y4 = Z2
          @ Abs2
          @ Rep2 )
       => ( quotient3_a_c_c
          @ ( relcompp_a_a_a @ R1
            @ ( relcompp_a_a_a
              @ ^ [Y4: a,Z2: a] : Y4 = Z2
              @ R1 ) )
          @ ( comp_a_c_c_a @ Abs2 @ Abs1 )
          @ ( comp_a_a_c_c @ Rep1 @ Rep2 ) ) ) ) ).

% OOO_eq_quotient3
thf(fact_325_rev__implies__def,axiom,
    ( rev_implies
    = ( ^ [X3: $o,Y3: $o] :
          ( Y3
         => X3 ) ) ) ).

% rev_implies_def
thf(fact_326_pos__fun__distr,axiom,
    ! [R: a > a > $o,S2: ( c > c ) > ( c > c ) > $o,R5: a > b > $o,S4: ( c > c ) > ( d > d ) > $o] : ( ord_le469275661_d_d_o @ ( relcom1813708708_b_d_d @ ( bNF_re1143700905_c_c_c @ R @ S2 ) @ ( bNF_re802603882_c_d_d @ R5 @ S4 ) ) @ ( bNF_re802603882_c_d_d @ ( relcompp_a_a_b @ R @ R5 ) @ ( relcompp_c_c_c_c_d_d @ S2 @ S4 ) ) ) ).

% pos_fun_distr
thf(fact_327_pos__fun__distr,axiom,
    ! [R: c > c > $o,S2: c > c > $o,R5: c > d > $o,S4: c > d > $o] : ( ord_le1338099484_d_d_o @ ( relcompp_c_c_c_c_d_d @ ( bNF_rel_fun_c_c_c_c @ R @ S2 ) @ ( bNF_rel_fun_c_d_c_d @ R5 @ S4 ) ) @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_c_d @ R @ R5 ) @ ( relcompp_c_c_d @ S2 @ S4 ) ) ) ).

% pos_fun_distr
thf(fact_328_pos__fun__distr,axiom,
    ! [R: a > b > $o,S2: ( c > c ) > ( d > d ) > $o,R5: b > b > $o,S4: ( d > d ) > ( d > d ) > $o] : ( ord_le469275661_d_d_o @ ( relcom1887247779_b_d_d @ ( bNF_re802603882_c_d_d @ R @ S2 ) @ ( bNF_re1844863849_d_d_d @ R5 @ S4 ) ) @ ( bNF_re802603882_c_d_d @ ( relcompp_a_b_b @ R @ R5 ) @ ( relcompp_c_c_d_d_d_d @ S2 @ S4 ) ) ) ).

% pos_fun_distr
thf(fact_329_pos__fun__distr,axiom,
    ! [R: c > d > $o,S2: c > d > $o,R5: d > d > $o,S4: d > d > $o] : ( ord_le1338099484_d_d_o @ ( relcompp_c_c_d_d_d_d @ ( bNF_rel_fun_c_d_c_d @ R @ S2 ) @ ( bNF_rel_fun_d_d_d_d @ R5 @ S4 ) ) @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_d_d @ R @ R5 ) @ ( relcompp_c_d_d @ S2 @ S4 ) ) ) ).

% pos_fun_distr
thf(fact_330_fun__mono,axiom,
    ! [C: a > b > $o,A: a > b > $o,B: ( c > c ) > ( d > d ) > $o,D2: ( c > c ) > ( d > d ) > $o] :
      ( ( ord_less_eq_a_b_o @ C @ A )
     => ( ( ord_le1338099484_d_d_o @ B @ D2 )
       => ( ord_le469275661_d_d_o @ ( bNF_re802603882_c_d_d @ A @ B ) @ ( bNF_re802603882_c_d_d @ C @ D2 ) ) ) ) ).

% fun_mono
thf(fact_331_fun__mono,axiom,
    ! [C: c > d > $o,A: c > d > $o,B: c > d > $o,D2: c > d > $o] :
      ( ( ord_less_eq_c_d_o @ C @ A )
     => ( ( ord_less_eq_c_d_o @ B @ D2 )
       => ( ord_le1338099484_d_d_o @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ ( bNF_rel_fun_c_d_c_d @ C @ D2 ) ) ) ) ).

