TPTP Problem File: SLH0523^1.p

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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Safe_Range_RC/0021_Relational_Calculus/prob_00153_004484__16491128_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1834 ( 760 unt; 549 typ;   0 def)
%            Number of atoms       : 3995 (1617 equ;   0 cnn)
%            Maximal formula atoms :   33 (   3 avg)
%            Number of connectives : 13294 ( 584   ~;  66   |; 202   &;10787   @)
%                                         (   0 <=>;1655  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Number of types       :  102 ( 101 usr)
%            Number of type conns  : 2866 (2866   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  451 ( 448 usr;  18 con; 0-8 aty)
%            Number of variables   : 4883 ( 683   ^;4136   !;  64   ?;4883   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 14:25:19.048
%------------------------------------------------------------------------------
% Could-be-implicit typings (101)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J_J,type,
    set_Pr5230901268616262395_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    produc3037992005704992583_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    produc1132964494702330949_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    set_Pr6389665502131816719_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J,type,
    produc4757046405955173714_nat_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J,type,
    produc5835360497134304175_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J_Mt__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    produc1804248201533131239term_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J_J,type,
    list_l8061852110034028019term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc859450856879609959at_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J_J_J,type,
    list_l817302191665554424st_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J_J,type,
    list_l2091321360379043710term_a: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    list_P6715635879285576557term_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    set_Pr8746100912127681095term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_Mt__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    produc4326814125627636033st_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J_J,type,
    list_l1385115009661955117st_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    list_P5515249976196357096st_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    list_P1278887176763996782term_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
    list_l244765108730386536_a_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J_J,type,
    list_l6982237060500878094term_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    set_Pr3519640174511814030st_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    set_Pr8506649411934229524term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    produc2716692642101138535term_a: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    list_P7940050157051400743st_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J_J,type,
    list_l580434486376402077st_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_J_J,type,
    list_l1426301840766861085at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    set_Pr3451248702717554689st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc5687659380679742808st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    produc8693150660649129694term_a: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J_J,type,
    list_P8631410397356380632_a_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    list_P3286917297074265982term_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J_J,type,
    set_Pr9207961096868460158_a_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    set_Pr3863467996586345508term_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__a_J_Mt__List__Olist_Itf__a_J_J_J,type,
    set_Pr4048851178543822343list_a: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    relati8250976376238479564at_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    relati4454658568062418871term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc1828647624359046049st_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    list_P7736225833432154391st_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    list_P5364314822750548887at_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    list_l3264859301627795341at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    set_Pr698032948827214833st_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    set_Pr7549493975000385137at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_li5450038453877631591at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J,type,
    produc6996333795985575112_a_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    produc7526962659421474158term_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_J_J,type,
    list_l8916639730647128606_b_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    relati5277550215419191316term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc3963297410138542439list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__a_J_Mt__List__Olist_Itf__a_J_J,type,
    produc9164743771328383783list_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    list_l929788865687709653term_a: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    set_li7681422004278482351term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    produc4575160907756185873st_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    produc1540777390238407569at_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    list_P6011104703257516679at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(ty_n_t__List__Olist_It__Relational____Calculus__Oterm_It__Nat__Onat_J_J,type,
    list_R114826772386431851rm_nat: $tType ).

thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_J,type,
    list_P9189103929441591694_b_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    list_list_list_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Relational____Calculus__Oterm_It__Nat__Onat_J_J,type,
    set_Re1456376870491094545rm_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_J,type,
    set_Pr1307281990691478580_b_nat: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
    set_list_list_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_It__Nat__Onat_Mt__Nat__Onat_J,type,
    relati7126052417554554232at_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_It__List__Olist_Itf__a_J_J,type,
    relati383187284260386255list_a: $tType ).

thf(ty_n_t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    list_R6823256787227418703term_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
    list_list_list_a: $tType ).

thf(ty_n_t__Set__Oset_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    set_Re5178783185447174953term_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
    set_Product_prod_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
    set_Product_prod_a_a: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
    set_list_list_a: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__b_Mt__Nat__Onat_J,type,
    relati1059154107580485063_b_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__a_Mt__Nat__Onat_J,type,
    relati9047081815478866374_a_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_It__Nat__Onat_Mtf__b_J,type,
    relati3061873246650996333_nat_b: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_It__Nat__Onat_Mtf__a_J,type,
    relati3061873242347767532_nat_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    product_prod_nat_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    relational_term_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__b_Mtf__b_J,type,
    relational_fmla_b_b: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__b_Mtf__a_J,type,
    relational_fmla_b_a: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
    relational_fmla_a_b: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_Itf__a_Mtf__a_J,type,
    relational_fmla_a_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    product_prod_b_nat: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    list_list_nat: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    set_list_nat: $tType ).

thf(ty_n_t__Relational____Calculus__Ofmla_I_Eo_M_Eo_J,type,
    relational_fmla_o_o: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_Itf__b_J,type,
    relational_term_b: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_Itf__a_J,type,
    relational_term_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
    product_prod_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    product_prod_a_a: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_Itf__b_J_J,type,
    list_list_b: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
    list_list_a: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    set_list_b: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
    set_list_a: $tType ).

thf(ty_n_t__Relational____Calculus__Oterm_I_Eo_J,type,
    relational_term_o: $tType ).

thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
    list_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__List__Olist_Itf__b_J,type,
    list_b: $tType ).

thf(ty_n_t__List__Olist_Itf__a_J,type,
    list_a: $tType ).

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

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

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

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

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

% Explicit typings (448)
thf(sy_c_Basic__BNFs_Opred__fun_001tf__a_001_Eo,type,
    basic_pred_fun_a_o: ( a > $o ) > ( $o > $o ) > ( a > $o ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001tf__a_001tf__a,type,
    basic_pred_fun_a_a: ( a > $o ) > ( a > $o ) > ( a > a ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001tf__b_001_Eo,type,
    basic_pred_fun_b_o: ( b > $o ) > ( $o > $o ) > ( b > $o ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001tf__b_001tf__b,type,
    basic_pred_fun_b_b: ( b > $o ) > ( b > $o ) > ( b > b ) > $o ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001tf__a,type,
    comp_o_o_a: ( $o > $o ) > ( a > $o ) > a > $o ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001tf__b,type,
    comp_o_o_b: ( $o > $o ) > ( b > $o ) > b > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
    comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001tf__a,type,
    comp_nat_o_a: ( nat > $o ) > ( a > nat ) > a > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001tf__b,type,
    comp_nat_o_b: ( nat > $o ) > ( b > nat ) > b > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001tf__a_001_Eo_001t__Nat__Onat,type,
    comp_a_o_nat: ( a > $o ) > ( nat > a ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001tf__a_001_Eo_001tf__a,type,
    comp_a_o_a: ( a > $o ) > ( a > a ) > a > $o ).

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__b_001_Eo_001t__Nat__Onat,type,
    comp_b_o_nat: ( b > $o ) > ( nat > b ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001tf__b_001_Eo_001tf__b,type,
    comp_b_o_b: ( b > $o ) > ( b > b ) > b > $o ).

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_Ofun__upd_001t__Nat__Onat_001tf__a,type,
    fun_upd_nat_a: ( nat > a ) > nat > a > nat > a ).

thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001_Eo,type,
    minus_minus_o: $o > $o > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
    minus_646659088055828811list_a: set_list_a > set_list_a > set_list_a ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    minus_3019981187013541264term_a: set_Re5178783185447174953term_a > set_Re5178783185447174953term_a > set_Re5178783185447174953term_a ).

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

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__b_J,type,
    minus_minus_set_b: set_b > set_b > set_b ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Nat__Onat_M_Eo_J,type,
    uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(sy_c_HOL_OThe_001t__Nat__Onat,type,
    the_nat: ( nat > $o ) > nat ).

thf(sy_c_HOL_OUniq_001t__Nat__Onat,type,
    uniq_nat: ( nat > $o ) > $o ).

thf(sy_c_HOL_Oundefined_001_Eo,type,
    undefined_o: $o ).

thf(sy_c_HOL_Oundefined_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    undefi8139585145400706743term_a: list_R6823256787227418703term_a ).

thf(sy_c_HOL_Oundefined_001t__Nat__Onat,type,
    undefined_nat: nat ).

thf(sy_c_HOL_Oundefined_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
    undefi1992772029223621943la_a_b: relational_fmla_a_b ).

thf(sy_c_HOL_Oundefined_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    undefi4938429376670434993term_a: relational_term_a ).

thf(sy_c_HOL_Oundefined_001tf__b,type,
    undefined_b: b ).

thf(sy_c_If_001t__Nat__Onat,type,
    if_nat: $o > nat > nat > nat ).

thf(sy_c_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
    if_Rel1279876242545935705la_a_b: $o > relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
    inf_inf_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_I_062_It__Nat__Onat_Mtf__a_J_M_Eo_J_J,type,
    sup_su9031902984018088378at_a_o: ( ( product_prod_b_nat > set_list_a ) > ( nat > a ) > $o ) > ( ( product_prod_b_nat > set_list_a ) > ( nat > a ) > $o ) > ( product_prod_b_nat > set_list_a ) > ( nat > a ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
    sup_sup_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_Itf__a_J_M_Eo_J,type,
    sup_sup_list_a_o: ( list_a > $o ) > ( list_a > $o ) > list_a > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
    sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
    sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    sup_su798857527126471912_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_M_Eo_J_J,type,
    sup_su4853332313885595128at_a_o: ( relational_fmla_a_b > produc5835360497134304175_nat_a > $o ) > ( relational_fmla_a_b > produc5835360497134304175_nat_a > $o ) > relational_fmla_a_b > produc5835360497134304175_nat_a > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Relational____Calculus__Oterm_Itf__a_J_M_Eo_J,type,
    sup_su927640514972811808rm_a_o: ( relational_term_a > $o ) > ( relational_term_a > $o ) > relational_term_a > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
    sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__b_M_062_It__Nat__Onat_M_Eo_J_J,type,
    sup_sup_b_nat_o: ( b > nat > $o ) > ( b > nat > $o ) > b > nat > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__b_M_Eo_J,type,
    sup_sup_b_o: ( b > $o ) > ( b > $o ) > b > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_Eo,type,
    sup_sup_o: $o > $o > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
    sup_sup_set_list_a: set_list_a > set_list_a > set_list_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    sup_su4018038469549967587_nat_a: set_Pr6389665502131816719_nat_a > set_Pr6389665502131816719_nat_a > set_Pr6389665502131816719_nat_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J_J,type,
    sup_su1345088743400656423_nat_a: set_Pr5230901268616262395_nat_a > set_Pr5230901268616262395_nat_a > set_Pr5230901268616262395_nat_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_J,type,
    sup_su6056130500584125792_b_nat: set_Pr1307281990691478580_b_nat > set_Pr1307281990691478580_b_nat > set_Pr1307281990691478580_b_nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    sup_su8474575085660790013term_a: set_Re5178783185447174953term_a > set_Re5178783185447174953term_a > set_Re5178783185447174953term_a ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
    sup_sup_set_a: set_a > set_a > set_a ).

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

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    concat1372613522848609122st_nat: list_l1385115009661955117st_nat > list_P7940050157051400743st_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    concat2287713305843873746at_nat: list_l1426301840766861085at_nat > list_P5364314822750548887at_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    concat7563411073997271517term_a: list_l2091321360379043710term_a > list_P1278887176763996782term_a ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    concat5322096823361652050st_nat: list_l580434486376402077st_nat > list_P7736225833432154391st_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    concat7691415812945658306at_nat: list_l3264859301627795341at_nat > list_P6011104703257516679at_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    concat1451816756709061613term_a: list_l6982237060500878094term_a > list_P3286917297074265982term_a ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    concat4557919794027884631st_nat: list_l817302191665554424st_nat > list_P5515249976196357096st_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J,type,
    concat921187893273162567_a_nat: list_l244765108730386536_a_nat > list_P8631410397356380632_a_nat ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    concat7580753900580267688term_a: list_l8061852110034028019term_a > list_P6715635879285576557term_a ).

thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    concat8173426066143602685_b_nat: list_l8916639730647128606_b_nat > list_P9189103929441591694_b_nat ).

thf(sy_c_List_Ocoset_001t__Nat__Onat,type,
    coset_nat: list_nat > set_nat ).

thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
    filter_nat: ( nat > $o ) > list_nat > list_nat ).

thf(sy_c_List_Olinorder__class_Oinsort__insert__key_001t__Nat__Onat_001t__Nat__Onat,type,
    linord1921536354676448932at_nat: ( nat > nat ) > nat > list_nat > list_nat ).

thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    list_a6876179990855209945st_nat: ( list_nat > list_list_nat > $o ) > list_list_nat > list_list_list_nat > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
    list_a1787013445579514253list_a: ( list_a > list_list_a > $o ) > list_list_a > list_list_list_a > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    list_a5155878676884504761st_nat: ( nat > list_nat > $o ) > list_nat > list_list_nat > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    list_a6131682974029072717at_nat: ( product_prod_nat_nat > list_P6011104703257516679at_nat > $o ) > list_P6011104703257516679at_nat > list_l3264859301627795341at_nat > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__Relational____Calculus__Oterm_It__Nat__Onat_J_001t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    list_a2842054329120570431rm_nat: ( relational_term_nat > relational_term_nat > $o ) > list_R114826772386431851rm_nat > list_R114826772386431851rm_nat > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    list_a3044844760545493709term_a: ( relational_term_a > list_R6823256787227418703term_a > $o ) > list_R6823256787227418703term_a > list_l929788865687709653term_a > $o ).

thf(sy_c_List_Olist_Olist__all2_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    list_a3533670403825157575term_a: ( relational_term_a > relational_term_a > $o ) > list_R6823256787227418703term_a > list_R6823256787227418703term_a > $o ).

thf(sy_c_List_Olist_Olist__all2_001tf__a_001t__List__Olist_Itf__a_J,type,
    list_all2_a_list_a: ( a > list_a > $o ) > list_a > list_list_a > $o ).

thf(sy_c_List_Olist_Olist__all2_001tf__b_001t__List__Olist_Itf__b_J,type,
    list_all2_b_list_b: ( b > list_b > $o ) > list_b > list_list_b > $o ).

thf(sy_c_List_Olist_Olist__all_001t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    list_a4621116280679065895rm_nat: ( relational_term_nat > $o ) > list_R114826772386431851rm_nat > $o ).

thf(sy_c_List_Olist_Olist__all_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    list_a1394079704683284733term_a: ( relational_term_a > $o ) > list_R6823256787227418703term_a > $o ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
    map_li7225945977422193158st_nat: ( list_nat > list_nat ) > list_list_nat > list_list_nat ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    map_li5408149218522361217st_nat: ( list_nat > list_P7940050157051400743st_nat ) > list_list_nat > list_l1385115009661955117st_nat ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    map_li978161544836236273at_nat: ( list_nat > list_P5364314822750548887at_nat ) > list_list_nat > list_l1426301840766861085at_nat ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    map_li705091637597845140term_a: ( list_nat > list_P1278887176763996782term_a ) > list_list_nat > list_l2091321360379043710term_a ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    map_li6665866383299509243st_nat: ( list_nat > produc1828647624359046049st_nat ) > list_list_nat > list_P7940050157051400743st_nat ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    map_li4248376968112746091st_nat: ( list_nat > produc4575160907756185873st_nat ) > list_list_nat > list_P7736225833432154391st_nat ).

thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    map_li9072881189266824318st_nat: ( list_nat > produc5687659380679742808st_nat ) > list_list_nat > list_P5515249976196357096st_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    map_na3788553780025637377st_nat: ( nat > list_P7736225833432154391st_nat ) > list_nat > list_l580434486376402077st_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    map_na4561905831291441265at_nat: ( nat > list_P6011104703257516679at_nat ) > list_nat > list_l3264859301627795341at_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    map_na7892716985596332564term_a: ( nat > list_P3286917297074265982term_a ) > list_nat > list_l6982237060500878094term_a ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    map_na91578518272332155at_nat: ( nat > produc1540777390238407569at_nat ) > list_nat > list_P5364314822750548887at_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    map_na7298421622053143531at_nat: ( nat > product_prod_nat_nat ) > list_nat > list_P6011104703257516679at_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J,type,
    map_na8727431924180384350_a_nat: ( nat > produc6996333795985575112_a_nat ) > list_nat > list_P8631410397356380632_a_nat ).

thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    map_na5915426433201511956_b_nat: ( nat > product_prod_b_nat ) > list_nat > list_P9189103929441591694_b_nat ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_It__Nat__Onat_J_001t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    map_Re5644085056688888188rm_nat: ( relational_term_nat > relational_term_nat ) > list_R114826772386431851rm_nat > list_R114826772386431851rm_nat ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    map_Re1576213583866461421st_nat: ( relational_term_a > list_P5515249976196357096st_nat ) > list_R6823256787227418703term_a > list_l817302191665554424st_nat ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J_J,type,
    map_Re2296423716969871709_a_nat: ( relational_term_a > list_P8631410397356380632_a_nat ) > list_R6823256787227418703term_a > list_l244765108730386536_a_nat ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J_J,type,
    map_Re4862523635040833576term_a: ( relational_term_a > list_P6715635879285576557term_a ) > list_R6823256787227418703term_a > list_l8061852110034028019term_a ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    map_Re2358163980262620771term_a: ( relational_term_a > produc8693150660649129694term_a ) > list_R6823256787227418703term_a > list_P1278887176763996782term_a ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    map_Re7545003512584125299term_a: ( relational_term_a > produc7526962659421474158term_a ) > list_R6823256787227418703term_a > list_P3286917297074265982term_a ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    map_Re1021565884873730722term_a: ( relational_term_a > produc2716692642101138535term_a ) > list_R6823256787227418703term_a > list_P6715635879285576557term_a ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    map_Re5736185711816362116term_a: ( relational_term_a > relational_term_a ) > list_R6823256787227418703term_a > list_R6823256787227418703term_a ).

thf(sy_c_List_Olist_Omap_001t__Relational____Calculus__Oterm_Itf__a_J_001tf__a,type,
    map_Re419313091343012409rm_a_a: ( relational_term_a > a ) > list_R6823256787227418703term_a > list_a ).

thf(sy_c_List_Olist_Omap_001tf__b_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_J,type,
    map_b_599084904809770697_b_nat: ( b > list_P9189103929441591694_b_nat ) > list_b > list_l8916639730647128606_b_nat ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    set_list_list_nat2: list_list_list_nat > set_list_list_nat ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
    set_list_list_a2: list_list_list_a > set_list_list_a ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
    set_list_nat2: list_list_nat > set_list_nat ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_li2962362208618583836at_nat: list_l3264859301627795341at_nat > set_li5450038453877631591at_nat ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    set_li1177193810238305892term_a: list_l929788865687709653term_a > set_li7681422004278482351term_a ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__a_J,type,
    set_list_a2: list_list_a > set_list_a ).

thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__b_J,type,
    set_list_b2: list_list_b > set_list_b ).

thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
    set_nat2: list_nat > set_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    set_Pr3842133991353686454st_nat: list_P7940050157051400743st_nat > set_Pr3451248702717554689st_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    set_Pr7715406932454250534at_nat: list_P5364314822750548887at_nat > set_Pr7549493975000385137at_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    set_Pr1016787399942107785term_a: list_P1278887176763996782term_a > set_Pr8506649411934229524term_a ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    set_Pr1526418413117253030st_nat: list_P7736225833432154391st_nat > set_Pr698032948827214833st_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    set_Pr7861135356763781785term_a: list_P3286917297074265982term_a > set_Pr3863467996586345508term_a ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    set_Pr7234668156827496707st_nat: list_P5515249976196357096st_nat > set_Pr3519640174511814030st_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Nat__Onat_J,type,
    set_Pr7330506493327882739_a_nat: list_P8631410397356380632_a_nat > set_Pr9207961096868460158_a_nat ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    set_Pr5711402074887782140term_a: list_P6715635879285576557term_a > set_Pr8746100912127681095term_a ).

thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    set_Pr2160427703459429033_b_nat: list_P9189103929441591694_b_nat > set_Pr1307281990691478580_b_nat ).

thf(sy_c_List_Olist_Oset_001t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    set_Re212469413022677766rm_nat: list_R114826772386431851rm_nat > set_Re1456376870491094545rm_nat ).

thf(sy_c_List_Olist_Oset_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    set_Re3569617851344498910term_a: list_R6823256787227418703term_a > set_Re5178783185447174953term_a ).

thf(sy_c_List_Olist_Oset_001tf__a,type,
    set_a2: list_a > set_a ).

thf(sy_c_List_Olist_Oset_001tf__b,type,
    set_b2: list_b > set_b ).

thf(sy_c_List_Opartition_001t__List__Olist_It__Nat__Onat_J,type,
    partition_list_nat: ( list_nat > $o ) > list_list_nat > produc4326814125627636033st_nat ).

thf(sy_c_List_Opartition_001t__Nat__Onat,type,
    partition_nat: ( nat > $o ) > list_nat > produc1828647624359046049st_nat ).