% fun_mono
thf(fact_332_neg__fun__distr1,axiom,
    ! [R: a > a > $o,R5: a > b > $o,S2: ( c > c ) > ( c > c ) > $o,S4: ( c > c ) > ( d > d ) > $o] :
      ( ( left_unique_a_a @ R )
     => ( ( right_total_a_a @ R )
       => ( ( right_unique_a_b @ R5 )
         => ( ( left_total_a_b @ R5 )
           => ( ord_le469275661_d_d_o @ ( bNF_re802603882_c_d_d @ ( relcompp_a_a_b @ R @ R5 ) @ ( relcompp_c_c_c_c_d_d @ S2 @ S4 ) ) @ ( relcom1813708708_b_d_d @ ( bNF_re1143700905_c_c_c @ R @ S2 ) @ ( bNF_re802603882_c_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_333_neg__fun__distr1,axiom,
    ! [R: a > b > $o,R5: b > b > $o,S2: ( c > c ) > ( d > d ) > $o,S4: ( d > d ) > ( d > d ) > $o] :
      ( ( left_unique_a_b @ R )
     => ( ( right_total_a_b @ R )
       => ( ( right_unique_b_b @ R5 )
         => ( ( left_total_b_b @ R5 )
           => ( ord_le469275661_d_d_o @ ( bNF_re802603882_c_d_d @ ( relcompp_a_b_b @ R @ R5 ) @ ( relcompp_c_c_d_d_d_d @ S2 @ S4 ) ) @ ( relcom1887247779_b_d_d @ ( bNF_re802603882_c_d_d @ R @ S2 ) @ ( bNF_re1844863849_d_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_334_neg__fun__distr1,axiom,
    ! [R: c > c > $o,R5: c > d > $o,S2: c > c > $o,S4: c > d > $o] :
      ( ( left_unique_c_c @ R )
     => ( ( right_total_c_c @ R )
       => ( ( right_unique_c_d @ R5 )
         => ( ( left_total_c_d @ R5 )
           => ( ord_le1338099484_d_d_o @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_c_d @ R @ R5 ) @ ( relcompp_c_c_d @ S2 @ S4 ) ) @ ( relcompp_c_c_c_c_d_d @ ( bNF_rel_fun_c_c_c_c @ R @ S2 ) @ ( bNF_rel_fun_c_d_c_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_335_neg__fun__distr1,axiom,
    ! [R: c > d > $o,R5: d > d > $o,S2: c > d > $o,S4: d > d > $o] :
      ( ( left_unique_c_d @ R )
     => ( ( right_total_c_d @ R )
       => ( ( right_unique_d_d @ R5 )
         => ( ( left_total_d_d @ R5 )
           => ( ord_le1338099484_d_d_o @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_d_d @ R @ R5 ) @ ( relcompp_c_d_d @ S2 @ S4 ) ) @ ( relcompp_c_c_d_d_d_d @ ( bNF_rel_fun_c_d_c_d @ R @ S2 ) @ ( bNF_rel_fun_d_d_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_336_right__unique__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( right_total_a_b @ A )
     => ( ( right_unique_c_c_d_d @ B )
       => ( right_2142487_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% right_unique_fun
thf(fact_337_right__unique__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( right_total_c_d @ A )
     => ( ( right_unique_c_d @ B )
       => ( right_unique_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% right_unique_fun
thf(fact_338_left__unique__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( left_total_a_b @ A )
     => ( ( left_unique_c_c_d_d @ B )
       => ( left_u1654071760_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% left_unique_fun
thf(fact_339_left__unique__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( left_total_c_d @ A )
     => ( ( left_unique_c_d @ B )
       => ( left_unique_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% left_unique_fun
thf(fact_340_right__total__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( right_unique_a_b @ A )
     => ( ( right_total_c_c_d_d @ B )
       => ( right_386984928_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% right_total_fun
thf(fact_341_right__total__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( right_unique_c_d @ A )
     => ( ( right_total_c_d @ B )
       => ( right_total_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% right_total_fun
thf(fact_342_left__total__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( left_unique_a_b @ A )
     => ( ( left_total_c_c_d_d @ B )
       => ( left_t1993719015_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% left_total_fun
thf(fact_343_left__total__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( left_unique_c_d @ A )
     => ( ( left_total_c_d @ B )
       => ( left_total_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% left_total_fun
thf(fact_344_neg__fun__distr2,axiom,
    ! [R5: a > b > $o,S4: ( c > c ) > ( d > d ) > $o,R: a > a > $o,S2: ( c > c ) > ( c > c ) > $o] :
      ( ( right_unique_a_b @ R5 )
     => ( ( left_total_a_b @ R5 )
       => ( ( left_unique_c_c_d_d @ S4 )
         => ( ( right_total_c_c_d_d @ S4 )
           => ( ord_le469275661_d_d_o @ ( bNF_re802603882_c_d_d @ ( relcompp_a_a_b @ R @ R5 ) @ ( relcompp_c_c_c_c_d_d @ S2 @ S4 ) ) @ ( relcom1813708708_b_d_d @ ( bNF_re1143700905_c_c_c @ R @ S2 ) @ ( bNF_re802603882_c_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_345_neg__fun__distr2,axiom,
    ! [R5: b > b > $o,S4: ( d > d ) > ( d > d ) > $o,R: a > b > $o,S2: ( c > c ) > ( d > d ) > $o] :
      ( ( right_unique_b_b @ R5 )
     => ( ( left_total_b_b @ R5 )
       => ( ( left_unique_d_d_d_d @ S4 )
         => ( ( right_total_d_d_d_d @ S4 )
           => ( ord_le469275661_d_d_o @ ( bNF_re802603882_c_d_d @ ( relcompp_a_b_b @ R @ R5 ) @ ( relcompp_c_c_d_d_d_d @ S2 @ S4 ) ) @ ( relcom1887247779_b_d_d @ ( bNF_re802603882_c_d_d @ R @ S2 ) @ ( bNF_re1844863849_d_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_346_neg__fun__distr2,axiom,
    ! [R5: c > d > $o,S4: c > d > $o,R: c > c > $o,S2: c > c > $o] :
      ( ( right_unique_c_d @ R5 )
     => ( ( left_total_c_d @ R5 )
       => ( ( left_unique_c_d @ S4 )
         => ( ( right_total_c_d @ S4 )
           => ( ord_le1338099484_d_d_o @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_c_d @ R @ R5 ) @ ( relcompp_c_c_d @ S2 @ S4 ) ) @ ( relcompp_c_c_c_c_d_d @ ( bNF_rel_fun_c_c_c_c @ R @ S2 ) @ ( bNF_rel_fun_c_d_c_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_347_neg__fun__distr2,axiom,
    ! [R5: d > d > $o,S4: d > d > $o,R: c > d > $o,S2: c > d > $o] :
      ( ( right_unique_d_d @ R5 )
     => ( ( left_total_d_d @ R5 )
       => ( ( left_unique_d_d @ S4 )
         => ( ( right_total_d_d @ S4 )
           => ( ord_le1338099484_d_d_o @ ( bNF_rel_fun_c_d_c_d @ ( relcompp_c_d_d @ R @ R5 ) @ ( relcompp_c_d_d @ S2 @ S4 ) ) @ ( relcompp_c_c_d_d_d_d @ ( bNF_rel_fun_c_d_c_d @ R @ S2 ) @ ( bNF_rel_fun_d_d_d_d @ R5 @ S4 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_348_bi__unique__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bi_total_a_b @ A )
     => ( ( bi_unique_c_c_d_d @ B )
       => ( bi_uni844770768_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% bi_unique_fun
thf(fact_349_bi__unique__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( bi_total_c_d @ A )
     => ( ( bi_unique_c_d @ B )
       => ( bi_unique_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% bi_unique_fun
thf(fact_350_bi__total__fun,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bi_unique_a_b @ A )
     => ( ( bi_total_c_c_d_d @ B )
       => ( bi_total_a_c_c_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) ) ).

% bi_total_fun
thf(fact_351_bi__total__fun,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( bi_unique_c_d @ A )
     => ( ( bi_total_c_d @ B )
       => ( bi_total_c_c_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) ) ).

% bi_total_fun
thf(fact_352_fun__upd__transfer,axiom,
    ! [A: a > b > $o,B: ( c > c ) > ( d > d ) > $o] :
      ( ( bi_unique_a_b @ A )
     => ( bNF_re1424479610_b_d_d @ ( bNF_re802603882_c_d_d @ A @ B ) @ ( bNF_re1573878111_b_d_d @ A @ ( bNF_re1145286186_b_d_d @ B @ ( bNF_re802603882_c_d_d @ A @ B ) ) ) @ fun_upd_a_c_c @ fun_upd_b_d_d ) ) ).

% fun_upd_transfer
thf(fact_353_fun__upd__transfer,axiom,
    ! [A: c > d > $o,B: c > d > $o] :
      ( ( bi_unique_c_d @ A )
     => ( bNF_re1941803873_d_d_d @ ( bNF_rel_fun_c_d_c_d @ A @ B ) @ ( bNF_re822780063_d_d_d @ A @ ( bNF_re1972258794_c_d_d @ B @ ( bNF_rel_fun_c_d_c_d @ A @ B ) ) ) @ fun_upd_c_c @ fun_upd_d_d ) ) ).

% fun_upd_transfer

% Helper facts (9)
thf(help_If_2_1_If_001tf__a_T,axiom,
    ! [X: a,Y: a] :
      ( ( if_a @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__a_T,axiom,
    ! [X: a,Y: a] :
      ( ( if_a @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001tf__b_T,axiom,
    ! [X: b,Y: b] :
      ( ( if_b @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__b_T,axiom,
    ! [X: b,Y: b] :
      ( ( if_b @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001tf__c_T,axiom,
    ! [X: c,Y: c] :
      ( ( if_c @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__c_T,axiom,
    ! [X: c,Y: c] :
      ( ( if_c @ $true @ X @ Y )
      = X ) ).

thf(help_If_3_1_If_001tf__d_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001tf__d_T,axiom,
    ! [X: d,Y: d] :
      ( ( if_d @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001tf__d_T,axiom,
    ! [X: d,Y: d] :
      ( ( if_d @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    finite746615251te_a_c @ f1 ).

%------------------------------------------------------------------------------