thf(sy_c_List_Opartition_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    partit3301487080212054984term_a: ( relational_term_a > $o ) > list_R6823256787227418703term_a > produc1804248201533131239term_a ).

thf(sy_c_List_Opartition_001tf__a,type,
    partition_a: ( a > $o ) > list_a > produc9164743771328383783list_a ).

thf(sy_c_List_Opartition_001tf__b,type,
    partition_b: ( b > $o ) > list_b > produc3963297410138542439list_b ).

thf(sy_c_List_Oproduct__lists_001t__List__Olist_It__Nat__Onat_J,type,
    produc6783906451316923569st_nat: list_list_list_nat > list_list_list_nat ).

thf(sy_c_List_Oproduct__lists_001t__List__Olist_Itf__a_J,type,
    product_lists_list_a: list_list_list_a > list_list_list_a ).

thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
    product_lists_nat: list_list_nat > list_list_nat ).

thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc8746550462604311920at_nat: list_l3264859301627795341at_nat > list_l3264859301627795341at_nat ).

thf(sy_c_List_Oproduct__lists_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc708360400047254840term_a: list_l929788865687709653term_a > list_l929788865687709653term_a ).

thf(sy_c_List_Oproduct__lists_001tf__a,type,
    product_lists_a: list_list_a > list_list_a ).

thf(sy_c_List_Oproduct__lists_001tf__b,type,
    product_lists_b: list_list_b > list_list_b ).

thf(sy_c_List_Ounion_001t__List__Olist_It__Nat__Onat_J,type,
    union_list_nat: list_list_nat > list_list_nat > list_list_nat ).

thf(sy_c_List_Ounion_001t__Nat__Onat,type,
    union_nat: list_nat > list_nat > list_nat ).

thf(sy_c_List_Ounion_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    union_2615200886310307395term_a: list_R6823256787227418703term_a > list_R6823256787227418703term_a > list_R6823256787227418703term_a ).

thf(sy_c_List_Ounion_001tf__a,type,
    union_a: list_a > list_a > list_a ).

thf(sy_c_List_Ounion_001tf__b,type,
    union_b: list_b > list_b > list_b ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    size_s88622898042387131term_a: list_R6823256787227418703term_a > nat ).

thf(sy_c_Order__Relation_OAboveS_001t__Nat__Onat,type,
    order_AboveS_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Order__Relation_OAbove_001t__Nat__Onat,type,
    order_Above_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Order__Relation_OUnderS_001t__Nat__Onat,type,
    order_UnderS_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Order__Relation_OUnder_001t__Nat__Onat,type,
    order_Under_nat: set_Pr1261947904930325089at_nat > set_nat > set_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
    bot_bot_nat_o: nat > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    bot_bot_set_list_nat: set_list_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
    bot_bot_set_list_a: set_list_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
    bot_bot_set_nat: set_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    bot_bo8783692591515826581term_a: set_Re5178783185447174953term_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
    bot_bot_set_b: set_b ).

thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Nat__Onat_M_Eo_J,type,
    ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
    ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_M_Eo_J,type,
    ord_le7191224889845164944_a_b_o: ( relational_fmla_a_b > $o ) > ( relational_fmla_a_b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J,type,
    ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__b_M_Eo_J,type,
    ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_Eo_M_Eo_J,type,
    top_top_o_o: $o > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
    top_top_nat_o: nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
    top_top_set_nat: set_nat ).

thf(sy_c_Partial__Function_Oflat__lub_001t__Nat__Onat,type,
    partial_flat_lub_nat: nat > set_nat > nat ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_001_062_It__Nat__Onat_Mtf__a_J,type,
    produc4953239424914856836_nat_a: ( product_prod_nat_nat > set_list_a ) > ( nat > a ) > produc4757046405955173714_nat_a ).

thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_001_062_It__Nat__Onat_Mtf__a_J,type,
    produc2895298938842563487_nat_a: ( product_prod_b_nat > set_list_a ) > ( nat > a ) > produc5835360497134304175_nat_a ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    produc7129799990162260089st_nat: list_list_nat > list_list_nat > produc4326814125627636033st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
    produc1298395424260782409at_nat: list_nat > nat > produc1540777390238407569at_nat ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc1713630904918897680term_a: list_nat > relational_term_a > produc8693150660649129694term_a ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    produc3676283718292092247term_a: list_R6823256787227418703term_a > list_R6823256787227418703term_a > produc1804248201533131239term_a ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
    produc6837034575241423639list_a: list_a > list_a > produc9164743771328383783list_a ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1564554178308465111list_b: list_b > list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    produc8282810413953273033st_nat: nat > list_nat > produc4575160907756185873st_nat ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc1842950163714375456term_a: nat > relational_term_a > produc7526962659421474158term_a ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(sy_c_Product__Type_OPair_001t__Relational____Calculus__Ofmla_Itf__a_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J,type,
    produc2574091134533170497_nat_a: relati9047081815478866374_a_nat > produc4757046405955173714_nat_a > produc3037992005704992583_nat_a ).

thf(sy_c_Product__Type_OPair_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J,type,
    produc6598558901832717687_nat_a: relational_fmla_a_b > produc5835360497134304175_nat_a > produc1132964494702330949_nat_a ).

thf(sy_c_Product__Type_OPair_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc8752702772314489554st_nat: relational_term_a > list_nat > produc5687659380679742808st_nat ).

thf(sy_c_Product__Type_OPair_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Nat__Onat,type,
    produc7406852975468742850_a_nat: relational_term_a > nat > produc6996333795985575112_a_nat ).

thf(sy_c_Product__Type_OPair_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc5718452834064904663term_a: relational_term_a > relational_term_a > produc2716692642101138535term_a ).

thf(sy_c_Product__Type_OPair_001tf__a_001tf__a,type,
    product_Pair_a_a: a > a > product_prod_a_a ).

thf(sy_c_Product__Type_OPair_001tf__b_001t__Nat__Onat,type,
    product_Pair_b_nat: b > nat > product_prod_b_nat ).

thf(sy_c_Product__Type_OPair_001tf__b_001tf__b,type,
    product_Pair_b_b: b > b > product_prod_b_b ).

thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(sy_c_Product__Type_Oproduct_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc8400933694960370452st_nat: set_list_nat > set_list_nat > set_Pr3451248702717554689st_nat ).

thf(sy_c_Product__Type_Oproduct_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
    produc3452567005806842372at_nat: set_list_nat > set_nat > set_Pr7549493975000385137at_nat ).

thf(sy_c_Product__Type_Oproduct_001t__List__Olist_It__Nat__Onat_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc6328962015167006485term_a: set_list_nat > set_Re5178783185447174953term_a > set_Pr8506649411934229524term_a ).

thf(sy_c_Product__Type_Oproduct_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    produc1213609958644557188st_nat: set_nat > set_list_nat > set_Pr698032948827214833st_nat ).

thf(sy_c_Product__Type_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
    produc929334515565554804at_nat: set_nat > set_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Product__Type_Oproduct_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc1855389550465800357term_a: set_nat > set_Re5178783185447174953term_a > set_Pr3863467996586345508term_a ).

thf(sy_c_Product__Type_Oproduct_001t__Relational____Calculus__Oterm_Itf__a_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc4144661845707822551st_nat: set_Re5178783185447174953term_a > set_list_nat > set_Pr3519640174511814030st_nat ).

thf(sy_c_Product__Type_Oproduct_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Nat__Onat,type,
    produc7419292362220167751_a_nat: set_Re5178783185447174953term_a > set_nat > set_Pr9207961096868460158_a_nat ).

thf(sy_c_Product__Type_Oproduct_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    produc4551712939481758866term_a: set_Re5178783185447174953term_a > set_Re5178783185447174953term_a > set_Pr8746100912127681095term_a ).

thf(sy_c_Product__Type_Oproduct_001tf__b_001t__Nat__Onat,type,
    produc7267454701016561149_b_nat: set_b > set_nat > set_Pr1307281990691478580_b_nat ).

thf(sy_c_Relation_OField_001t__Nat__Onat,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

thf(sy_c_Relation_OId__on_001t__List__Olist_It__Nat__Onat_J,type,
    id_on_list_nat: set_list_nat > set_Pr3451248702717554689st_nat ).

thf(sy_c_Relation_OId__on_001t__List__Olist_Itf__a_J,type,
    id_on_list_a: set_list_a > set_Pr4048851178543822343list_a ).

thf(sy_c_Relation_OId__on_001t__Nat__Onat,type,
    id_on_nat: set_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(sy_c_Relation_OId__on_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    id_on_2009952563750624742term_a: set_Re5178783185447174953term_a > set_Pr8746100912127681095term_a ).

thf(sy_c_Relation_OId__on_001tf__a,type,
    id_on_a: set_a > set_Product_prod_a_a ).

thf(sy_c_Relation_OId__on_001tf__b,type,
    id_on_b: set_b > set_Product_prod_b_b ).

thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
    refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relation_Otrans__on_001t__Nat__Onat,type,
    trans_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Relational__Calculus_OEXISTS_001tf__a_001tf__b,type,
    relati7004044288120072026TS_a_b: list_nat > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Oeval__term_001tf__a,type,
    relati1177013128715261720term_a: ( nat > a ) > relational_term_a > a ).

thf(sy_c_Relational__Calculus_Oeval__terms_001tf__a,type,
    relati4772805863405912879erms_a: ( nat > a ) > list_R6823256787227418703term_a > list_a ).

thf(sy_c_Relational__Calculus_Oexists_001tf__a_001tf__b,type,
    relati3989891337220013914ts_a_b: nat > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_OBool_001t__Nat__Onat_001t__Nat__Onat,type,
    relati4833799250026832501at_nat: $o > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OBool_001tf__a_001t__Nat__Onat,type,
    relati9034565498597818939_a_nat: $o > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OBool_001tf__a_001tf__b,type,
    relational_Bool_a_b: $o > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_OConj_001t__Nat__Onat_001t__Nat__Onat,type,
    relati8628237474745418483at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OConj_001tf__a_001t__Nat__Onat,type,
    relati2542520632142267709_a_nat: relati9047081815478866374_a_nat > relati9047081815478866374_a_nat > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OConj_001tf__a_001tf__b,type,
    relational_Conj_a_b: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_ODisj_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7949253455907248103at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_ODisj_001tf__a_001t__Nat__Onat,type,
    relati9106205213788308809_a_nat: relati9047081815478866374_a_nat > relati9047081815478866374_a_nat > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_ODisj_001tf__a_001tf__b,type,
    relational_Disj_a_b: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_OEq_001t__Nat__Onat_001t__Nat__Onat,type,
    relati8266145252267328119at_nat: nat > relational_term_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OEq_001tf__a_001t__Nat__Onat,type,
    relational_Eq_a_nat: nat > relational_term_a > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OEq_001tf__a_001tf__b,type,
    relational_Eq_a_b: nat > relational_term_a > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_OExists_001t__Nat__Onat_001t__Nat__Onat,type,
    relati524807352525265095at_nat: nat > relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OExists_001tf__a_001t__Nat__Onat,type,
    relati6314223733442460777_a_nat: nat > relati9047081815478866374_a_nat > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OExists_001tf__a_001tf__b,type,
    relati591517084277583526ts_a_b: nat > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_ONeg_001t__Nat__Onat_001t__Nat__Onat,type,
    relati3679007509795571081at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_ONeg_001tf__a_001t__Nat__Onat,type,
    relational_Neg_a_nat: relati9047081815478866374_a_nat > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_ONeg_001tf__a_001tf__b,type,
    relational_Neg_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_OPred_001t__Nat__Onat_001t__Nat__Onat,type,
    relati5908763325135257836at_nat: nat > list_R114826772386431851rm_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OPred_001t__Nat__Onat_001tf__a,type,
    relati6362048942677509346_nat_a: nat > list_R6823256787227418703term_a > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_OPred_001tf__b_001tf__a,type,
    relational_Pred_b_a: b > list_R6823256787227418703term_a > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001_Eo,type,
    relati6637215556741570915_b_a_o: ( b > list_R6823256787227418703term_a > $o ) > ( $o > $o ) > ( nat > relational_term_a > $o ) > ( relational_fmla_a_b > $o ) > ( relational_fmla_a_b > relational_fmla_a_b > $o ) > ( relational_fmla_a_b > relational_fmla_a_b > $o ) > ( nat > relational_fmla_a_b > $o ) > relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    relati130711325911436314term_a: ( b > list_R6823256787227418703term_a > list_R6823256787227418703term_a ) > ( $o > list_R6823256787227418703term_a ) > ( nat > relational_term_a > list_R6823256787227418703term_a ) > ( relational_fmla_a_b > list_R6823256787227418703term_a ) > ( relational_fmla_a_b > relational_fmla_a_b > list_R6823256787227418703term_a ) > ( relational_fmla_a_b > relational_fmla_a_b > list_R6823256787227418703term_a ) > ( nat > relational_fmla_a_b > list_R6823256787227418703term_a ) > relational_fmla_a_b > list_R6823256787227418703term_a ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001t__Nat__Onat,type,
    relati5872380936867403461_a_nat: ( b > list_R6823256787227418703term_a > nat ) > ( $o > nat ) > ( nat > relational_term_a > nat ) > ( relational_fmla_a_b > nat ) > ( relational_fmla_a_b > relational_fmla_a_b > nat ) > ( relational_fmla_a_b > relational_fmla_a_b > nat ) > ( nat > relational_fmla_a_b > nat ) > relational_fmla_a_b > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
    relati5004271986839035796la_a_b: ( b > list_R6823256787227418703term_a > relational_fmla_a_b ) > ( $o > relational_fmla_a_b ) > ( nat > relational_term_a > relational_fmla_a_b ) > ( relational_fmla_a_b > relational_fmla_a_b ) > ( relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b ) > ( relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b ) > ( nat > relational_fmla_a_b > relational_fmla_a_b ) > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati8448653393198995860term_a: ( b > list_R6823256787227418703term_a > relational_term_a ) > ( $o > relational_term_a ) > ( nat > relational_term_a > relational_term_a ) > ( relational_fmla_a_b > relational_term_a ) > ( relational_fmla_a_b > relational_fmla_a_b > relational_term_a ) > ( relational_fmla_a_b > relational_fmla_a_b > relational_term_a ) > ( nat > relational_fmla_a_b > relational_term_a ) > relational_fmla_a_b > relational_term_a ).

thf(sy_c_Relational__Calculus_Ofmla_Ocase__fmla_001tf__b_001tf__a_001tf__b,type,
    relati4214321532279288650_b_a_b: ( b > list_R6823256787227418703term_a > b ) > ( $o > b ) > ( nat > relational_term_a > b ) > ( relational_fmla_a_b > b ) > ( relational_fmla_a_b > relational_fmla_a_b > b ) > ( relational_fmla_a_b > relational_fmla_a_b > b ) > ( nat > relational_fmla_a_b > b ) > relational_fmla_a_b > b ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Bool_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6819674536432757887at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Bool_001tf__a_001tf__b,type,
    relati6551038146797045342ol_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Conj_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1390740724296568061at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Conj_001tf__a_001tf__b,type,
    relati8168519172193746908nj_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Disj_001t__Nat__Onat_001t__Nat__Onat,type,
    relati711756705458397681at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Disj_001tf__a_001tf__b,type,
    relati5350680195807439568sj_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Eq_001t__Nat__Onat_001t__Nat__Onat,type,
    relati8448989431961727361at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Eq_001tf__a_001tf__b,type,
    relational_is_Eq_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Exists_001t__Nat__Onat_001t__Nat__Onat,type,
    relati9085378286500150737at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Exists_001tf__a_001tf__b,type,
    relati5212983245281121968ts_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Neg_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7690703371482896639at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Neg_001tf__a_001tf__b,type,
    relati4321004860440572638eg_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Pred_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7894638611541183222at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Ois__Pred_001tf__a_001tf__b,type,
    relati3644702733014758741ed_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    relati9000828793121449555at_nat: ( nat > nat ) > ( nat > nat ) > relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001t__Nat__Onat_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati6239555138786084081term_a: ( nat > nat ) > ( relational_term_a > relational_term_a ) > relati4454658568062418871term_a > relati4454658568062418871term_a ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__a_001tf__a,type,
    relati7067003805275219505at_a_a: ( nat > nat ) > ( a > a ) > relati3061873242347767532_nat_a > relati3061873242347767532_nat_a ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__b_001tf__b,type,
    relati4279548223302543473at_b_b: ( nat > nat ) > ( b > b ) > relati3061873246650996333_nat_b > relati3061873246650996333_nat_b ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001t__Nat__Onat_001tf__a_001t__Nat__Onat_001tf__b,type,
    relati6662804208382264336_nat_b: ( nat > a ) > ( nat > b ) > relati7126052417554554232at_nat > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001_Eo_001tf__a_001_Eo,type,
    relati2737375947961860675_o_a_o: ( a > $o ) > ( a > $o ) > relational_fmla_a_a > relational_fmla_o_o ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001_Eo_001tf__b_001_Eo,type,
    relati9061525585352242178_o_b_o: ( a > $o ) > ( b > $o ) > relational_fmla_a_b > relational_fmla_o_o ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001t__Nat__Onat_001tf__b_001t__Nat__Onat,type,
    relati4067908648865739920_b_nat: ( a > nat ) > ( b > nat ) > relational_fmla_a_b > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001tf__a_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1332168654638169905at_nat: ( a > a ) > ( nat > nat ) > relati9047081815478866374_a_nat > relati9047081815478866374_a_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001tf__a_001tf__a_001tf__a,type,
    relati7308306074370631695_a_a_a: ( a > a ) > ( a > a ) > relational_fmla_a_a > relational_fmla_a_a ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__a_001tf__a_001tf__b_001tf__b,type,
    relati4520850492397955663_a_b_b: ( a > a ) > ( b > b ) > relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__b_001_Eo_001tf__a_001_Eo,type,
    relati9075677475533109250_o_a_o: ( b > $o ) > ( a > $o ) > relational_fmla_b_a > relational_fmla_o_o ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__b_001_Eo_001tf__b_001_Eo,type,
    relati6176455076068714945_o_b_o: ( b > $o ) > ( b > $o ) > relational_fmla_b_b > relational_fmla_o_o ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__b_001tf__b_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7072134983273611633at_nat: ( b > b ) > ( nat > nat ) > relati1059154107580485063_b_nat > relati1059154107580485063_b_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__b_001tf__b_001tf__a_001tf__a,type,
    relati5169114689998785103_b_a_a: ( b > b ) > ( a > a ) > relational_fmla_b_a > relational_fmla_b_a ).

thf(sy_c_Relational__Calculus_Ofmla_Omap__fmla_001tf__b_001tf__b_001tf__b_001tf__b,type,
    relati2381659108026109071_b_b_b: ( b > b ) > ( b > b ) > relational_fmla_b_b > relational_fmla_b_b ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6725209092851823240at_nat: ( nat > $o ) > ( nat > $o ) > relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati8756168980023174033term_a: ( nat > $o ) > ( relational_term_a > $o ) > relati4454658568062418871term_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001t__Nat__Onat_001tf__a,type,
    relati2149557458355847750_nat_a: ( nat > $o ) > ( a > $o ) > relati3061873242347767532_nat_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001t__Nat__Onat_001tf__b,type,
    relati2149557458355847751_nat_b: ( nat > $o ) > ( b > $o ) > relati3061873246650996333_nat_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__a_001t__Nat__Onat,type,
    relati7340997994032337128_a_nat: ( a > $o ) > ( nat > $o ) > relati9047081815478866374_a_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__a_001tf__a,type,
    relati3660035184769383398la_a_a: ( a > $o ) > ( a > $o ) > relational_fmla_a_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__a_001tf__b,type,
    relati3660035184769383399la_a_b: ( a > $o ) > ( b > $o ) > relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__b_001t__Nat__Onat,type,
    relati8576442322988731625_b_nat: ( b > $o ) > ( nat > $o ) > relati1059154107580485063_b_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__b_001tf__a,type,
    relati872579602796707365la_b_a: ( b > $o ) > ( a > $o ) > relational_fmla_b_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Opred__fmla_001tf__b_001tf__b,type,
    relati872579602796707366la_b_b: ( b > $o ) > ( b > $o ) > relational_fmla_b_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    relati3787705992210192720at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > relati7126052417554554232at_nat > relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati682952617693115246term_a: ( nat > nat > $o ) > ( relational_term_a > relational_term_a > $o ) > relati4454658568062418871term_a > relati4454658568062418871term_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__a_001tf__a,type,
    relati6795990927467486894at_a_a: ( nat > nat > $o ) > ( a > a > $o ) > relati3061873242347767532_nat_a > relati3061873242347767532_nat_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__a_001tf__b,type,
    relati6795990927467486895at_a_b: ( nat > nat > $o ) > ( a > b > $o ) > relati3061873242347767532_nat_a > relati3061873246650996333_nat_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__b_001tf__a,type,
    relati4008535345494810861at_b_a: ( nat > nat > $o ) > ( b > a > $o ) > relati3061873246650996333_nat_b > relati3061873242347767532_nat_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001t__Nat__Onat_001tf__b_001tf__b,type,
    relati4008535345494810862at_b_b: ( nat > nat > $o ) > ( b > b > $o ) > relati3061873246650996333_nat_b > relati3061873246650996333_nat_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001tf__b_001tf__a_001t__Nat__Onat,type,
    relati3704324866205733229_a_nat: ( nat > b > $o ) > ( a > nat > $o ) > relati3061873242347767532_nat_a > relati1059154107580485063_b_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001tf__b_001tf__a_001tf__b,type,
    relati1197779377367012002_b_a_b: ( nat > b > $o ) > ( a > b > $o ) > relati3061873242347767532_nat_a > relational_fmla_b_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001tf__b_001tf__b_001t__Nat__Onat,type,
    relati4939769195162127726_b_nat: ( nat > b > $o ) > ( b > nat > $o ) > relati3061873246650996333_nat_b > relati1059154107580485063_b_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001tf__b_001tf__b_001tf__a,type,
    relati7633695832249111776_b_b_a: ( nat > b > $o ) > ( b > a > $o ) > relati3061873246650996333_nat_b > relational_fmla_b_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001t__Nat__Onat_001tf__b_001tf__b_001tf__b,type,
    relati7633695832249111777_b_b_b: ( nat > b > $o ) > ( b > b > $o ) > relati3061873246650996333_nat_b > relational_fmla_b_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__a_001tf__a_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1061155776830437294at_nat: ( a > a > $o ) > ( nat > nat > $o ) > relati9047081815478866374_a_nat > relati9047081815478866374_a_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__a_001tf__a_001tf__a_001tf__a,type,
    relati2023595154190345740_a_a_a: ( a > a > $o ) > ( a > a > $o ) > relational_fmla_a_a > relational_fmla_a_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__a_001tf__a_001tf__b_001tf__b,type,
    relati8459511609072445516_a_b_b: ( a > a > $o ) > ( b > b > $o ) > relational_fmla_a_b > relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__b_001tf__b_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6801122105465879022at_nat: ( b > b > $o ) > ( nat > nat > $o ) > relati1059154107580485063_b_nat > relati1059154107580485063_b_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__b_001tf__b_001tf__a_001tf__a,type,
    relati9107775806673274956_b_a_a: ( b > b > $o ) > ( a > a > $o ) > relational_fmla_b_a > relational_fmla_b_a > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Orel__fmla_001tf__b_001tf__b_001tf__b_001tf__b,type,
    relati6320320224700598924_b_b_b: ( b > b > $o ) > ( b > b > $o ) > relational_fmla_b_b > relational_fmla_b_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6321887899146193334at_nat: relati7126052417554554232at_nat > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati5193166848434641379term_a: relati4454658568062418871term_a > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001t__Nat__Onat_001tf__a,type,
    relati3496649326765169304_nat_a: relati3061873242347767532_nat_a > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001t__Nat__Onat_001tf__b,type,
    relati3496649326765169305_nat_b: relati3061873246650996333_nat_b > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__a_001t__Nat__Onat,type,
    relati8688089862441658682_a_nat: relati9047081815478866374_a_nat > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__a_001tf__a,type,
    relati3071123380395136020la_a_a: relational_fmla_a_a > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__a_001tf__b,type,
    relati3071123380395136021la_a_b: relational_fmla_a_b > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__b_001t__Nat__Onat,type,
    relati700162154543277371_b_nat: relati1059154107580485063_b_nat > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__b_001tf__a,type,
    relati283667798422459987la_b_a: relational_fmla_b_a > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oset1__fmla_001tf__b_001tf__b,type,
    relati283667798422459988la_b_b: relational_fmla_b_b > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001t__Nat__Onat_001t__Nat__Onat,type,
    relati2567137625159299127at_nat: relati7126052417554554232at_nat > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001t__Nat__Onat_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati172813024183515810term_a: relati4454658568062418871term_a > set_Re5178783185447174953term_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001t__Nat__Onat_001tf__a,type,
    relati410893084775174743_nat_a: relati3061873242347767532_nat_a > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001t__Nat__Onat_001tf__b,type,
    relati410893084775174744_nat_b: relati3061873246650996333_nat_b > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__a_001t__Nat__Onat,type,
    relati5602333620451664121_a_nat: relati9047081815478866374_a_nat > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__a_001tf__a,type,
    relati8924981150291758613la_a_a: relational_fmla_a_a > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__a_001tf__b,type,
    relati8924981150291758614la_a_b: relational_fmla_a_b > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__b_001t__Nat__Onat,type,
    relati6837777949408058618_b_nat: relati1059154107580485063_b_nat > set_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__b_001tf__a,type,
    relati6137525568319082580la_b_a: relational_fmla_b_a > set_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oset2__fmla_001tf__b_001tf__b,type,
    relati6137525568319082581la_b_b: relational_fmla_b_b > set_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Bool_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6920817008271761646at_nat: relati7126052417554554232at_nat > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Bool_001tf__a_001tf__b,type,
    relati2638701775882563405ol_a_b: relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Conj1_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7354301834588295945at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Conj1_001tf__a_001tf__b,type,
    relati5154284022127734760j1_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Conj2_001t__Nat__Onat_001t__Nat__Onat,type,
    relati953304347844971274at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Conj2_001tf__a_001tf__b,type,
    relati1527130600461089641j2_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Disj1_001t__Nat__Onat_001t__Nat__Onat,type,
    relati6345216041161915157at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Disj1_001tf__a_001tf__b,type,
    relati3334262663314506228j1_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Disj2_001t__Nat__Onat_001t__Nat__Onat,type,
    relati9167590591273366294at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Disj2_001tf__a_001tf__b,type,
    relati8930481278502636917j2_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Eq1_001t__Nat__Onat_001t__Nat__Onat,type,
    relati7752113415457843205at_nat: relati7126052417554554232at_nat > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Eq1_001tf__a_001tf__b,type,
    relati5459635069493737188q1_a_b: relational_fmla_a_b > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Eq2_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1351115928714518534at_nat: relati7126052417554554232at_nat > relational_term_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Eq2_001tf__a_001tf__b,type,
    relati1832481647827092069q2_a_b: relational_fmla_a_b > relational_term_a ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Exists1_001t__Nat__Onat_001t__Nat__Onat,type,
    relati833352998049382069at_nat: relati7126052417554554232at_nat > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Exists1_001tf__a_001tf__b,type,
    relati9218598872894977428s1_a_b: relational_fmla_a_b > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Exists2_001t__Nat__Onat_001t__Nat__Onat,type,
    relati3655727548160833206at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Exists2_001tf__a_001tf__b,type,
    relati5591445451228332309s2_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Neg_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1324934566682089680at_nat: relati7126052417554554232at_nat > relati7126052417554554232at_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Neg_001tf__a_001tf__b,type,
    relati5982302313924697647eg_a_b: relational_fmla_a_b > relational_fmla_a_b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Pred1_001t__Nat__Onat_001t__Nat__Onat,type,
    relati1808126365878915920at_nat: relati7126052417554554232at_nat > nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Pred1_001tf__a_001tf__b,type,
    relati91604085239814319d1_a_b: relational_fmla_a_b > b ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Pred2_001t__Nat__Onat_001t__Nat__Onat,type,
    relati4630500915990367057at_nat: relati7126052417554554232at_nat > list_R114826772386431851rm_nat ).

thf(sy_c_Relational__Calculus_Ofmla_Oun__Pred2_001tf__a_001tf__b,type,
    relati5687822700427945008d2_a_b: relational_fmla_a_b > list_R6823256787227418703term_a ).

thf(sy_c_Relational__Calculus_Ofv_001tf__a_001tf__b,type,
    relational_fv_a_b: relational_fmla_a_b > set_nat ).

thf(sy_c_Relational__Calculus_Ofv__rel_001tf__a_001tf__b,type,
    relati5703530512245835757el_a_b: relational_fmla_a_b > relational_fmla_a_b > $o ).

thf(sy_c_Relational__Calculus_Ofv__term__set_001tf__a,type,
    relati6004689760767320788_set_a: relational_term_a > set_nat ).

thf(sy_c_Relational__Calculus_Ofv__terms__set_001t__Nat__Onat,type,
    relati1372350980941296761et_nat: list_R114826772386431851rm_nat > set_nat ).

thf(sy_c_Relational__Calculus_Ofv__terms__set_001tf__a,type,
    relati4569515538964159125_set_a: list_R6823256787227418703term_a > set_nat ).

thf(sy_c_Relational__Calculus_Osat_001tf__a_001t__Nat__Onat,type,
    relational_sat_a_nat: relati9047081815478866374_a_nat > ( product_prod_nat_nat > set_list_a ) > ( nat > a ) > $o ).

thf(sy_c_Relational__Calculus_Osat_001tf__a_001tf__b,type,
    relational_sat_a_b: relational_fmla_a_b > ( product_prod_b_nat > set_list_a ) > ( nat > a ) > $o ).

thf(sy_c_Relational__Calculus_Osat__rel_001tf__a_001t__Nat__Onat,type,
    relati9040413291598363742_a_nat: produc3037992005704992583_nat_a > produc3037992005704992583_nat_a > $o ).

thf(sy_c_Relational__Calculus_Osat__rel_001tf__a_001tf__b,type,
    relati4321809963887231473el_a_b: produc1132964494702330949_nat_a > produc1132964494702330949_nat_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_OConst_001t__Nat__Onat,type,
    relational_Const_nat: nat > relational_term_nat ).

thf(sy_c_Relational__Calculus_Oterm_OVar_001t__Nat__Onat,type,
    relational_Var_nat: nat > relational_term_nat ).

thf(sy_c_Relational__Calculus_Oterm_OVar_001tf__a,type,
    relational_Var_a: nat > relational_term_a ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
    relati6186803337415672399list_a: ( list_a > list_a ) > relati383187284260386255list_a > relati383187284260386255list_a ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Nat__Onat_001t__Nat__Onat,type,
    relati2575597170284168561at_nat: ( nat > nat ) > relational_term_nat > relational_term_nat ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Nat__Onat_001tf__a,type,
    relati8433428048552826781_nat_a: ( nat > a ) > relational_term_nat > relational_term_a ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    relati505408293679640079at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > relati8250976376238479564at_nat > relati8250976376238479564at_nat ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati3034611374901186831term_a: ( relational_term_a > relational_term_a ) > relati5277550215419191316term_a > relati5277550215419191316term_a ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__a_001_Eo,type,
    relati632880486827351913rm_a_o: ( a > $o ) > relational_term_a > relational_term_o ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__a_001t__Nat__Onat,type,
    relati4401496547374540351_a_nat: ( a > nat ) > relational_term_a > relational_term_nat ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__a_001tf__a,type,
    relati3585320759856631375rm_a_a: ( a > a ) > relational_term_a > relational_term_a ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__b_001_Eo,type,
    relati6957030124217733416rm_b_o: ( b > $o ) > relational_term_b > relational_term_o ).

thf(sy_c_Relational__Calculus_Oterm_Omap__term_001tf__b_001tf__b,type,
    relati797865177883955343rm_b_b: ( b > b ) > relational_term_b > relational_term_b ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__List__Olist_Itf__a_J,type,
    relati4353722553127530653list_a: ( list_a > $o ) > relati383187284260386255list_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__Nat__Onat,type,
    relati2679609588974042615rm_nat: ( nat > $o ) > relational_term_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    relati751324514532473370at_nat: ( product_prod_nat_nat > $o ) > relati8250976376238479564at_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati9185991753150389474term_a: ( relational_term_a > $o ) > relati5277550215419191316term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001tf__a,type,
    relati6920953664156333207term_a: ( a > $o ) > relational_term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Opred__term_001tf__b,type,
    relati6920953664156333208term_b: ( b > $o ) > relational_term_b > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
    relati8847882339280608716list_a: ( list_a > list_a > $o ) > relati383187284260386255list_a > relati383187284260386255list_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001t__Nat__Onat,type,
    relati2881564729679077486at_nat: ( nat > nat > $o ) > relational_term_nat > relational_term_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001tf__a,type,
    relati6955175908526440928_nat_a: ( nat > a > $o ) > relational_term_nat > relational_term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Nat__Onat_001tf__b,type,
    relati6955175908526440929_nat_b: ( nat > b > $o ) > relational_term_nat > relational_term_b > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    relati8728558461388257676at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > relati8250976376238479564at_nat > relati8250976376238479564at_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001t__Relational____Calculus__Oterm_Itf__a_J_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati2794329474471028620term_a: ( relational_term_a > relational_term_a > $o ) > relati5277550215419191316term_a > relati5277550215419191316term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001t__Nat__Onat,type,
    relati2923244407348154498_a_nat: ( a > nat > $o ) > relational_term_a > relational_term_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001tf__a,type,
    relati3163788165526728396rm_a_a: ( a > a > $o ) > relational_term_a > relational_term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__a_001tf__b,type,
    relati3163788165526728397rm_a_b: ( a > b > $o ) > relational_term_a > relational_term_b > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001t__Nat__Onat,type,
    relati4158688736304548995_b_nat: ( b > nat > $o ) > relational_term_b > relational_term_nat > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati5843166439758153046term_a: ( b > relational_term_a > $o ) > relational_term_b > relati5277550215419191316term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001tf__a,type,
    relati376332583554052363rm_b_a: ( b > a > $o ) > relational_term_b > relational_term_a > $o ).

thf(sy_c_Relational__Calculus_Oterm_Orel__term_001tf__b_001tf__b,type,
    relati376332583554052364rm_b_b: ( b > b > $o ) > relational_term_b > relational_term_b > $o ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__List__Olist_Itf__a_J,type,
    relati1115505217504806350list_a: relati383187284260386255list_a > set_list_a ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__Nat__Onat,type,
    relati7416457470477713926rm_nat: relational_term_nat > set_nat ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    relati3132094035298600779at_nat: relati8250976376238479564at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    relati2372589673864734099term_a: relati5277550215419191316term_a > set_Re5178783185447174953term_a ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001tf__a,type,
    relati2096729434547099208term_a: relational_term_a > set_a ).

thf(sy_c_Relational__Calculus_Oterm_Oset__term_001tf__b,type,
    relati2096729434547099209term_b: relational_term_b > set_b ).

thf(sy_c_Set_OBall_001t__List__Olist_Itf__a_J,type,
    ball_list_a: set_list_a > ( list_a > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Nat__Onat,type,
    ball_nat: set_nat > ( nat > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    ball_P8096063237992195499at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > $o ) > $o ).

thf(sy_c_Set_OBall_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    ball_R4883633954770375667term_a: set_Re5178783185447174953term_a > ( relational_term_a > $o ) > $o ).

thf(sy_c_Set_OBall_001tf__a,type,
    ball_a: set_a > ( a > $o ) > $o ).

thf(sy_c_Set_OBall_001tf__b,type,
    ball_b: set_b > ( b > $o ) > $o ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
    collec5989764272469232197st_nat: ( list_list_nat > $o ) > set_list_list_nat ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
    collect_list_list_a: ( list_list_a > $o ) > set_list_list_a ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    collec3343600615725829874at_nat: ( list_P6011104703257516679at_nat > $o ) > set_li5450038453877631591at_nat ).

thf(sy_c_Set_OCollect_001t__List__Olist_It__Relational____Calculus__Oterm_Itf__a_J_J,type,
    collec8200894614646537018term_a: ( list_R6823256787227418703term_a > $o ) > set_li7681422004278482351term_a ).

thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
    collect_list_a: ( list_a > $o ) > set_list_a ).

thf(sy_c_Set_OCollect_001t__List__Olist_Itf__b_J,type,
    collect_list_b: ( list_b > $o ) > set_list_b ).

thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_OCollect_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    collec7376311432011962548term_a: ( relational_term_a > $o ) > set_Re5178783185447174953term_a ).

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_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
    insert_list_nat: list_nat > set_list_nat > set_list_nat ).

thf(sy_c_Set_Oinsert_001t__List__Olist_Itf__a_J,type,
    insert_list_a: list_a > set_list_a > set_list_a ).

thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
    insert_nat: nat > set_nat > set_nat ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_Oinsert_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    insert8574850016668666393term_a: relational_term_a > set_Re5178783185447174953term_a > set_Re5178783185447174953term_a ).

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

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

thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
    is_singleton_nat: set_nat > $o ).

thf(sy_c_Set_Opairwise_001t__Nat__Onat,type,
    pairwise_nat: ( nat > nat > $o ) > set_nat > $o ).

thf(sy_c_Set_Oremove_001t__Nat__Onat,type,
    remove_nat: nat > set_nat > set_nat ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    accp_P3115975753873020414_nat_a: ( produc3037992005704992583_nat_a > produc3037992005704992583_nat_a > $o ) > produc3037992005704992583_nat_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    accp_P6721201822162371452_nat_a: ( produc1132964494702330949_nat_a > produc1132964494702330949_nat_a > $o ) > produc1132964494702330949_nat_a > $o ).

thf(sy_c_Wellfounded_Oaccp_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J,type,
    accp_R989495437599811158la_a_b: ( relational_fmla_a_b > relational_fmla_a_b > $o ) > relational_fmla_a_b > $o ).

thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
    member_list_a: list_a > set_list_a > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J,type,
    member9198066416134578520_nat_a: produc5835360497134304175_nat_a > set_Pr6389665502131816719_nat_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_Itf__a_J_Mt__List__Olist_Itf__a_J_J,type,
    member8191768239178080336list_a: produc9164743771328383783list_a > set_Pr4048851178543822343list_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_Itf__a_J_J_J_M_062_It__Nat__Onat_Mtf__a_J_J_J,type,
    member6570610415612139612_nat_a: produc1132964494702330949_nat_a > set_Pr5230901268616262395_nat_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Relational____Calculus__Oterm_Itf__a_J_Mt__Relational____Calculus__Oterm_Itf__a_J_J,type,
    member5548800708997798032term_a: produc2716692642101138535term_a > set_Pr8746100912127681095term_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    member1426531477525435216od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    member6959632917342813205_b_nat: product_prod_b_nat > set_Pr1307281990691478580_b_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
    member7862447936710763792od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).

thf(sy_c_member_001t__Relational____Calculus__Oterm_It__Nat__Onat_J,type,
    member5011674626906061938rm_nat: relational_term_nat > set_Re1456376870491094545rm_nat > $o ).

thf(sy_c_member_001t__Relational____Calculus__Oterm_Itf__a_J,type,
    member5466445112152945266term_a: relational_term_a > set_Re5178783185447174953term_a > $o ).

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

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

thf(sy_v_I,type,
    i: product_prod_b_nat > set_list_a ).

thf(sy_v__092_060phi_062_H____,type,
    phi: relational_fmla_a_b ).

thf(sy_v__092_060psi_062____,type,
    psi: relational_fmla_a_b ).

thf(sy_v__092_060sigma_062_H_H_H____,type,
    sigma: nat > a ).

thf(sy_v__092_060sigma_062_H_H____,type,
    sigma2: nat > a ).

% Relevant facts (1279)
thf(fact_0__092_060open_062_I_092_060And_062n_O_An_A_092_060in_062_Afv_A_092_060phi_062_A_092_060Longrightarrow_062_A_092_060sigma_062_An_A_061_A_092_060sigma_062_H_An_J_A_092_060Longrightarrow_062_Asat_A_092_060phi_062_AI_A_092_060sigma_062_A_061_Asat_A_092_060phi_062_AI_A_092_060sigma_062_H_092_060close_062,axiom,
    ( ! [N: nat] :
        ( ( member_nat @ N @ ( relational_fv_a_b @ phi ) )
       => ( ( sigma2 @ N )
          = ( sigma @ N ) ) )
   => ( ( relational_sat_a_b @ phi @ i @ sigma2 )
      = ( relational_sat_a_b @ phi @ i @ sigma ) ) ) ).

% \<open>(\<And>n. n \<in> fv \<phi> \<Longrightarrow> \<sigma> n = \<sigma>' n) \<Longrightarrow> sat \<phi> I \<sigma> = sat \<phi> I \<sigma>'\<close>
thf(fact_1__092_060open_062_I_092_060And_062n_O_An_A_092_060in_062_Afv_A_092_060psi_062_A_092_060Longrightarrow_062_A_092_060sigma_062_An_A_061_A_092_060sigma_062_H_An_J_A_092_060Longrightarrow_062_Asat_A_092_060psi_062_AI_A_092_060sigma_062_A_061_Asat_A_092_060psi_062_AI_A_092_060sigma_062_H_092_060close_062,axiom,
    ( ! [N: nat] :
        ( ( member_nat @ N @ ( relational_fv_a_b @ psi ) )
       => ( ( sigma2 @ N )
          = ( sigma @ N ) ) )
   => ( ( relational_sat_a_b @ psi @ i @ sigma2 )
      = ( relational_sat_a_b @ psi @ i @ sigma ) ) ) ).

% \<open>(\<And>n. n \<in> fv \<psi> \<Longrightarrow> \<sigma> n = \<sigma>' n) \<Longrightarrow> sat \<psi> I \<sigma> = sat \<psi> I \<sigma>'\<close>
thf(fact_2_Conj_Oprems,axiom,
    ! [N2: nat] :
      ( ( member_nat @ N2 @ ( relational_fv_a_b @ ( relational_Conj_a_b @ phi @ psi ) ) )
     => ( ( sigma2 @ N2 )
        = ( sigma @ N2 ) ) ) ).

% Conj.prems
thf(fact_3_fmla_Oinject_I5_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ( ( ( relational_Conj_a_b @ X51 @ X52 )
        = ( relational_Conj_a_b @ Y51 @ Y52 ) )
      = ( ( X51 = Y51 )
        & ( X52 = Y52 ) ) ) ).

% fmla.inject(5)
thf(fact_4_Conj_OIH_I2_J,axiom,
    ! [Sigma: nat > a,Sigma2: nat > a] :
      ( ! [N: nat] :
          ( ( member_nat @ N @ ( relational_fv_a_b @ psi ) )
         => ( ( Sigma @ N )
            = ( Sigma2 @ N ) ) )
     => ( ( relational_sat_a_b @ psi @ i @ Sigma )
        = ( relational_sat_a_b @ psi @ i @ Sigma2 ) ) ) ).

% Conj.IH(2)
thf(fact_5_Conj_OIH_I1_J,axiom,
    ! [Sigma: nat > a,Sigma2: nat > a] :
      ( ! [N: nat] :
          ( ( member_nat @ N @ ( relational_fv_a_b @ phi ) )
         => ( ( Sigma @ N )
            = ( Sigma2 @ N ) ) )
     => ( ( relational_sat_a_b @ phi @ i @ Sigma )
        = ( relational_sat_a_b @ phi @ i @ Sigma2 ) ) ) ).

% Conj.IH(1)
thf(fact_6_sat_Osimps_I5_J,axiom,
    ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Conj_a_b @ Phi @ Psi ) @ I @ Sigma )
      = ( ( relational_sat_a_b @ Phi @ I @ Sigma )
        & ( relational_sat_a_b @ Psi @ I @ Sigma ) ) ) ).

% sat.simps(5)
thf(fact_7_fmla_Opred__inject_I5_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: relati7126052417554554232at_nat,Aa: relati7126052417554554232at_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati8628237474745418483at_nat @ A @ Aa ) )
      = ( ( relati6725209092851823240at_nat @ P1 @ P2 @ A )
        & ( relati6725209092851823240at_nat @ P1 @ P2 @ Aa ) ) ) ).

% fmla.pred_inject(5)
thf(fact_8_fmla_Opred__inject_I5_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: relational_fmla_a_b,Aa: relational_fmla_a_b] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Conj_a_b @ A @ Aa ) )
      = ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ A )
        & ( relati3660035184769383399la_a_b @ P1 @ P2 @ Aa ) ) ) ).

% fmla.pred_inject(5)
thf(fact_9_fmla_Osel_I8_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati1527130600461089641j2_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = X52 ) ).

% fmla.sel(8)
thf(fact_10_fmla_Osel_I7_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati5154284022127734760j1_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = X51 ) ).

% fmla.sel(7)
thf(fact_11_fmla_Osimps_I54_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = ( F5 @ X51 @ X52 ) ) ).

% fmla.simps(54)
thf(fact_12_fmla_Odisc_I47_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(47)
thf(fact_13_fmla_Odisc_I26_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati4321004860440572638eg_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(26)
thf(fact_14_fmla_Odisc_I19_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relational_is_Eq_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(19)
thf(fact_15_fmla_Odisc_I12_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati6551038146797045342ol_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(12)
thf(fact_16_fmla_Odisc_I5_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati3644702733014758741ed_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(5)
thf(fact_17_fmla_Odisc_I40_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati5350680195807439568sj_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(40)
thf(fact_18_fmla_Odisc_I33_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] : ( relati8168519172193746908nj_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.disc(33)
thf(fact_19_fmla_Ocollapse_I5_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ( ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(5)
thf(fact_20_fmla_Odisc__eq__case_I7_J,axiom,
    ( relati5212983245281121968ts_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $true ) ) ).

% fmla.disc_eq_case(7)
thf(fact_21_fmla_Odisc__eq__case_I6_J,axiom,
    ( relati5350680195807439568sj_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $true
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(6)
thf(fact_22_fmla_Odisc__eq__case_I5_J,axiom,
    ( relati8168519172193746908nj_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $true
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(5)
thf(fact_23_fmla_Odisc__eq__case_I4_J,axiom,
    ( relati4321004860440572638eg_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $true
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(4)
thf(fact_24_fmla_Odisc__eq__case_I3_J,axiom,
    ( relational_is_Eq_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $true
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(3)
thf(fact_25_fmla_Odisc__eq__case_I2_J,axiom,
    ( relati6551038146797045342ol_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $false
      @ ^ [Uu: $o] : $true
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(2)
thf(fact_26_fmla_Odisc__eq__case_I1_J,axiom,
    ( relati3644702733014758741ed_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu: b,Uv: list_R6823256787227418703term_a] : $true
      @ ^ [Uu: $o] : $false
      @ ^ [Uu: nat,Uv: relational_term_a] : $false
      @ ^ [Uu: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: relational_fmla_a_b,Uv: relational_fmla_a_b] : $false
      @ ^ [Uu: nat,Uv: relational_fmla_a_b] : $false ) ) ).

% fmla.disc_eq_case(1)
thf(fact_27_fmla_Odistinct__disc_I42_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(42)
thf(fact_28_fmla_Odistinct__disc_I41_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(41)
thf(fact_29_fmla_Odistinct__disc_I40_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(40)
thf(fact_30_fmla_Odistinct__disc_I39_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(39)
thf(fact_31_fmla_Odistinct__disc_I38_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(38)
thf(fact_32_fmla_Odistinct__disc_I37_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(37)
thf(fact_33_fmla_Odistinct__disc_I36_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(36)
thf(fact_34_fmla_Odistinct__disc_I35_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(35)
thf(fact_35_fmla_Odistinct__disc_I34_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(34)
thf(fact_36_fmla_Odistinct__disc_I33_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(33)
thf(fact_37_fmla_Odistinct__disc_I32_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(32)
thf(fact_38_fmla_Odistinct__disc_I31_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(31)
thf(fact_39_fmla_Odistinct__disc_I30_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(30)
thf(fact_40_fmla_Odistinct__disc_I29_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(29)
thf(fact_41_fmla_Odistinct__disc_I28_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(28)
thf(fact_42_fmla_Odistinct__disc_I27_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(27)
thf(fact_43_fmla_Odistinct__disc_I26_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(26)
thf(fact_44_fmla_Odistinct__disc_I25_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(25)
thf(fact_45_mem__Collect__eq,axiom,
    ! [A: b,P: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_46_mem__Collect__eq,axiom,
    ! [A: a,P: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_47_mem__Collect__eq,axiom,
    ! [A: relational_term_a,P: relational_term_a > $o] :
      ( ( member5466445112152945266term_a @ A @ ( collec7376311432011962548term_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_48_mem__Collect__eq,axiom,
    ! [A: list_a,P: list_a > $o] :
      ( ( member_list_a @ A @ ( collect_list_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_49_mem__Collect__eq,axiom,
    ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
      ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_50_mem__Collect__eq,axiom,
    ! [A: list_nat,P: list_nat > $o] :
      ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_51_mem__Collect__eq,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_52_Collect__mem__eq,axiom,
    ! [A2: set_b] :
      ( ( collect_b
        @ ^ [X: b] : ( member_b @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_53_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X: a] : ( member_a @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_54_Collect__mem__eq,axiom,
    ! [A2: set_Re5178783185447174953term_a] :
      ( ( collec7376311432011962548term_a
        @ ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_55_Collect__mem__eq,axiom,
    ! [A2: set_list_a] :
      ( ( collect_list_a
        @ ^ [X: list_a] : ( member_list_a @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_56_Collect__mem__eq,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] :
      ( ( collec3392354462482085612at_nat
        @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_57_Collect__mem__eq,axiom,
    ! [A2: set_list_nat] :
      ( ( collect_list_nat
        @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_58_Collect__mem__eq,axiom,
    ! [A2: set_nat] :
      ( ( collect_nat
        @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_59_Collect__cong,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ! [X2: nat] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_nat @ P )
        = ( collect_nat @ Q ) ) ) ).

% Collect_cong
thf(fact_60_Collect__cong,axiom,
    ! [P: list_nat > $o,Q: list_nat > $o] :
      ( ! [X2: list_nat] :
          ( ( P @ X2 )
          = ( Q @ X2 ) )
     => ( ( collect_list_nat @ P )
        = ( collect_list_nat @ Q ) ) ) ).

% Collect_cong
thf(fact_61_fmla_Odistinct__disc_I24_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(24)
thf(fact_62_fmla_Odistinct__disc_I23_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(23)
thf(fact_63_fmla_Odistinct__disc_I22_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(22)
thf(fact_64_fmla_Odistinct__disc_I21_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(21)
thf(fact_65_fmla_Odistinct__disc_I20_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(20)
thf(fact_66_fmla_Odistinct__disc_I19_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(19)
thf(fact_67_fmla_Odistinct__disc_I18_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(18)
thf(fact_68_fmla_Odistinct__disc_I17_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(17)
thf(fact_69_fmla_Odistinct__disc_I16_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(16)
thf(fact_70_fmla_Odistinct__disc_I15_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(15)
thf(fact_71_fmla_Odistinct__disc_I14_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(14)
thf(fact_72_fmla_Odistinct__disc_I13_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(13)
thf(fact_73_fmla_Odistinct__disc_I12_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(12)
thf(fact_74_fmla_Odistinct__disc_I11_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.distinct_disc(11)
thf(fact_75_fmla_Odistinct__disc_I10_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(10)
thf(fact_76_fmla_Odistinct__disc_I9_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(9)
thf(fact_77_fmla_Odistinct__disc_I8_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(8)
thf(fact_78_fmla_Odistinct__disc_I7_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.distinct_disc(7)
thf(fact_79_fmla_Odistinct__disc_I6_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(6)
thf(fact_80_fmla_Odistinct__disc_I5_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.distinct_disc(5)
thf(fact_81_fmla_Odistinct__disc_I4_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(4)
thf(fact_82_fmla_Odistinct__disc_I3_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.distinct_disc(3)
thf(fact_83_fmla_Odistinct__disc_I2_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ~ ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.distinct_disc(2)
thf(fact_84_fmla_Odistinct__disc_I1_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ~ ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.distinct_disc(1)
thf(fact_85_fmla_Oexhaust__disc,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ~ ( relati3644702733014758741ed_a_b @ Fmla )
     => ( ~ ( relati6551038146797045342ol_a_b @ Fmla )
       => ( ~ ( relational_is_Eq_a_b @ Fmla )
         => ( ~ ( relati4321004860440572638eg_a_b @ Fmla )
           => ( ~ ( relati8168519172193746908nj_a_b @ Fmla )
             => ( ~ ( relati5350680195807439568sj_a_b @ Fmla )
               => ( relati5212983245281121968ts_a_b @ Fmla ) ) ) ) ) ) ) ).

% fmla.exhaust_disc
thf(fact_86_fmla_Opred__True,axiom,
    ( ( relati6725209092851823240at_nat
      @ ^ [Uu: nat] : $true
      @ ^ [Uu: nat] : $true )
    = ( ^ [Uu: relati7126052417554554232at_nat] : $true ) ) ).

% fmla.pred_True
thf(fact_87_fmla_Opred__True,axiom,
    ( ( relati3660035184769383399la_a_b
      @ ^ [Uu: a] : $true
      @ ^ [Uu: b] : $true )
    = ( ^ [Uu: relational_fmla_a_b] : $true ) ) ).

% fmla.pred_True
thf(fact_88_fmla_Ocase__distrib,axiom,
    ! [H: relational_fmla_a_b > relational_fmla_a_b,F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,Fmla: relational_fmla_a_b] :
      ( ( H @ ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
      = ( relati5004271986839035796la_a_b
        @ ^ [X1: b,X22: list_R6823256787227418703term_a] : ( H @ ( F1 @ X1 @ X22 ) )
        @ ^ [X: $o] : ( H @ ( F2 @ X ) )
        @ ^ [X1: nat,X22: relational_term_a] : ( H @ ( F3 @ X1 @ X22 ) )
        @ ^ [X: relational_fmla_a_b] : ( H @ ( F4 @ X ) )
        @ ^ [X1: relational_fmla_a_b,X22: relational_fmla_a_b] : ( H @ ( F5 @ X1 @ X22 ) )
        @ ^ [X1: relational_fmla_a_b,X22: relational_fmla_a_b] : ( H @ ( F6 @ X1 @ X22 ) )
        @ ^ [X1: nat,X22: relational_fmla_a_b] : ( H @ ( F7 @ X1 @ X22 ) )
        @ Fmla ) ) ).

% fmla.case_distrib
thf(fact_89_is__Conj__def,axiom,
    ( relati8168519172193746908nj_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X512: relational_fmla_a_b,X522: relational_fmla_a_b] :
          ( Fmla2
          = ( relational_Conj_a_b @ X512 @ X522 ) ) ) ) ).

% is_Conj_def
thf(fact_90_fmla_OdiscI_I5_J,axiom,
    ! [Fmla: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( Fmla
        = ( relational_Conj_a_b @ X51 @ X52 ) )
     => ( relati8168519172193746908nj_a_b @ Fmla ) ) ).

% fmla.discI(5)
thf(fact_91_is__Bool__exists,axiom,
    ! [X3: nat,Q: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ ( relati3989891337220013914ts_a_b @ X3 @ Q ) )
      = ( relati6551038146797045342ol_a_b @ Q ) ) ).

% is_Bool_exists
thf(fact_92_fmla_Oset__sel_I12_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xt: nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( member_nat @ Xt @ ( relati2567137625159299127at_nat @ ( relati953304347844971274at_nat @ A ) ) )
       => ( member_nat @ Xt @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(12)
thf(fact_93_fmla_Oset__sel_I12_J,axiom,
    ! [A: relational_fmla_a_b,Xt: b] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( member_b @ Xt @ ( relati8924981150291758614la_a_b @ ( relati1527130600461089641j2_a_b @ A ) ) )
       => ( member_b @ Xt @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(12)
thf(fact_94_fmla_Oset__sel_I11_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xr: nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( member_nat @ Xr @ ( relati2567137625159299127at_nat @ ( relati7354301834588295945at_nat @ A ) ) )
       => ( member_nat @ Xr @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(11)
thf(fact_95_fmla_Oset__sel_I11_J,axiom,
    ! [A: relational_fmla_a_b,Xr: b] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( member_b @ Xr @ ( relati8924981150291758614la_a_b @ ( relati5154284022127734760j1_a_b @ A ) ) )
       => ( member_b @ Xr @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(11)
thf(fact_96_fmla_Oset__sel_I5_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xg: nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( member_nat @ Xg @ ( relati6321887899146193334at_nat @ ( relati953304347844971274at_nat @ A ) ) )
       => ( member_nat @ Xg @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(5)
thf(fact_97_fmla_Oset__sel_I5_J,axiom,
    ! [A: relational_fmla_a_b,Xg: a] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( member_a @ Xg @ ( relati3071123380395136021la_a_b @ ( relati1527130600461089641j2_a_b @ A ) ) )
       => ( member_a @ Xg @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(5)
thf(fact_98_fmla_Oset__sel_I4_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xe: nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( member_nat @ Xe @ ( relati6321887899146193334at_nat @ ( relati7354301834588295945at_nat @ A ) ) )
       => ( member_nat @ Xe @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(4)
thf(fact_99_fmla_Oset__sel_I4_J,axiom,
    ! [A: relational_fmla_a_b,Xe: a] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( member_a @ Xe @ ( relati3071123380395136021la_a_b @ ( relati5154284022127734760j1_a_b @ A ) ) )
       => ( member_a @ Xe @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(4)
thf(fact_100_fmla_Omap__sel_I8_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( relati953304347844971274at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati953304347844971274at_nat @ A ) ) ) ) ).

% fmla.map_sel(8)
thf(fact_101_fmla_Omap__sel_I8_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( relati1527130600461089641j2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati1527130600461089641j2_a_b @ A ) ) ) ) ).

% fmla.map_sel(8)
thf(fact_102_fmla_Omap__sel_I7_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati1390740724296568061at_nat @ A )
     => ( ( relati7354301834588295945at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati7354301834588295945at_nat @ A ) ) ) ) ).

% fmla.map_sel(7)
thf(fact_103_fmla_Omap__sel_I7_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati8168519172193746908nj_a_b @ A )
     => ( ( relati5154284022127734760j1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5154284022127734760j1_a_b @ A ) ) ) ) ).

% fmla.map_sel(7)
thf(fact_104_fv_Osimps_I5_J,axiom,
    ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relational_Conj_a_b @ Phi @ Psi ) )
      = ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) ) ).

% fv.simps(5)
thf(fact_105_un__Conj1__def,axiom,
    ( relati5154284022127734760j1_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [X512: relational_fmla_a_b,X522: relational_fmla_a_b] : X512
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).

% un_Conj1_def
thf(fact_106_un__Conj2__def,axiom,
    ( relati1527130600461089641j2_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [X512: relational_fmla_a_b,X522: relational_fmla_a_b] : X522
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).

% un_Conj2_def
thf(fact_107_fmla_Omap__cong__pred,axiom,
    ! [X3: relational_fmla_a_b,Ya: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G2: b > b] :
      ( ( X3 = Ya )
     => ( ( relati3660035184769383399la_a_b
          @ ^ [Z1: a] :
              ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) )
          @ ^ [Z2: b] :
              ( ( F2 @ Z2 )
              = ( G2 @ Z2 ) )
          @ Ya )
       => ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X3 )
          = ( relati4520850492397955663_a_b_b @ G1 @ G2 @ Ya ) ) ) ) ).

% fmla.map_cong_pred
thf(fact_108_fmla_Omap__cong__pred,axiom,
    ! [X3: relati7126052417554554232at_nat,Ya: relati7126052417554554232at_nat,F1: nat > nat,G1: nat > nat,F2: nat > nat,G2: nat > nat] :
      ( ( X3 = Ya )
     => ( ( relati6725209092851823240at_nat
          @ ^ [Z1: nat] :
              ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) )
          @ ^ [Z2: nat] :
              ( ( F2 @ Z2 )
              = ( G2 @ Z2 ) )
          @ Ya )
       => ( ( relati9000828793121449555at_nat @ F1 @ F2 @ X3 )
          = ( relati9000828793121449555at_nat @ G1 @ G2 @ Ya ) ) ) ) ).

% fmla.map_cong_pred
thf(fact_109_fmla_Opred__inject_I4_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: relati7126052417554554232at_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati3679007509795571081at_nat @ A ) )
      = ( relati6725209092851823240at_nat @ P1 @ P2 @ A ) ) ).

% fmla.pred_inject(4)
thf(fact_110_fmla_Opred__inject_I4_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: relational_fmla_a_b] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Neg_a_b @ A ) )
      = ( relati3660035184769383399la_a_b @ P1 @ P2 @ A ) ) ).

% fmla.pred_inject(4)
thf(fact_111_fmla_Oinject_I4_J,axiom,
    ! [X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
      ( ( ( relational_Neg_a_b @ X4 )
        = ( relational_Neg_a_b @ Y4 ) )
      = ( X4 = Y4 ) ) ).

% fmla.inject(4)
thf(fact_112_fmla_Omap__disc__iff_I5_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati8168519172193746908nj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati8168519172193746908nj_a_b @ A ) ) ).

% fmla.map_disc_iff(5)
thf(fact_113_fmla_Omap__disc__iff_I5_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati1390740724296568061at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati1390740724296568061at_nat @ A ) ) ).

% fmla.map_disc_iff(5)
thf(fact_114_fmla_Omap__disc__iff_I6_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati5350680195807439568sj_a_b @ A ) ) ).

% fmla.map_disc_iff(6)
thf(fact_115_fmla_Omap__disc__iff_I6_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati711756705458397681at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati711756705458397681at_nat @ A ) ) ).

% fmla.map_disc_iff(6)
thf(fact_116_fmla_Omap__disc__iff_I1_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati3644702733014758741ed_a_b @ A ) ) ).

% fmla.map_disc_iff(1)
thf(fact_117_fmla_Omap__disc__iff_I1_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati7894638611541183222at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati7894638611541183222at_nat @ A ) ) ).

% fmla.map_disc_iff(1)
thf(fact_118_fmla_Omap__disc__iff_I2_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati6551038146797045342ol_a_b @ A ) ) ).

% fmla.map_disc_iff(2)
thf(fact_119_fmla_Omap__disc__iff_I2_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati6819674536432757887at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati6819674536432757887at_nat @ A ) ) ).

% fmla.map_disc_iff(2)
thf(fact_120_fmla_Omap__disc__iff_I3_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relational_is_Eq_a_b @ A ) ) ).

% fmla.map_disc_iff(3)
thf(fact_121_fmla_Omap__disc__iff_I3_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati8448989431961727361at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati8448989431961727361at_nat @ A ) ) ).

% fmla.map_disc_iff(3)
thf(fact_122_fmla_Omap__disc__iff_I4_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati4321004860440572638eg_a_b @ A ) ) ).

% fmla.map_disc_iff(4)
thf(fact_123_fmla_Omap__disc__iff_I4_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati7690703371482896639at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati7690703371482896639at_nat @ A ) ) ).

% fmla.map_disc_iff(4)
thf(fact_124_fmla_Omap__disc__iff_I7_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,A: relati7126052417554554232at_nat] :
      ( ( relati9085378286500150737at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
      = ( relati9085378286500150737at_nat @ A ) ) ).

% fmla.map_disc_iff(7)
thf(fact_125_fmla_Omap__disc__iff_I7_J,axiom,
    ! [F1: a > a,F2: b > b,A: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
      = ( relati5212983245281121968ts_a_b @ A ) ) ).

% fmla.map_disc_iff(7)
thf(fact_126_fmla_Omap__ident__strong,axiom,
    ! [T: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati9000828793121449555at_nat @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_127_fmla_Omap__ident__strong,axiom,
    ! [T: relati3061873246650996333_nat_b,F1: nat > nat,F2: b > b] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati4279548223302543473at_b_b @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_128_fmla_Omap__ident__strong,axiom,
    ! [T: relati3061873242347767532_nat_a,F1: nat > nat,F2: a > a] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati7067003805275219505at_a_a @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_129_fmla_Omap__ident__strong,axiom,
    ! [T: relati1059154107580485063_b_nat,F1: b > b,F2: nat > nat] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati700162154543277371_b_nat @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati7072134983273611633at_nat @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_130_fmla_Omap__ident__strong,axiom,
    ! [T: relational_fmla_b_b,F1: b > b,F2: b > b] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati283667798422459988la_b_b @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati2381659108026109071_b_b_b @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_131_fmla_Omap__ident__strong,axiom,
    ! [T: relational_fmla_b_a,F1: b > b,F2: a > a] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati283667798422459987la_b_a @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati5169114689998785103_b_a_a @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_132_fmla_Omap__ident__strong,axiom,
    ! [T: relati9047081815478866374_a_nat,F1: a > a,F2: nat > nat] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati8688089862441658682_a_nat @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati1332168654638169905at_nat @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_133_fmla_Omap__ident__strong,axiom,
    ! [T: relational_fmla_a_a,F1: a > a,F2: a > a] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136020la_a_a @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati7308306074370631695_a_a_a @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_134_fmla_Omap__ident__strong,axiom,
    ! [T: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_135_fmla_Omap__ident__strong,axiom,
    ! [T: relati4454658568062418871term_a,F1: nat > nat,F2: relational_term_a > relational_term_a] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati5193166848434641379term_a @ T ) )
         => ( ( F1 @ Z12 )
            = Z12 ) )
     => ( ! [Z22: relational_term_a] :
            ( ( member5466445112152945266term_a @ Z22 @ ( relati172813024183515810term_a @ T ) )
           => ( ( F2 @ Z22 )
              = Z22 ) )
       => ( ( relati6239555138786084081term_a @ F1 @ F2 @ T )
          = T ) ) ) ).

% fmla.map_ident_strong
thf(fact_136_fmla_Oinj__map__strong,axiom,
    ! [X3: relational_fmla_a_b,Xa: relational_fmla_a_b,F1: a > a,F1a: a > a,F2: b > b,F2a: b > b] :
      ( ! [Z12: a,Z1a: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ X3 ) )
         => ( ( member_a @ Z1a @ ( relati3071123380395136021la_a_b @ Xa ) )
           => ( ( ( F1 @ Z12 )
                = ( F1a @ Z1a ) )
             => ( Z12 = Z1a ) ) ) )
     => ( ! [Z22: b,Z2a: b] :
            ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X3 ) )
           => ( ( member_b @ Z2a @ ( relati8924981150291758614la_a_b @ Xa ) )
             => ( ( ( F2 @ Z22 )
                  = ( F2a @ Z2a ) )
               => ( Z22 = Z2a ) ) ) )
       => ( ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X3 )
            = ( relati4520850492397955663_a_b_b @ F1a @ F2a @ Xa ) )
         => ( X3 = Xa ) ) ) ) ).

% fmla.inj_map_strong
thf(fact_137_fmla_Oinj__map__strong,axiom,
    ! [X3: relati7126052417554554232at_nat,Xa: relati7126052417554554232at_nat,F1: nat > nat,F1a: nat > nat,F2: nat > nat,F2a: nat > nat] :
      ( ! [Z12: nat,Z1a: nat] :
          ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ X3 ) )
         => ( ( member_nat @ Z1a @ ( relati6321887899146193334at_nat @ Xa ) )
           => ( ( ( F1 @ Z12 )
                = ( F1a @ Z1a ) )
             => ( Z12 = Z1a ) ) ) )
     => ( ! [Z22: nat,Z2a: nat] :
            ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X3 ) )
           => ( ( member_nat @ Z2a @ ( relati2567137625159299127at_nat @ Xa ) )
             => ( ( ( F2 @ Z22 )
                  = ( F2a @ Z2a ) )
               => ( Z22 = Z2a ) ) ) )
       => ( ( ( relati9000828793121449555at_nat @ F1 @ F2 @ X3 )
            = ( relati9000828793121449555at_nat @ F1a @ F2a @ Xa ) )
         => ( X3 = Xa ) ) ) ) ).

% fmla.inj_map_strong
thf(fact_138_fmla_Omap__cong0,axiom,
    ! [X3: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G2: b > b] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ X3 ) )
         => ( ( F1 @ Z12 )
            = ( G1 @ Z12 ) ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X3 ) )
           => ( ( F2 @ Z22 )
              = ( G2 @ Z22 ) ) )
       => ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X3 )
          = ( relati4520850492397955663_a_b_b @ G1 @ G2 @ X3 ) ) ) ) ).

% fmla.map_cong0
thf(fact_139_fmla_Omap__cong0,axiom,
    ! [X3: relati7126052417554554232at_nat,F1: nat > nat,G1: nat > nat,F2: nat > nat,G2: nat > nat] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ X3 ) )
         => ( ( F1 @ Z12 )
            = ( G1 @ Z12 ) ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X3 ) )
           => ( ( F2 @ Z22 )
              = ( G2 @ Z22 ) ) )
       => ( ( relati9000828793121449555at_nat @ F1 @ F2 @ X3 )
          = ( relati9000828793121449555at_nat @ G1 @ G2 @ X3 ) ) ) ) ).

% fmla.map_cong0
thf(fact_140_fmla_Omap__cong,axiom,
    ! [X3: relational_fmla_a_b,Ya: relational_fmla_a_b,F1: a > a,G1: a > a,F2: b > b,G2: b > b] :
      ( ( X3 = Ya )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ Ya ) )
           => ( ( F1 @ Z12 )
              = ( G1 @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ Ya ) )
             => ( ( F2 @ Z22 )
                = ( G2 @ Z22 ) ) )
         => ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X3 )
            = ( relati4520850492397955663_a_b_b @ G1 @ G2 @ Ya ) ) ) ) ) ).

% fmla.map_cong
thf(fact_141_fmla_Omap__cong,axiom,
    ! [X3: relati7126052417554554232at_nat,Ya: relati7126052417554554232at_nat,F1: nat > nat,G1: nat > nat,F2: nat > nat,G2: nat > nat] :
      ( ( X3 = Ya )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ Ya ) )
           => ( ( F1 @ Z12 )
              = ( G1 @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya ) )
             => ( ( F2 @ Z22 )
                = ( G2 @ Z22 ) ) )
         => ( ( relati9000828793121449555at_nat @ F1 @ F2 @ X3 )
            = ( relati9000828793121449555at_nat @ G1 @ G2 @ Ya ) ) ) ) ) ).

% fmla.map_cong
thf(fact_142_fmla_Oset__intros_I3_J,axiom,
    ! [Yc: a,X4: relational_fmla_a_b] :
      ( ( member_a @ Yc @ ( relati3071123380395136021la_a_b @ X4 ) )
     => ( member_a @ Yc @ ( relati3071123380395136021la_a_b @ ( relational_Neg_a_b @ X4 ) ) ) ) ).

% fmla.set_intros(3)
thf(fact_143_fmla_Oset__intros_I3_J,axiom,
    ! [Yc: nat,X4: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yc @ ( relati6321887899146193334at_nat @ X4 ) )
     => ( member_nat @ Yc @ ( relati6321887899146193334at_nat @ ( relati3679007509795571081at_nat @ X4 ) ) ) ) ).

% fmla.set_intros(3)
thf(fact_144_fmla_Oset__intros_I10_J,axiom,
    ! [Ys: b,X4: relational_fmla_a_b] :
      ( ( member_b @ Ys @ ( relati8924981150291758614la_a_b @ X4 ) )
     => ( member_b @ Ys @ ( relati8924981150291758614la_a_b @ ( relational_Neg_a_b @ X4 ) ) ) ) ).

% fmla.set_intros(10)
thf(fact_145_fmla_Oset__intros_I10_J,axiom,
    ! [Ys: nat,X4: relati7126052417554554232at_nat] :
      ( ( member_nat @ Ys @ ( relati2567137625159299127at_nat @ X4 ) )
     => ( member_nat @ Ys @ ( relati2567137625159299127at_nat @ ( relati3679007509795571081at_nat @ X4 ) ) ) ) ).

% fmla.set_intros(10)
thf(fact_146_fmla_Osimps_I67_J,axiom,
    ! [F1: a > a,F2: b > b,X4: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Neg_a_b @ X4 ) )
      = ( relational_Neg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X4 ) ) ) ).

% fmla.simps(67)
thf(fact_147_fmla_Osimps_I67_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X4: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati3679007509795571081at_nat @ X4 ) )
      = ( relati3679007509795571081at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X4 ) ) ) ).

% fmla.simps(67)
thf(fact_148_fmla_Osimps_I123_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ( ( relati3071123380395136021la_a_b @ ( relational_Neg_a_b @ X4 ) )
      = ( relati3071123380395136021la_a_b @ X4 ) ) ).

% fmla.simps(123)
thf(fact_149_fmla_Osimps_I123_J,axiom,
    ! [X4: relati7126052417554554232at_nat] :
      ( ( relati6321887899146193334at_nat @ ( relati3679007509795571081at_nat @ X4 ) )
      = ( relati6321887899146193334at_nat @ X4 ) ) ).

% fmla.simps(123)
thf(fact_150_fmla_Osimps_I130_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ( ( relati8924981150291758614la_a_b @ ( relational_Neg_a_b @ X4 ) )
      = ( relati8924981150291758614la_a_b @ X4 ) ) ).

% fmla.simps(130)
thf(fact_151_fmla_Osimps_I130_J,axiom,
    ! [X4: relati7126052417554554232at_nat] :
      ( ( relati2567137625159299127at_nat @ ( relati3679007509795571081at_nat @ X4 ) )
      = ( relati2567137625159299127at_nat @ X4 ) ) ).

% fmla.simps(130)
thf(fact_152_fmla_Omap__ident,axiom,
    ! [T: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b
        @ ^ [X: a] : X
        @ ^ [X: b] : X
        @ T )
      = T ) ).

% fmla.map_ident
thf(fact_153_fmla_Omap__ident,axiom,
    ! [T: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat
        @ ^ [X: nat] : X
        @ ^ [X: nat] : X
        @ T )
      = T ) ).

% fmla.map_ident
thf(fact_154_fmla_Osimps_I124_J,axiom,
    ! [X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ( ( relati6321887899146193334at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) )
      = ( sup_sup_set_nat @ ( relati6321887899146193334at_nat @ X51 ) @ ( relati6321887899146193334at_nat @ X52 ) ) ) ).

% fmla.simps(124)
thf(fact_155_fmla_Osimps_I124_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = ( sup_sup_set_a @ ( relati3071123380395136021la_a_b @ X51 ) @ ( relati3071123380395136021la_a_b @ X52 ) ) ) ).

% fmla.simps(124)
thf(fact_156_fmla_Osimps_I131_J,axiom,
    ! [X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ( ( relati2567137625159299127at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) )
      = ( sup_sup_set_nat @ ( relati2567137625159299127at_nat @ X51 ) @ ( relati2567137625159299127at_nat @ X52 ) ) ) ).

% fmla.simps(131)
thf(fact_157_fmla_Osimps_I131_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = ( sup_sup_set_b @ ( relati8924981150291758614la_a_b @ X51 ) @ ( relati8924981150291758614la_a_b @ X52 ) ) ) ).

% fmla.simps(131)
thf(fact_158_fmla_Opred__mono__strong,axiom,
    ! [P1: nat > $o,P2: nat > $o,X3: relati7126052417554554232at_nat,P1a: nat > $o,P2a: nat > $o] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ X3 )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati6725209092851823240at_nat @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_159_fmla_Opred__mono__strong,axiom,
    ! [P1: a > $o,P2: b > $o,X3: relational_fmla_a_b,P1a: a > $o,P2a: b > $o] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ X3 )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati3660035184769383399la_a_b @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_160_fmla_Opred__mono__strong,axiom,
    ! [P1: nat > $o,P2: b > $o,X3: relati3061873246650996333_nat_b,P1a: nat > $o,P2a: b > $o] :
      ( ( relati2149557458355847751_nat_b @ P1 @ P2 @ X3 )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati2149557458355847751_nat_b @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_161_fmla_Opred__mono__strong,axiom,
    ! [P1: nat > $o,P2: a > $o,X3: relati3061873242347767532_nat_a,P1a: nat > $o,P2a: a > $o] :
      ( ( relati2149557458355847750_nat_a @ P1 @ P2 @ X3 )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati2149557458355847750_nat_a @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_162_fmla_Opred__mono__strong,axiom,
    ! [P1: b > $o,P2: nat > $o,X3: relati1059154107580485063_b_nat,P1a: b > $o,P2a: nat > $o] :
      ( ( relati8576442322988731625_b_nat @ P1 @ P2 @ X3 )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati700162154543277371_b_nat @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati8576442322988731625_b_nat @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_163_fmla_Opred__mono__strong,axiom,
    ! [P1: b > $o,P2: b > $o,X3: relational_fmla_b_b,P1a: b > $o,P2a: b > $o] :
      ( ( relati872579602796707366la_b_b @ P1 @ P2 @ X3 )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati283667798422459988la_b_b @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati872579602796707366la_b_b @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_164_fmla_Opred__mono__strong,axiom,
    ! [P1: b > $o,P2: a > $o,X3: relational_fmla_b_a,P1a: b > $o,P2a: a > $o] :
      ( ( relati872579602796707365la_b_a @ P1 @ P2 @ X3 )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati283667798422459987la_b_a @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati872579602796707365la_b_a @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_165_fmla_Opred__mono__strong,axiom,
    ! [P1: a > $o,P2: nat > $o,X3: relati9047081815478866374_a_nat,P1a: a > $o,P2a: nat > $o] :
      ( ( relati7340997994032337128_a_nat @ P1 @ P2 @ X3 )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati8688089862441658682_a_nat @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati7340997994032337128_a_nat @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_166_fmla_Opred__mono__strong,axiom,
    ! [P1: a > $o,P2: a > $o,X3: relational_fmla_a_a,P1a: a > $o,P2a: a > $o] :
      ( ( relati3660035184769383398la_a_a @ P1 @ P2 @ X3 )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati3071123380395136020la_a_a @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati3660035184769383398la_a_a @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_167_fmla_Opred__mono__strong,axiom,
    ! [P1: nat > $o,P2: relational_term_a > $o,X3: relati4454658568062418871term_a,P1a: nat > $o,P2a: relational_term_a > $o] :
      ( ( relati8756168980023174033term_a @ P1 @ P2 @ X3 )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati5193166848434641379term_a @ X3 ) )
           => ( ( P1 @ Z12 )
             => ( P1a @ Z12 ) ) )
       => ( ! [Z22: relational_term_a] :
              ( ( member5466445112152945266term_a @ Z22 @ ( relati172813024183515810term_a @ X3 ) )
             => ( ( P2 @ Z22 )
               => ( P2a @ Z22 ) ) )
         => ( relati8756168980023174033term_a @ P1a @ P2a @ X3 ) ) ) ) ).

% fmla.pred_mono_strong
thf(fact_168_fmla_Opred__cong,axiom,
    ! [X3: relati7126052417554554232at_nat,Ya: relati7126052417554554232at_nat,P1: nat > $o,P1a: nat > $o,P2: nat > $o,P2a: nat > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati6725209092851823240at_nat @ P1 @ P2 @ X3 )
            = ( relati6725209092851823240at_nat @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_169_fmla_Opred__cong,axiom,
    ! [X3: relational_fmla_a_b,Ya: relational_fmla_a_b,P1: a > $o,P1a: a > $o,P2: b > $o,P2a: b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ X3 )
            = ( relati3660035184769383399la_a_b @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_170_fmla_Opred__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,P1: nat > $o,P1a: nat > $o,P2: b > $o,P2a: b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati2149557458355847751_nat_b @ P1 @ P2 @ X3 )
            = ( relati2149557458355847751_nat_b @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_171_fmla_Opred__cong,axiom,
    ! [X3: relati3061873242347767532_nat_a,Ya: relati3061873242347767532_nat_a,P1: nat > $o,P1a: nat > $o,P2: a > $o,P2a: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati2149557458355847750_nat_a @ P1 @ P2 @ X3 )
            = ( relati2149557458355847750_nat_a @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_172_fmla_Opred__cong,axiom,
    ! [X3: relati1059154107580485063_b_nat,Ya: relati1059154107580485063_b_nat,P1: b > $o,P1a: b > $o,P2: nat > $o,P2a: nat > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati700162154543277371_b_nat @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati8576442322988731625_b_nat @ P1 @ P2 @ X3 )
            = ( relati8576442322988731625_b_nat @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_173_fmla_Opred__cong,axiom,
    ! [X3: relational_fmla_b_b,Ya: relational_fmla_b_b,P1: b > $o,P1a: b > $o,P2: b > $o,P2a: b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati283667798422459988la_b_b @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: b] :
              ( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati872579602796707366la_b_b @ P1 @ P2 @ X3 )
            = ( relati872579602796707366la_b_b @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_174_fmla_Opred__cong,axiom,
    ! [X3: relational_fmla_b_a,Ya: relational_fmla_b_a,P1: b > $o,P1a: b > $o,P2: a > $o,P2a: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: b] :
            ( ( member_b @ Z12 @ ( relati283667798422459987la_b_a @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati872579602796707365la_b_a @ P1 @ P2 @ X3 )
            = ( relati872579602796707365la_b_a @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_175_fmla_Opred__cong,axiom,
    ! [X3: relati9047081815478866374_a_nat,Ya: relati9047081815478866374_a_nat,P1: a > $o,P1a: a > $o,P2: nat > $o,P2a: nat > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati8688089862441658682_a_nat @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: nat] :
              ( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati7340997994032337128_a_nat @ P1 @ P2 @ X3 )
            = ( relati7340997994032337128_a_nat @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_176_fmla_Opred__cong,axiom,
    ! [X3: relational_fmla_a_a,Ya: relational_fmla_a_a,P1: a > $o,P1a: a > $o,P2: a > $o,P2a: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: a] :
            ( ( member_a @ Z12 @ ( relati3071123380395136020la_a_a @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: a] :
              ( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati3660035184769383398la_a_a @ P1 @ P2 @ X3 )
            = ( relati3660035184769383398la_a_a @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_177_fmla_Opred__cong,axiom,
    ! [X3: relati4454658568062418871term_a,Ya: relati4454658568062418871term_a,P1: nat > $o,P1a: nat > $o,P2: relational_term_a > $o,P2a: relational_term_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z12: nat] :
            ( ( member_nat @ Z12 @ ( relati5193166848434641379term_a @ Ya ) )
           => ( ( P1 @ Z12 )
              = ( P1a @ Z12 ) ) )
       => ( ! [Z22: relational_term_a] :
              ( ( member5466445112152945266term_a @ Z22 @ ( relati172813024183515810term_a @ Ya ) )
             => ( ( P2 @ Z22 )
                = ( P2a @ Z22 ) ) )
         => ( ( relati8756168980023174033term_a @ P1 @ P2 @ X3 )
            = ( relati8756168980023174033term_a @ P1a @ P2a @ Ya ) ) ) ) ) ).

% fmla.pred_cong
thf(fact_178_fmla_Odistinct_I31_J,axiom,
    ! [X4: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relational_Neg_a_b @ X4 )
     != ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.distinct(31)
thf(fact_179_fmla_Osimps_I68_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati8628237474745418483at_nat @ X51 @ X52 ) )
      = ( relati8628237474745418483at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X51 ) @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X52 ) ) ) ).

% fmla.simps(68)
thf(fact_180_fmla_Osimps_I68_J,axiom,
    ! [F1: a > a,F2: b > b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Conj_a_b @ X51 @ X52 ) )
      = ( relational_Conj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X51 ) @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X52 ) ) ) ).

% fmla.simps(68)
thf(fact_181_sat_Osimps_I4_J,axiom,
    ! [Phi: relational_fmla_a_b,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Neg_a_b @ Phi ) @ I @ Sigma )
      = ( ~ ( relational_sat_a_b @ Phi @ I @ Sigma ) ) ) ).

% sat.simps(4)
thf(fact_182_fmla_Odisc_I32_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relati8168519172193746908nj_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(32)
thf(fact_183_fmla_Odisc_I39_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relati5350680195807439568sj_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(39)
thf(fact_184_fmla_Odisc_I4_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relati3644702733014758741ed_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(4)
thf(fact_185_fv_Osimps_I4_J,axiom,
    ! [Phi: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relational_Neg_a_b @ Phi ) )
      = ( relational_fv_a_b @ Phi ) ) ).

% fv.simps(4)
thf(fact_186_is__Neg__def,axiom,
    ( relati4321004860440572638eg_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X42: relational_fmla_a_b] :
          ( Fmla2
          = ( relational_Neg_a_b @ X42 ) ) ) ) ).

% is_Neg_def
thf(fact_187_fmla_Osimps_I53_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X4: relational_fmla_a_b] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Neg_a_b @ X4 ) )
      = ( F4 @ X4 ) ) ).

% fmla.simps(53)
thf(fact_188_fmla_OdiscI_I4_J,axiom,
    ! [Fmla: relational_fmla_a_b,X4: relational_fmla_a_b] :
      ( ( Fmla
        = ( relational_Neg_a_b @ X4 ) )
     => ( relati4321004860440572638eg_a_b @ Fmla ) ) ).

% fmla.discI(4)
thf(fact_189_fmla_Odisc_I11_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relati6551038146797045342ol_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(11)
thf(fact_190_fmla_Odisc_I18_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relational_is_Eq_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(18)
thf(fact_191_fmla_Odisc_I25_J,axiom,
    ! [X4: relational_fmla_a_b] : ( relati4321004860440572638eg_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(25)
thf(fact_192_fmla_Odisc_I46_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.disc(46)
thf(fact_193_fmla_Oset__intros_I5_J,axiom,
    ! [Yg: nat,X52: relati7126052417554554232at_nat,X51: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yg @ ( relati6321887899146193334at_nat @ X52 ) )
     => ( member_nat @ Yg @ ( relati6321887899146193334at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(5)
thf(fact_194_fmla_Oset__intros_I5_J,axiom,
    ! [Yg: a,X52: relational_fmla_a_b,X51: relational_fmla_a_b] :
      ( ( member_a @ Yg @ ( relati3071123380395136021la_a_b @ X52 ) )
     => ( member_a @ Yg @ ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(5)
thf(fact_195_fmla_Oset__intros_I4_J,axiom,
    ! [Ye: nat,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ( ( member_nat @ Ye @ ( relati6321887899146193334at_nat @ X51 ) )
     => ( member_nat @ Ye @ ( relati6321887899146193334at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(4)
thf(fact_196_fmla_Oset__intros_I4_J,axiom,
    ! [Ye: a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( member_a @ Ye @ ( relati3071123380395136021la_a_b @ X51 ) )
     => ( member_a @ Ye @ ( relati3071123380395136021la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(4)
thf(fact_197_fmla_Oset__intros_I12_J,axiom,
    ! [Yw: nat,X52: relati7126052417554554232at_nat,X51: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yw @ ( relati2567137625159299127at_nat @ X52 ) )
     => ( member_nat @ Yw @ ( relati2567137625159299127at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(12)
thf(fact_198_fmla_Oset__intros_I12_J,axiom,
    ! [Yw: b,X52: relational_fmla_a_b,X51: relational_fmla_a_b] :
      ( ( member_b @ Yw @ ( relati8924981150291758614la_a_b @ X52 ) )
     => ( member_b @ Yw @ ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(12)
thf(fact_199_fmla_Oset__intros_I11_J,axiom,
    ! [Yu: nat,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yu @ ( relati2567137625159299127at_nat @ X51 ) )
     => ( member_nat @ Yu @ ( relati2567137625159299127at_nat @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(11)
thf(fact_200_fmla_Oset__intros_I11_J,axiom,
    ! [Yu: b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( member_b @ Yu @ ( relati8924981150291758614la_a_b @ X51 ) )
     => ( member_b @ Yu @ ( relati8924981150291758614la_a_b @ ( relational_Conj_a_b @ X51 @ X52 ) ) ) ) ).

% fmla.set_intros(11)
thf(fact_201_Un__iff,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( sup_su8474575085660790013term_a @ A2 @ B ) )
      = ( ( member5466445112152945266term_a @ C @ A2 )
        | ( member5466445112152945266term_a @ C @ B ) ) ) ).

% Un_iff
thf(fact_202_Un__iff,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( sup_sup_set_list_a @ A2 @ B ) )
      = ( ( member_list_a @ C @ A2 )
        | ( member_list_a @ C @ B ) ) ) ).

% Un_iff
thf(fact_203_Un__iff,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A2 @ B ) )
      = ( ( member8440522571783428010at_nat @ C @ A2 )
        | ( member8440522571783428010at_nat @ C @ B ) ) ) ).

% Un_iff
thf(fact_204_Un__iff,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( sup_sup_set_a @ A2 @ B ) )
      = ( ( member_a @ C @ A2 )
        | ( member_a @ C @ B ) ) ) ).

% Un_iff
thf(fact_205_Un__iff,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( sup_sup_set_b @ A2 @ B ) )
      = ( ( member_b @ C @ A2 )
        | ( member_b @ C @ B ) ) ) ).

% Un_iff
thf(fact_206_Un__iff,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
      = ( ( member_nat @ C @ A2 )
        | ( member_nat @ C @ B ) ) ) ).

% Un_iff
thf(fact_207_UnCI,axiom,
    ! [C: relational_term_a,B: set_Re5178783185447174953term_a,A2: set_Re5178783185447174953term_a] :
      ( ( ~ ( member5466445112152945266term_a @ C @ B )
       => ( member5466445112152945266term_a @ C @ A2 ) )
     => ( member5466445112152945266term_a @ C @ ( sup_su8474575085660790013term_a @ A2 @ B ) ) ) ).

% UnCI
thf(fact_208_UnCI,axiom,
    ! [C: list_a,B: set_list_a,A2: set_list_a] :
      ( ( ~ ( member_list_a @ C @ B )
       => ( member_list_a @ C @ A2 ) )
     => ( member_list_a @ C @ ( sup_sup_set_list_a @ A2 @ B ) ) ) ).

% UnCI
thf(fact_209_UnCI,axiom,
    ! [C: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( ~ ( member8440522571783428010at_nat @ C @ B )
       => ( member8440522571783428010at_nat @ C @ A2 ) )
     => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A2 @ B ) ) ) ).

% UnCI
thf(fact_210_UnCI,axiom,
    ! [C: a,B: set_a,A2: set_a] :
      ( ( ~ ( member_a @ C @ B )
       => ( member_a @ C @ A2 ) )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnCI
thf(fact_211_UnCI,axiom,
    ! [C: b,B: set_b,A2: set_b] :
      ( ( ~ ( member_b @ C @ B )
       => ( member_b @ C @ A2 ) )
     => ( member_b @ C @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnCI
thf(fact_212_UnCI,axiom,
    ! [C: nat,B: set_nat,A2: set_nat] :
      ( ( ~ ( member_nat @ C @ B )
       => ( member_nat @ C @ A2 ) )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).

% UnCI
thf(fact_213_sup__apply,axiom,
    ( sup_sup_nat_o
    = ( ^ [F: nat > $o,G: nat > $o,X: nat] : ( sup_sup_o @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% sup_apply
thf(fact_214_sup_Oright__idem,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B2 ) @ B2 )
      = ( sup_sup_set_nat @ A @ B2 ) ) ).

% sup.right_idem
thf(fact_215_sup_Oright__idem,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B2 ) @ B2 )
      = ( sup_sup_set_a @ A @ B2 ) ) ).

% sup.right_idem
thf(fact_216_sup_Oright__idem,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( sup_sup_set_b @ ( sup_sup_set_b @ A @ B2 ) @ B2 )
      = ( sup_sup_set_b @ A @ B2 ) ) ).

% sup.right_idem
thf(fact_217_sup_Oright__idem,axiom,
    ! [A: nat > $o,B2: nat > $o] :
      ( ( sup_sup_nat_o @ ( sup_sup_nat_o @ A @ B2 ) @ B2 )
      = ( sup_sup_nat_o @ A @ B2 ) ) ).

% sup.right_idem
thf(fact_218_sup__left__idem,axiom,
    ! [X3: set_nat,Y: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ X3 @ Y ) )
      = ( sup_sup_set_nat @ X3 @ Y ) ) ).

% sup_left_idem
thf(fact_219_sup__left__idem,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
      = ( sup_sup_set_a @ X3 @ Y ) ) ).

% sup_left_idem
thf(fact_220_sup__left__idem,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ X3 @ Y ) )
      = ( sup_sup_set_b @ X3 @ Y ) ) ).

% sup_left_idem
thf(fact_221_sup__left__idem,axiom,
    ! [X3: nat > $o,Y: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ X3 @ Y ) )
      = ( sup_sup_nat_o @ X3 @ Y ) ) ).

% sup_left_idem
thf(fact_222_sup_Oleft__idem,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B2 ) )
      = ( sup_sup_set_nat @ A @ B2 ) ) ).

% sup.left_idem
thf(fact_223_sup_Oleft__idem,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B2 ) )
      = ( sup_sup_set_a @ A @ B2 ) ) ).

% sup.left_idem
thf(fact_224_sup_Oleft__idem,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( sup_sup_set_b @ A @ ( sup_sup_set_b @ A @ B2 ) )
      = ( sup_sup_set_b @ A @ B2 ) ) ).

% sup.left_idem
thf(fact_225_sup_Oleft__idem,axiom,
    ! [A: nat > $o,B2: nat > $o] :
      ( ( sup_sup_nat_o @ A @ ( sup_sup_nat_o @ A @ B2 ) )
      = ( sup_sup_nat_o @ A @ B2 ) ) ).

% sup.left_idem
thf(fact_226_sup__idem,axiom,
    ! [X3: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ X3 )
      = X3 ) ).

% sup_idem
thf(fact_227_sup__idem,axiom,
    ! [X3: set_a] :
      ( ( sup_sup_set_a @ X3 @ X3 )
      = X3 ) ).

% sup_idem
thf(fact_228_sup__idem,axiom,
    ! [X3: set_b] :
      ( ( sup_sup_set_b @ X3 @ X3 )
      = X3 ) ).

% sup_idem
thf(fact_229_sup__idem,axiom,
    ! [X3: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ X3 )
      = X3 ) ).

% sup_idem
thf(fact_230_sup_Oidem,axiom,
    ! [A: set_nat] :
      ( ( sup_sup_set_nat @ A @ A )
      = A ) ).

% sup.idem
thf(fact_231_sup_Oidem,axiom,
    ! [A: set_a] :
      ( ( sup_sup_set_a @ A @ A )
      = A ) ).

% sup.idem
thf(fact_232_sup_Oidem,axiom,
    ! [A: set_b] :
      ( ( sup_sup_set_b @ A @ A )
      = A ) ).

% sup.idem
thf(fact_233_sup_Oidem,axiom,
    ! [A: nat > $o] :
      ( ( sup_sup_nat_o @ A @ A )
      = A ) ).

% sup.idem
thf(fact_234_Collect__disj__eq,axiom,
    ! [P: list_nat > $o,Q: list_nat > $o] :
      ( ( collect_list_nat
        @ ^ [X: list_nat] :
            ( ( P @ X )
            | ( Q @ X ) ) )
      = ( sup_sup_set_list_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_235_Collect__disj__eq,axiom,
    ! [P: nat > $o,Q: nat > $o] :
      ( ( collect_nat
        @ ^ [X: nat] :
            ( ( P @ X )
            | ( Q @ X ) ) )
      = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_236_Collect__disj__eq,axiom,
    ! [P: a > $o,Q: a > $o] :
      ( ( collect_a
        @ ^ [X: a] :
            ( ( P @ X )
            | ( Q @ X ) ) )
      = ( sup_sup_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_237_Collect__disj__eq,axiom,
    ! [P: b > $o,Q: b > $o] :
      ( ( collect_b
        @ ^ [X: b] :
            ( ( P @ X )
            | ( Q @ X ) ) )
      = ( sup_sup_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) ) ) ).

% Collect_disj_eq
thf(fact_238_Un__def,axiom,
    ( sup_su8474575085660790013term_a
    = ( ^ [A3: set_Re5178783185447174953term_a,B3: set_Re5178783185447174953term_a] :
          ( collec7376311432011962548term_a
          @ ^ [X: relational_term_a] :
              ( ( member5466445112152945266term_a @ X @ A3 )
              | ( member5466445112152945266term_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_239_Un__def,axiom,
    ( sup_sup_set_list_a
    = ( ^ [A3: set_list_a,B3: set_list_a] :
          ( collect_list_a
          @ ^ [X: list_a] :
              ( ( member_list_a @ X @ A3 )
              | ( member_list_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_240_Un__def,axiom,
    ( sup_su6327502436637775413at_nat
    = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
          ( collec3392354462482085612at_nat
          @ ^ [X: product_prod_nat_nat] :
              ( ( member8440522571783428010at_nat @ X @ A3 )
              | ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_241_Un__def,axiom,
    ( sup_sup_set_list_nat
    = ( ^ [A3: set_list_nat,B3: set_list_nat] :
          ( collect_list_nat
          @ ^ [X: list_nat] :
              ( ( member_list_nat @ X @ A3 )
              | ( member_list_nat @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_242_Un__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A3 )
              | ( member_a @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_243_Un__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A3: set_b,B3: set_b] :
          ( collect_b
          @ ^ [X: b] :
              ( ( member_b @ X @ A3 )
              | ( member_b @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_244_Un__def,axiom,
    ( sup_sup_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A3 )
              | ( member_nat @ X @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_245_sup__set__def,axiom,
    ( sup_su8474575085660790013term_a
    = ( ^ [A3: set_Re5178783185447174953term_a,B3: set_Re5178783185447174953term_a] :
          ( collec7376311432011962548term_a
          @ ( sup_su927640514972811808rm_a_o
            @ ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ A3 )
            @ ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_246_sup__set__def,axiom,
    ( sup_sup_set_list_a
    = ( ^ [A3: set_list_a,B3: set_list_a] :
          ( collect_list_a
          @ ( sup_sup_list_a_o
            @ ^ [X: list_a] : ( member_list_a @ X @ A3 )
            @ ^ [X: list_a] : ( member_list_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_247_sup__set__def,axiom,
    ( sup_su6327502436637775413at_nat
    = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
          ( collec3392354462482085612at_nat
          @ ( sup_su798857527126471912_nat_o
            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A3 )
            @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_248_sup__set__def,axiom,
    ( sup_sup_set_list_nat
    = ( ^ [A3: set_list_nat,B3: set_list_nat] :
          ( collect_list_nat
          @ ( sup_sup_list_nat_o
            @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 )
            @ ^ [X: list_nat] : ( member_list_nat @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_249_sup__set__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( collect_a
          @ ( sup_sup_a_o
            @ ^ [X: a] : ( member_a @ X @ A3 )
            @ ^ [X: a] : ( member_a @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_250_sup__set__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A3: set_b,B3: set_b] :
          ( collect_b
          @ ( sup_sup_b_o
            @ ^ [X: b] : ( member_b @ X @ A3 )
            @ ^ [X: b] : ( member_b @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_251_sup__set__def,axiom,
    ( sup_sup_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( collect_nat
          @ ( sup_sup_nat_o
            @ ^ [X: nat] : ( member_nat @ X @ A3 )
            @ ^ [X: nat] : ( member_nat @ X @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_252_inf__sup__aci_I8_J,axiom,
    ! [X3: set_nat,Y: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ X3 @ Y ) )
      = ( sup_sup_set_nat @ X3 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_253_inf__sup__aci_I8_J,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
      = ( sup_sup_set_a @ X3 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_254_inf__sup__aci_I8_J,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ X3 @ Y ) )
      = ( sup_sup_set_b @ X3 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_255_inf__sup__aci_I8_J,axiom,
    ! [X3: nat > $o,Y: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ X3 @ Y ) )
      = ( sup_sup_nat_o @ X3 @ Y ) ) ).

% inf_sup_aci(8)
thf(fact_256_inf__sup__aci_I7_J,axiom,
    ! [X3: set_nat,Y: set_nat,Z: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ Y @ Z ) )
      = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X3 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_257_inf__sup__aci_I7_J,axiom,
    ! [X3: set_a,Y: set_a,Z: set_a] :
      ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z ) )
      = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_258_inf__sup__aci_I7_J,axiom,
    ! [X3: set_b,Y: set_b,Z: set_b] :
      ( ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ Y @ Z ) )
      = ( sup_sup_set_b @ Y @ ( sup_sup_set_b @ X3 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_259_inf__sup__aci_I7_J,axiom,
    ! [X3: nat > $o,Y: nat > $o,Z: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ Y @ Z ) )
      = ( sup_sup_nat_o @ Y @ ( sup_sup_nat_o @ X3 @ Z ) ) ) ).

% inf_sup_aci(7)
thf(fact_260_inf__sup__aci_I6_J,axiom,
    ! [X3: set_nat,Y: set_nat,Z: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X3 @ Y ) @ Z )
      = ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_261_inf__sup__aci_I6_J,axiom,
    ! [X3: set_a,Y: set_a,Z: set_a] :
      ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z )
      = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_262_inf__sup__aci_I6_J,axiom,
    ! [X3: set_b,Y: set_b,Z: set_b] :
      ( ( sup_sup_set_b @ ( sup_sup_set_b @ X3 @ Y ) @ Z )
      = ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_263_inf__sup__aci_I6_J,axiom,
    ! [X3: nat > $o,Y: nat > $o,Z: nat > $o] :
      ( ( sup_sup_nat_o @ ( sup_sup_nat_o @ X3 @ Y ) @ Z )
      = ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ Y @ Z ) ) ) ).

% inf_sup_aci(6)
thf(fact_264_inf__sup__aci_I5_J,axiom,
    ( sup_sup_set_nat
    = ( ^ [X: set_nat,Y2: set_nat] : ( sup_sup_set_nat @ Y2 @ X ) ) ) ).

% inf_sup_aci(5)
thf(fact_265_inf__sup__aci_I5_J,axiom,
    ( sup_sup_set_a
    = ( ^ [X: set_a,Y2: set_a] : ( sup_sup_set_a @ Y2 @ X ) ) ) ).

% inf_sup_aci(5)
thf(fact_266_inf__sup__aci_I5_J,axiom,
    ( sup_sup_set_b
    = ( ^ [X: set_b,Y2: set_b] : ( sup_sup_set_b @ Y2 @ X ) ) ) ).

% inf_sup_aci(5)
thf(fact_267_inf__sup__aci_I5_J,axiom,
    ( sup_sup_nat_o
    = ( ^ [X: nat > $o,Y2: nat > $o] : ( sup_sup_nat_o @ Y2 @ X ) ) ) ).

% inf_sup_aci(5)
thf(fact_268_sup_Oassoc,axiom,
    ! [A: set_nat,B2: set_nat,C: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B2 ) @ C )
      = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B2 @ C ) ) ) ).

% sup.assoc
thf(fact_269_sup_Oassoc,axiom,
    ! [A: set_a,B2: set_a,C: set_a] :
      ( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B2 ) @ C )
      = ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B2 @ C ) ) ) ).

% sup.assoc
thf(fact_270_sup_Oassoc,axiom,
    ! [A: set_b,B2: set_b,C: set_b] :
      ( ( sup_sup_set_b @ ( sup_sup_set_b @ A @ B2 ) @ C )
      = ( sup_sup_set_b @ A @ ( sup_sup_set_b @ B2 @ C ) ) ) ).

% sup.assoc
thf(fact_271_sup_Oassoc,axiom,
    ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
      ( ( sup_sup_nat_o @ ( sup_sup_nat_o @ A @ B2 ) @ C )
      = ( sup_sup_nat_o @ A @ ( sup_sup_nat_o @ B2 @ C ) ) ) ).

% sup.assoc
thf(fact_272_sup__assoc,axiom,
    ! [X3: set_nat,Y: set_nat,Z: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X3 @ Y ) @ Z )
      = ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_273_sup__assoc,axiom,
    ! [X3: set_a,Y: set_a,Z: set_a] :
      ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z )
      = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_274_sup__assoc,axiom,
    ! [X3: set_b,Y: set_b,Z: set_b] :
      ( ( sup_sup_set_b @ ( sup_sup_set_b @ X3 @ Y ) @ Z )
      = ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_275_sup__assoc,axiom,
    ! [X3: nat > $o,Y: nat > $o,Z: nat > $o] :
      ( ( sup_sup_nat_o @ ( sup_sup_nat_o @ X3 @ Y ) @ Z )
      = ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ Y @ Z ) ) ) ).

% sup_assoc
thf(fact_276_sup_Ocommute,axiom,
    ( sup_sup_set_nat
    = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).

% sup.commute
thf(fact_277_sup_Ocommute,axiom,
    ( sup_sup_set_a
    = ( ^ [A4: set_a,B4: set_a] : ( sup_sup_set_a @ B4 @ A4 ) ) ) ).

% sup.commute
thf(fact_278_sup_Ocommute,axiom,
    ( sup_sup_set_b
    = ( ^ [A4: set_b,B4: set_b] : ( sup_sup_set_b @ B4 @ A4 ) ) ) ).

% sup.commute
thf(fact_279_sup_Ocommute,axiom,
    ( sup_sup_nat_o
    = ( ^ [A4: nat > $o,B4: nat > $o] : ( sup_sup_nat_o @ B4 @ A4 ) ) ) ).

% sup.commute
thf(fact_280_sup__commute,axiom,
    ( sup_sup_set_nat
    = ( ^ [X: set_nat,Y2: set_nat] : ( sup_sup_set_nat @ Y2 @ X ) ) ) ).

% sup_commute
thf(fact_281_sup__commute,axiom,
    ( sup_sup_set_a
    = ( ^ [X: set_a,Y2: set_a] : ( sup_sup_set_a @ Y2 @ X ) ) ) ).

% sup_commute
thf(fact_282_sup__commute,axiom,
    ( sup_sup_set_b
    = ( ^ [X: set_b,Y2: set_b] : ( sup_sup_set_b @ Y2 @ X ) ) ) ).

% sup_commute
thf(fact_283_sup__commute,axiom,
    ( sup_sup_nat_o
    = ( ^ [X: nat > $o,Y2: nat > $o] : ( sup_sup_nat_o @ Y2 @ X ) ) ) ).

% sup_commute
thf(fact_284_sup_Oleft__commute,axiom,
    ! [B2: set_nat,A: set_nat,C: set_nat] :
      ( ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A @ C ) )
      = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B2 @ C ) ) ) ).

% sup.left_commute
thf(fact_285_sup_Oleft__commute,axiom,
    ! [B2: set_a,A: set_a,C: set_a] :
      ( ( sup_sup_set_a @ B2 @ ( sup_sup_set_a @ A @ C ) )
      = ( sup_sup_set_a @ A @ ( sup_sup_set_a @ B2 @ C ) ) ) ).

% sup.left_commute
thf(fact_286_sup_Oleft__commute,axiom,
    ! [B2: set_b,A: set_b,C: set_b] :
      ( ( sup_sup_set_b @ B2 @ ( sup_sup_set_b @ A @ C ) )
      = ( sup_sup_set_b @ A @ ( sup_sup_set_b @ B2 @ C ) ) ) ).

% sup.left_commute
thf(fact_287_sup_Oleft__commute,axiom,
    ! [B2: nat > $o,A: nat > $o,C: nat > $o] :
      ( ( sup_sup_nat_o @ B2 @ ( sup_sup_nat_o @ A @ C ) )
      = ( sup_sup_nat_o @ A @ ( sup_sup_nat_o @ B2 @ C ) ) ) ).

% sup.left_commute
thf(fact_288_sup__left__commute,axiom,
    ! [X3: set_nat,Y: set_nat,Z: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ ( sup_sup_set_nat @ Y @ Z ) )
      = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X3 @ Z ) ) ) ).

% sup_left_commute
thf(fact_289_sup__left__commute,axiom,
    ! [X3: set_a,Y: set_a,Z: set_a] :
      ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z ) )
      = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z ) ) ) ).

% sup_left_commute
thf(fact_290_sup__left__commute,axiom,
    ! [X3: set_b,Y: set_b,Z: set_b] :
      ( ( sup_sup_set_b @ X3 @ ( sup_sup_set_b @ Y @ Z ) )
      = ( sup_sup_set_b @ Y @ ( sup_sup_set_b @ X3 @ Z ) ) ) ).

% sup_left_commute
thf(fact_291_sup__left__commute,axiom,
    ! [X3: nat > $o,Y: nat > $o,Z: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ ( sup_sup_nat_o @ Y @ Z ) )
      = ( sup_sup_nat_o @ Y @ ( sup_sup_nat_o @ X3 @ Z ) ) ) ).

% sup_left_commute
thf(fact_292_sup__fun__def,axiom,
    ( sup_sup_nat_o
    = ( ^ [F: nat > $o,G: nat > $o,X: nat] : ( sup_sup_o @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% sup_fun_def
thf(fact_293_UnE,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( sup_su8474575085660790013term_a @ A2 @ B ) )
     => ( ~ ( member5466445112152945266term_a @ C @ A2 )
       => ( member5466445112152945266term_a @ C @ B ) ) ) ).

% UnE
thf(fact_294_UnE,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( sup_sup_set_list_a @ A2 @ B ) )
     => ( ~ ( member_list_a @ C @ A2 )
       => ( member_list_a @ C @ B ) ) ) ).

% UnE
thf(fact_295_UnE,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A2 @ B ) )
     => ( ~ ( member8440522571783428010at_nat @ C @ A2 )
       => ( member8440522571783428010at_nat @ C @ B ) ) ) ).

% UnE
thf(fact_296_UnE,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( sup_sup_set_a @ A2 @ B ) )
     => ( ~ ( member_a @ C @ A2 )
       => ( member_a @ C @ B ) ) ) ).

% UnE
thf(fact_297_UnE,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( sup_sup_set_b @ A2 @ B ) )
     => ( ~ ( member_b @ C @ A2 )
       => ( member_b @ C @ B ) ) ) ).

% UnE
thf(fact_298_UnE,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
     => ( ~ ( member_nat @ C @ A2 )
       => ( member_nat @ C @ B ) ) ) ).

% UnE
thf(fact_299_UnI1,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ A2 )
     => ( member5466445112152945266term_a @ C @ ( sup_su8474575085660790013term_a @ A2 @ B ) ) ) ).

% UnI1
thf(fact_300_UnI1,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ A2 )
     => ( member_list_a @ C @ ( sup_sup_set_list_a @ A2 @ B ) ) ) ).

% UnI1
thf(fact_301_UnI1,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ A2 )
     => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A2 @ B ) ) ) ).

% UnI1
thf(fact_302_UnI1,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ A2 )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnI1
thf(fact_303_UnI1,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ A2 )
     => ( member_b @ C @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnI1
thf(fact_304_UnI1,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ A2 )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).

% UnI1
thf(fact_305_UnI2,axiom,
    ! [C: relational_term_a,B: set_Re5178783185447174953term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ B )
     => ( member5466445112152945266term_a @ C @ ( sup_su8474575085660790013term_a @ A2 @ B ) ) ) ).

% UnI2
thf(fact_306_UnI2,axiom,
    ! [C: list_a,B: set_list_a,A2: set_list_a] :
      ( ( member_list_a @ C @ B )
     => ( member_list_a @ C @ ( sup_sup_set_list_a @ A2 @ B ) ) ) ).

% UnI2
thf(fact_307_UnI2,axiom,
    ! [C: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ B )
     => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A2 @ B ) ) ) ).

% UnI2
thf(fact_308_UnI2,axiom,
    ! [C: a,B: set_a,A2: set_a] :
      ( ( member_a @ C @ B )
     => ( member_a @ C @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnI2
thf(fact_309_UnI2,axiom,
    ! [C: b,B: set_b,A2: set_b] :
      ( ( member_b @ C @ B )
     => ( member_b @ C @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnI2
thf(fact_310_UnI2,axiom,
    ! [C: nat,B: set_nat,A2: set_nat] :
      ( ( member_nat @ C @ B )
     => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).

% UnI2
thf(fact_311_bex__Un,axiom,
    ! [A2: set_nat,B: set_nat,P: nat > $o] :
      ( ( ? [X: nat] :
            ( ( member_nat @ X @ ( sup_sup_set_nat @ A2 @ B ) )
            & ( P @ X ) ) )
      = ( ? [X: nat] :
            ( ( member_nat @ X @ A2 )
            & ( P @ X ) )
        | ? [X: nat] :
            ( ( member_nat @ X @ B )
            & ( P @ X ) ) ) ) ).

% bex_Un
thf(fact_312_bex__Un,axiom,
    ! [A2: set_a,B: set_a,P: a > $o] :
      ( ( ? [X: a] :
            ( ( member_a @ X @ ( sup_sup_set_a @ A2 @ B ) )
            & ( P @ X ) ) )
      = ( ? [X: a] :
            ( ( member_a @ X @ A2 )
            & ( P @ X ) )
        | ? [X: a] :
            ( ( member_a @ X @ B )
            & ( P @ X ) ) ) ) ).

% bex_Un
thf(fact_313_bex__Un,axiom,
    ! [A2: set_b,B: set_b,P: b > $o] :
      ( ( ? [X: b] :
            ( ( member_b @ X @ ( sup_sup_set_b @ A2 @ B ) )
            & ( P @ X ) ) )
      = ( ? [X: b] :
            ( ( member_b @ X @ A2 )
            & ( P @ X ) )
        | ? [X: b] :
            ( ( member_b @ X @ B )
            & ( P @ X ) ) ) ) ).

% bex_Un
thf(fact_314_ball__Un,axiom,
    ! [A2: set_nat,B: set_nat,P: nat > $o] :
      ( ( ! [X: nat] :
            ( ( member_nat @ X @ ( sup_sup_set_nat @ A2 @ B ) )
           => ( P @ X ) ) )
      = ( ! [X: nat] :
            ( ( member_nat @ X @ A2 )
           => ( P @ X ) )
        & ! [X: nat] :
            ( ( member_nat @ X @ B )
           => ( P @ X ) ) ) ) ).

% ball_Un
thf(fact_315_ball__Un,axiom,
    ! [A2: set_a,B: set_a,P: a > $o] :
      ( ( ! [X: a] :
            ( ( member_a @ X @ ( sup_sup_set_a @ A2 @ B ) )
           => ( P @ X ) ) )
      = ( ! [X: a] :
            ( ( member_a @ X @ A2 )
           => ( P @ X ) )
        & ! [X: a] :
            ( ( member_a @ X @ B )
           => ( P @ X ) ) ) ) ).

% ball_Un
thf(fact_316_ball__Un,axiom,
    ! [A2: set_b,B: set_b,P: b > $o] :
      ( ( ! [X: b] :
            ( ( member_b @ X @ ( sup_sup_set_b @ A2 @ B ) )
           => ( P @ X ) ) )
      = ( ! [X: b] :
            ( ( member_b @ X @ A2 )
           => ( P @ X ) )
        & ! [X: b] :
            ( ( member_b @ X @ B )
           => ( P @ X ) ) ) ) ).

% ball_Un
thf(fact_317_Un__assoc,axiom,
    ! [A2: set_nat,B: set_nat,C2: set_nat] :
      ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ C2 )
      = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).

% Un_assoc
thf(fact_318_Un__assoc,axiom,
    ! [A2: set_a,B: set_a,C2: set_a] :
      ( ( sup_sup_set_a @ ( sup_sup_set_a @ A2 @ B ) @ C2 )
      = ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B @ C2 ) ) ) ).

% Un_assoc
thf(fact_319_Un__assoc,axiom,
    ! [A2: set_b,B: set_b,C2: set_b] :
      ( ( sup_sup_set_b @ ( sup_sup_set_b @ A2 @ B ) @ C2 )
      = ( sup_sup_set_b @ A2 @ ( sup_sup_set_b @ B @ C2 ) ) ) ).

% Un_assoc
thf(fact_320_Un__absorb,axiom,
    ! [A2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ A2 )
      = A2 ) ).

% Un_absorb
thf(fact_321_Un__absorb,axiom,
    ! [A2: set_a] :
      ( ( sup_sup_set_a @ A2 @ A2 )
      = A2 ) ).

% Un_absorb
thf(fact_322_Un__absorb,axiom,
    ! [A2: set_b] :
      ( ( sup_sup_set_b @ A2 @ A2 )
      = A2 ) ).

% Un_absorb
thf(fact_323_Un__commute,axiom,
    ( sup_sup_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A3 ) ) ) ).

% Un_commute
thf(fact_324_Un__commute,axiom,
    ( sup_sup_set_a
    = ( ^ [A3: set_a,B3: set_a] : ( sup_sup_set_a @ B3 @ A3 ) ) ) ).

% Un_commute
thf(fact_325_Un__commute,axiom,
    ( sup_sup_set_b
    = ( ^ [A3: set_b,B3: set_b] : ( sup_sup_set_b @ B3 @ A3 ) ) ) ).

% Un_commute
thf(fact_326_Un__left__absorb,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B ) )
      = ( sup_sup_set_nat @ A2 @ B ) ) ).

% Un_left_absorb
thf(fact_327_Un__left__absorb,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ A2 @ B ) )
      = ( sup_sup_set_a @ A2 @ B ) ) ).

% Un_left_absorb
thf(fact_328_Un__left__absorb,axiom,
    ! [A2: set_b,B: set_b] :
      ( ( sup_sup_set_b @ A2 @ ( sup_sup_set_b @ A2 @ B ) )
      = ( sup_sup_set_b @ A2 @ B ) ) ).

% Un_left_absorb
thf(fact_329_Un__left__commute,axiom,
    ! [A2: set_nat,B: set_nat,C2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C2 ) )
      = ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A2 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_330_Un__left__commute,axiom,
    ! [A2: set_a,B: set_a,C2: set_a] :
      ( ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B @ C2 ) )
      = ( sup_sup_set_a @ B @ ( sup_sup_set_a @ A2 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_331_Un__left__commute,axiom,
    ! [A2: set_b,B: set_b,C2: set_b] :
      ( ( sup_sup_set_b @ A2 @ ( sup_sup_set_b @ B @ C2 ) )
      = ( sup_sup_set_b @ B @ ( sup_sup_set_b @ A2 @ C2 ) ) ) ).

% Un_left_commute
thf(fact_332_sup__Un__eq,axiom,
    ! [R: set_Re5178783185447174953term_a,S: set_Re5178783185447174953term_a] :
      ( ( sup_su927640514972811808rm_a_o
        @ ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ R )
        @ ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ S ) )
      = ( ^ [X: relational_term_a] : ( member5466445112152945266term_a @ X @ ( sup_su8474575085660790013term_a @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_333_sup__Un__eq,axiom,
    ! [R: set_list_a,S: set_list_a] :
      ( ( sup_sup_list_a_o
        @ ^ [X: list_a] : ( member_list_a @ X @ R )
        @ ^ [X: list_a] : ( member_list_a @ X @ S ) )
      = ( ^ [X: list_a] : ( member_list_a @ X @ ( sup_sup_set_list_a @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_334_sup__Un__eq,axiom,
    ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
      ( ( sup_su798857527126471912_nat_o
        @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ R )
        @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ S ) )
      = ( ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ ( sup_su6327502436637775413at_nat @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_335_sup__Un__eq,axiom,
    ! [R: set_a,S: set_a] :
      ( ( sup_sup_a_o
        @ ^ [X: a] : ( member_a @ X @ R )
        @ ^ [X: a] : ( member_a @ X @ S ) )
      = ( ^ [X: a] : ( member_a @ X @ ( sup_sup_set_a @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_336_sup__Un__eq,axiom,
    ! [R: set_b,S: set_b] :
      ( ( sup_sup_b_o
        @ ^ [X: b] : ( member_b @ X @ R )
        @ ^ [X: b] : ( member_b @ X @ S ) )
      = ( ^ [X: b] : ( member_b @ X @ ( sup_sup_set_b @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_337_sup__Un__eq,axiom,
    ! [R: set_nat,S: set_nat] :
      ( ( sup_sup_nat_o
        @ ^ [X: nat] : ( member_nat @ X @ R )
        @ ^ [X: nat] : ( member_nat @ X @ S ) )
      = ( ^ [X: nat] : ( member_nat @ X @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).

% sup_Un_eq
thf(fact_338_un__Exists2__def,axiom,
    ( relati5591445451228332309s2_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [X71: nat,X72: relational_fmla_a_b] : X72 ) ) ).

% un_Exists2_def
thf(fact_339_un__Disj2__def,axiom,
    ( relati8930481278502636917j2_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [X61: relational_fmla_a_b,X62: relational_fmla_a_b] : X62
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).

% un_Disj2_def
thf(fact_340_un__Disj1__def,axiom,
    ( relati3334262663314506228j1_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [X61: relational_fmla_a_b,X62: relational_fmla_a_b] : X61
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).

% un_Disj1_def
thf(fact_341_un__Neg__def,axiom,
    ( relati5982302313924697647eg_a_b
    = ( relati5004271986839035796la_a_b
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: $o] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi1992772029223621943la_a_b
      @ ^ [X42: relational_fmla_a_b] : X42
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi1992772029223621943la_a_b ) ) ).

% un_Neg_def
thf(fact_342_fmla_Ocollapse_I4_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati4321004860440572638eg_a_b @ Fmla )
     => ( ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(4)
thf(fact_343_un__Pred1__def,axiom,
    ( relati91604085239814319d1_a_b
    = ( relati4214321532279288650_b_a_b
      @ ^ [X11: b,X12: list_R6823256787227418703term_a] : X11
      @ ^ [Uu2: $o] : undefined_b
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefined_b
      @ ^ [Uu2: relational_fmla_a_b] : undefined_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_b
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_b
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefined_b ) ) ).

% un_Pred1_def
thf(fact_344_fmla_Omap__sel_I11_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati9085378286500150737at_nat @ A )
     => ( ( relati833352998049382069at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati833352998049382069at_nat @ A ) ) ) ).

% fmla.map_sel(11)
thf(fact_345_fmla_Omap__sel_I11_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati5212983245281121968ts_a_b @ A )
     => ( ( relati9218598872894977428s1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati9218598872894977428s1_a_b @ A ) ) ) ).

% fmla.map_sel(11)
thf(fact_346_fmla_Omap__sel_I4_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relational_is_Eq_a_b @ A )
     => ( ( relati5459635069493737188q1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati5459635069493737188q1_a_b @ A ) ) ) ).

% fmla.map_sel(4)
thf(fact_347_fmla_Omap__sel_I4_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati8448989431961727361at_nat @ A )
     => ( ( relati7752113415457843205at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati7752113415457843205at_nat @ A ) ) ) ).

% fmla.map_sel(4)
thf(fact_348_un__Exists1__def,axiom,
    ( relati9218598872894977428s1_a_b
    = ( relati5872380936867403461_a_nat
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefined_nat
      @ ^ [Uu2: $o] : undefined_nat
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefined_nat
      @ ^ [Uu2: relational_fmla_a_b] : undefined_nat
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
      @ ^ [X71: nat,X72: relational_fmla_a_b] : X71 ) ) ).

% un_Exists1_def
thf(fact_349_un__Eq1__def,axiom,
    ( relati5459635069493737188q1_a_b
    = ( relati5872380936867403461_a_nat
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefined_nat
      @ ^ [Uu2: $o] : undefined_nat
      @ ^ [X31: nat,X32: relational_term_a] : X31
      @ ^ [Uu2: relational_fmla_a_b] : undefined_nat
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_nat
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefined_nat ) ) ).

% un_Eq1_def
thf(fact_350_fmla_Osel_I6_J,axiom,
    ! [X4: relational_fmla_a_b] :
      ( ( relati5982302313924697647eg_a_b @ ( relational_Neg_a_b @ X4 ) )
      = X4 ) ).

% fmla.sel(6)
thf(fact_351_fmla_Omap__sel_I9_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( relati6345216041161915157at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati6345216041161915157at_nat @ A ) ) ) ) ).

% fmla.map_sel(9)
thf(fact_352_fmla_Omap__sel_I9_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( relati3334262663314506228j1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati3334262663314506228j1_a_b @ A ) ) ) ) ).

% fmla.map_sel(9)
thf(fact_353_fmla_Omap__sel_I10_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( relati9167590591273366294at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati9167590591273366294at_nat @ A ) ) ) ) ).

% fmla.map_sel(10)
thf(fact_354_fmla_Omap__sel_I10_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( relati8930481278502636917j2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati8930481278502636917j2_a_b @ A ) ) ) ) ).

% fmla.map_sel(10)
thf(fact_355_fmla_Oset__sel_I6_J,axiom,
    ! [A: relational_fmla_a_b,Xi: a] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( member_a @ Xi @ ( relati3071123380395136021la_a_b @ ( relati3334262663314506228j1_a_b @ A ) ) )
       => ( member_a @ Xi @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(6)
thf(fact_356_fmla_Oset__sel_I6_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xi: nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( member_nat @ Xi @ ( relati6321887899146193334at_nat @ ( relati6345216041161915157at_nat @ A ) ) )
       => ( member_nat @ Xi @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(6)
thf(fact_357_fmla_Oset__sel_I7_J,axiom,
    ! [A: relational_fmla_a_b,Xk: a] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( member_a @ Xk @ ( relati3071123380395136021la_a_b @ ( relati8930481278502636917j2_a_b @ A ) ) )
       => ( member_a @ Xk @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(7)
thf(fact_358_fmla_Oset__sel_I7_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xk: nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( member_nat @ Xk @ ( relati6321887899146193334at_nat @ ( relati9167590591273366294at_nat @ A ) ) )
       => ( member_nat @ Xk @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(7)
thf(fact_359_fmla_Omap__sel_I6_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati4321004860440572638eg_a_b @ A )
     => ( ( relati5982302313924697647eg_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5982302313924697647eg_a_b @ A ) ) ) ) ).

% fmla.map_sel(6)
thf(fact_360_fmla_Omap__sel_I6_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati7690703371482896639at_nat @ A )
     => ( ( relati1324934566682089680at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati1324934566682089680at_nat @ A ) ) ) ) ).

% fmla.map_sel(6)
thf(fact_361_fmla_Oset__sel_I13_J,axiom,
    ! [A: relational_fmla_a_b,Xv: b] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( member_b @ Xv @ ( relati8924981150291758614la_a_b @ ( relati3334262663314506228j1_a_b @ A ) ) )
       => ( member_b @ Xv @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(13)
thf(fact_362_fmla_Oset__sel_I13_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xv: nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( member_nat @ Xv @ ( relati2567137625159299127at_nat @ ( relati6345216041161915157at_nat @ A ) ) )
       => ( member_nat @ Xv @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(13)
thf(fact_363_fmla_Oset__sel_I14_J,axiom,
    ! [A: relational_fmla_a_b,Xx: b] :
      ( ( relati5350680195807439568sj_a_b @ A )
     => ( ( member_b @ Xx @ ( relati8924981150291758614la_a_b @ ( relati8930481278502636917j2_a_b @ A ) ) )
       => ( member_b @ Xx @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(14)
thf(fact_364_fmla_Oset__sel_I14_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xx: nat] :
      ( ( relati711756705458397681at_nat @ A )
     => ( ( member_nat @ Xx @ ( relati2567137625159299127at_nat @ ( relati9167590591273366294at_nat @ A ) ) )
       => ( member_nat @ Xx @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(14)
thf(fact_365_fmla_Oset__sel_I3_J,axiom,
    ! [A: relational_fmla_a_b,Xc: a] :
      ( ( relati4321004860440572638eg_a_b @ A )
     => ( ( member_a @ Xc @ ( relati3071123380395136021la_a_b @ ( relati5982302313924697647eg_a_b @ A ) ) )
       => ( member_a @ Xc @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(3)
thf(fact_366_fmla_Oset__sel_I3_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xc: nat] :
      ( ( relati7690703371482896639at_nat @ A )
     => ( ( member_nat @ Xc @ ( relati6321887899146193334at_nat @ ( relati1324934566682089680at_nat @ A ) ) )
       => ( member_nat @ Xc @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(3)
thf(fact_367_fmla_Oset__sel_I10_J,axiom,
    ! [A: relational_fmla_a_b,Xp: b] :
      ( ( relati4321004860440572638eg_a_b @ A )
     => ( ( member_b @ Xp @ ( relati8924981150291758614la_a_b @ ( relati5982302313924697647eg_a_b @ A ) ) )
       => ( member_b @ Xp @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(10)
thf(fact_368_fmla_Oset__sel_I10_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xp: nat] :
      ( ( relati7690703371482896639at_nat @ A )
     => ( ( member_nat @ Xp @ ( relati2567137625159299127at_nat @ ( relati1324934566682089680at_nat @ A ) ) )
       => ( member_nat @ Xp @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(10)
thf(fact_369_fmla_Omap__sel_I12_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati9085378286500150737at_nat @ A )
     => ( ( relati3655727548160833206at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati3655727548160833206at_nat @ A ) ) ) ) ).

% fmla.map_sel(12)
thf(fact_370_fmla_Omap__sel_I12_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati5212983245281121968ts_a_b @ A )
     => ( ( relati5591445451228332309s2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati5591445451228332309s2_a_b @ A ) ) ) ) ).

% fmla.map_sel(12)
thf(fact_371_fmla_Oset__sel_I8_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xm: nat] :
      ( ( relati9085378286500150737at_nat @ A )
     => ( ( member_nat @ Xm @ ( relati6321887899146193334at_nat @ ( relati3655727548160833206at_nat @ A ) ) )
       => ( member_nat @ Xm @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(8)
thf(fact_372_fmla_Oset__sel_I8_J,axiom,
    ! [A: relational_fmla_a_b,Xm: a] :
      ( ( relati5212983245281121968ts_a_b @ A )
     => ( ( member_a @ Xm @ ( relati3071123380395136021la_a_b @ ( relati5591445451228332309s2_a_b @ A ) ) )
       => ( member_a @ Xm @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(8)
thf(fact_373_fmla_Oset__sel_I15_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xz: nat] :
      ( ( relati9085378286500150737at_nat @ A )
     => ( ( member_nat @ Xz @ ( relati2567137625159299127at_nat @ ( relati3655727548160833206at_nat @ A ) ) )
       => ( member_nat @ Xz @ ( relati2567137625159299127at_nat @ A ) ) ) ) ).

% fmla.set_sel(15)
thf(fact_374_fmla_Oset__sel_I15_J,axiom,
    ! [A: relational_fmla_a_b,Xz: b] :
      ( ( relati5212983245281121968ts_a_b @ A )
     => ( ( member_b @ Xz @ ( relati8924981150291758614la_a_b @ ( relati5591445451228332309s2_a_b @ A ) ) )
       => ( member_b @ Xz @ ( relati8924981150291758614la_a_b @ A ) ) ) ) ).

% fmla.set_sel(15)
thf(fact_375_fmla_Omap__sel_I1_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati7894638611541183222at_nat @ A )
     => ( ( relati1808126365878915920at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( F2 @ ( relati1808126365878915920at_nat @ A ) ) ) ) ).

% fmla.map_sel(1)
thf(fact_376_fmla_Omap__sel_I1_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati3644702733014758741ed_a_b @ A )
     => ( ( relati91604085239814319d1_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( F2 @ ( relati91604085239814319d1_a_b @ A ) ) ) ) ).

% fmla.map_sel(1)
thf(fact_377_fmla_Oset__sel_I9_J,axiom,
    ! [A: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ A )
     => ( member_b @ ( relati91604085239814319d1_a_b @ A ) @ ( relati8924981150291758614la_a_b @ A ) ) ) ).

% fmla.set_sel(9)
thf(fact_378_fmla_Oset__sel_I9_J,axiom,
    ! [A: relati7126052417554554232at_nat] :
      ( ( relati7894638611541183222at_nat @ A )
     => ( member_nat @ ( relati1808126365878915920at_nat @ A ) @ ( relati2567137625159299127at_nat @ A ) ) ) ).

% fmla.set_sel(9)
thf(fact_379_sup1CI,axiom,
    ! [B: nat > $o,X3: nat,A2: nat > $o] :
      ( ( ~ ( B @ X3 )
       => ( A2 @ X3 ) )
     => ( sup_sup_nat_o @ A2 @ B @ X3 ) ) ).

% sup1CI
thf(fact_380_fmla_Oexpand,axiom,
    ! [Fmla: relational_fmla_a_b,Fmla3: relational_fmla_a_b] :
      ( ( ( relati3644702733014758741ed_a_b @ Fmla )
        = ( relati3644702733014758741ed_a_b @ Fmla3 ) )
     => ( ( ( relati3644702733014758741ed_a_b @ Fmla )
         => ( ( relati3644702733014758741ed_a_b @ Fmla3 )
           => ( ( ( relati91604085239814319d1_a_b @ Fmla )
                = ( relati91604085239814319d1_a_b @ Fmla3 ) )
              & ( ( relati5687822700427945008d2_a_b @ Fmla )
                = ( relati5687822700427945008d2_a_b @ Fmla3 ) ) ) ) )
       => ( ( ( relati6551038146797045342ol_a_b @ Fmla )
            = ( relati6551038146797045342ol_a_b @ Fmla3 ) )
         => ( ( ( relati6551038146797045342ol_a_b @ Fmla )
             => ( ( relati6551038146797045342ol_a_b @ Fmla3 )
               => ( ( relati2638701775882563405ol_a_b @ Fmla )
                  = ( relati2638701775882563405ol_a_b @ Fmla3 ) ) ) )
           => ( ( ( relational_is_Eq_a_b @ Fmla )
                = ( relational_is_Eq_a_b @ Fmla3 ) )
             => ( ( ( relational_is_Eq_a_b @ Fmla )
                 => ( ( relational_is_Eq_a_b @ Fmla3 )
                   => ( ( ( relati5459635069493737188q1_a_b @ Fmla )
                        = ( relati5459635069493737188q1_a_b @ Fmla3 ) )
                      & ( ( relati1832481647827092069q2_a_b @ Fmla )
                        = ( relati1832481647827092069q2_a_b @ Fmla3 ) ) ) ) )
               => ( ( ( relati4321004860440572638eg_a_b @ Fmla )
                    = ( relati4321004860440572638eg_a_b @ Fmla3 ) )
                 => ( ( ( relati4321004860440572638eg_a_b @ Fmla )
                     => ( ( relati4321004860440572638eg_a_b @ Fmla3 )
                       => ( ( relati5982302313924697647eg_a_b @ Fmla )
                          = ( relati5982302313924697647eg_a_b @ Fmla3 ) ) ) )
                   => ( ( ( relati8168519172193746908nj_a_b @ Fmla )
                        = ( relati8168519172193746908nj_a_b @ Fmla3 ) )
                     => ( ( ( relati8168519172193746908nj_a_b @ Fmla )
                         => ( ( relati8168519172193746908nj_a_b @ Fmla3 )
                           => ( ( ( relati5154284022127734760j1_a_b @ Fmla )
                                = ( relati5154284022127734760j1_a_b @ Fmla3 ) )
                              & ( ( relati1527130600461089641j2_a_b @ Fmla )
                                = ( relati1527130600461089641j2_a_b @ Fmla3 ) ) ) ) )
                       => ( ( ( relati5350680195807439568sj_a_b @ Fmla )
                            = ( relati5350680195807439568sj_a_b @ Fmla3 ) )
                         => ( ( ( relati5350680195807439568sj_a_b @ Fmla )
                             => ( ( relati5350680195807439568sj_a_b @ Fmla3 )
                               => ( ( ( relati3334262663314506228j1_a_b @ Fmla )
                                    = ( relati3334262663314506228j1_a_b @ Fmla3 ) )
                                  & ( ( relati8930481278502636917j2_a_b @ Fmla )
                                    = ( relati8930481278502636917j2_a_b @ Fmla3 ) ) ) ) )
                           => ( ( ( relati5212983245281121968ts_a_b @ Fmla )
                               => ( ( relati5212983245281121968ts_a_b @ Fmla3 )
                                 => ( ( ( relati9218598872894977428s1_a_b @ Fmla )
                                      = ( relati9218598872894977428s1_a_b @ Fmla3 ) )
                                    & ( ( relati5591445451228332309s2_a_b @ Fmla )
                                      = ( relati5591445451228332309s2_a_b @ Fmla3 ) ) ) ) )
                             => ( Fmla = Fmla3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% fmla.expand
thf(fact_381_fmla_Ocase__eq__if,axiom,
    ( relati5004271986839035796la_a_b
    = ( ^ [F12: b > list_R6823256787227418703term_a > relational_fmla_a_b,F22: $o > relational_fmla_a_b,F32: nat > relational_term_a > relational_fmla_a_b,F42: relational_fmla_a_b > relational_fmla_a_b,F52: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F62: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F72: nat > relational_fmla_a_b > relational_fmla_a_b,Fmla2: relational_fmla_a_b] : ( if_Rel1279876242545935705la_a_b @ ( relati3644702733014758741ed_a_b @ Fmla2 ) @ ( F12 @ ( relati91604085239814319d1_a_b @ Fmla2 ) @ ( relati5687822700427945008d2_a_b @ Fmla2 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati6551038146797045342ol_a_b @ Fmla2 ) @ ( F22 @ ( relati2638701775882563405ol_a_b @ Fmla2 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relational_is_Eq_a_b @ Fmla2 ) @ ( F32 @ ( relati5459635069493737188q1_a_b @ Fmla2 ) @ ( relati1832481647827092069q2_a_b @ Fmla2 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati4321004860440572638eg_a_b @ Fmla2 ) @ ( F42 @ ( relati5982302313924697647eg_a_b @ Fmla2 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati8168519172193746908nj_a_b @ Fmla2 ) @ ( F52 @ ( relati5154284022127734760j1_a_b @ Fmla2 ) @ ( relati1527130600461089641j2_a_b @ Fmla2 ) ) @ ( if_Rel1279876242545935705la_a_b @ ( relati5350680195807439568sj_a_b @ Fmla2 ) @ ( F62 @ ( relati3334262663314506228j1_a_b @ Fmla2 ) @ ( relati8930481278502636917j2_a_b @ Fmla2 ) ) @ ( F72 @ ( relati9218598872894977428s1_a_b @ Fmla2 ) @ ( relati5591445451228332309s2_a_b @ Fmla2 ) ) ) ) ) ) ) ) ) ) ).

% fmla.case_eq_if
thf(fact_382_sup1I2,axiom,
    ! [B: nat > $o,X3: nat,A2: nat > $o] :
      ( ( B @ X3 )
     => ( sup_sup_nat_o @ A2 @ B @ X3 ) ) ).

% sup1I2
thf(fact_383_sup1I1,axiom,
    ! [A2: nat > $o,X3: nat,B: nat > $o] :
      ( ( A2 @ X3 )
     => ( sup_sup_nat_o @ A2 @ B @ X3 ) ) ).

% sup1I1
thf(fact_384_sup1E,axiom,
    ! [A2: nat > $o,B: nat > $o,X3: nat] :
      ( ( sup_sup_nat_o @ A2 @ B @ X3 )
     => ( ~ ( A2 @ X3 )
       => ( B @ X3 ) ) ) ).

% sup1E
thf(fact_385_fmla_Ocollapse_I7_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5212983245281121968ts_a_b @ Fmla )
     => ( ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(7)
thf(fact_386_fmla_Ocollapse_I6_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati5350680195807439568sj_a_b @ Fmla )
     => ( ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(6)
thf(fact_387_fmla_Oinject_I6_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ( ( ( relational_Disj_a_b @ X612 @ X622 )
        = ( relational_Disj_a_b @ Y61 @ Y62 ) )
      = ( ( X612 = Y61 )
        & ( X622 = Y62 ) ) ) ).

% fmla.inject(6)
thf(fact_388_fmla_Oinject_I7_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
      ( ( ( relati591517084277583526ts_a_b @ X712 @ X722 )
        = ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) )
      = ( ( X712 = Y71 )
        & ( X722 = Y72 ) ) ) ).

% fmla.inject(7)
thf(fact_389_fmla_Opred__inject_I6_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: relati7126052417554554232at_nat,Aa: relati7126052417554554232at_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati7949253455907248103at_nat @ A @ Aa ) )
      = ( ( relati6725209092851823240at_nat @ P1 @ P2 @ A )
        & ( relati6725209092851823240at_nat @ P1 @ P2 @ Aa ) ) ) ).

% fmla.pred_inject(6)
thf(fact_390_fmla_Opred__inject_I6_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: relational_fmla_a_b,Aa: relational_fmla_a_b] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Disj_a_b @ A @ Aa ) )
      = ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ A )
        & ( relati3660035184769383399la_a_b @ P1 @ P2 @ Aa ) ) ) ).

% fmla.pred_inject(6)
thf(fact_391_fmla_Opred__inject_I7_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: nat,Aa: relati7126052417554554232at_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati524807352525265095at_nat @ A @ Aa ) )
      = ( relati6725209092851823240at_nat @ P1 @ P2 @ Aa ) ) ).

% fmla.pred_inject(7)
thf(fact_392_fmla_Opred__inject_I7_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: nat,Aa: relational_fmla_a_b] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relati591517084277583526ts_a_b @ A @ Aa ) )
      = ( relati3660035184769383399la_a_b @ P1 @ P2 @ Aa ) ) ).

% fmla.pred_inject(7)
thf(fact_393_fmla_Odistinct_I41_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Disj_a_b @ X612 @ X622 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(41)
thf(fact_394_un__Eq2__def,axiom,
    ( relati1832481647827092069q2_a_b
    = ( relati8448653393198995860term_a
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefi4938429376670434993term_a
      @ ^ [Uu2: $o] : undefi4938429376670434993term_a
      @ ^ [X31: nat,X32: relational_term_a] : X32
      @ ^ [Uu2: relational_fmla_a_b] : undefi4938429376670434993term_a
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi4938429376670434993term_a ) ) ).

% un_Eq2_def
thf(fact_395_un__Pred2__def,axiom,
    ( relati5687822700427945008d2_a_b
    = ( relati130711325911436314term_a
      @ ^ [X11: b,X12: list_R6823256787227418703term_a] : X12
      @ ^ [Uu2: $o] : undefi8139585145400706743term_a
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefi8139585145400706743term_a
      @ ^ [Uu2: relational_fmla_a_b] : undefi8139585145400706743term_a
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefi8139585145400706743term_a ) ) ).

% un_Pred2_def
thf(fact_396_fmla_Odistinct_I37_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relational_Conj_a_b @ X51 @ X52 )
     != ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.distinct(37)
thf(fact_397_fmla_Odistinct_I39_J,axiom,
    ! [X51: relational_fmla_a_b,X52: relational_fmla_a_b,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Conj_a_b @ X51 @ X52 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(39)
thf(fact_398_fmla_Odistinct_I33_J,axiom,
    ! [X4: relational_fmla_a_b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relational_Neg_a_b @ X4 )
     != ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.distinct(33)
thf(fact_399_fmla_Odistinct_I35_J,axiom,
    ! [X4: relational_fmla_a_b,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Neg_a_b @ X4 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(35)
thf(fact_400_fmla_Osimps_I69_J,axiom,
    ! [F1: a > a,F2: b > b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = ( relational_Disj_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X612 ) @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X622 ) ) ) ).

% fmla.simps(69)
thf(fact_401_fmla_Osimps_I69_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati7949253455907248103at_nat @ X612 @ X622 ) )
      = ( relati7949253455907248103at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X612 ) @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X622 ) ) ) ).

% fmla.simps(69)
thf(fact_402_fmla_Osimps_I70_J,axiom,
    ! [F1: a > a,F2: b > b,X712: nat,X722: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = ( relati591517084277583526ts_a_b @ X712 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X722 ) ) ) ).

% fmla.simps(70)
thf(fact_403_fmla_Osimps_I70_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X712: nat,X722: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati524807352525265095at_nat @ X712 @ X722 ) )
      = ( relati524807352525265095at_nat @ X712 @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X722 ) ) ) ).

% fmla.simps(70)
thf(fact_404_fmla_Oset__intros_I7_J,axiom,
    ! [Yk: a,X622: relational_fmla_a_b,X612: relational_fmla_a_b] :
      ( ( member_a @ Yk @ ( relati3071123380395136021la_a_b @ X622 ) )
     => ( member_a @ Yk @ ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(7)
thf(fact_405_fmla_Oset__intros_I7_J,axiom,
    ! [Yk: nat,X622: relati7126052417554554232at_nat,X612: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yk @ ( relati6321887899146193334at_nat @ X622 ) )
     => ( member_nat @ Yk @ ( relati6321887899146193334at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(7)
thf(fact_406_fmla_Oset__intros_I6_J,axiom,
    ! [Yi: a,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( member_a @ Yi @ ( relati3071123380395136021la_a_b @ X612 ) )
     => ( member_a @ Yi @ ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(6)
thf(fact_407_fmla_Oset__intros_I6_J,axiom,
    ! [Yi: nat,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yi @ ( relati6321887899146193334at_nat @ X612 ) )
     => ( member_nat @ Yi @ ( relati6321887899146193334at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(6)
thf(fact_408_fmla_Oset__intros_I14_J,axiom,
    ! [Za: b,X622: relational_fmla_a_b,X612: relational_fmla_a_b] :
      ( ( member_b @ Za @ ( relati8924981150291758614la_a_b @ X622 ) )
     => ( member_b @ Za @ ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(14)
thf(fact_409_fmla_Oset__intros_I14_J,axiom,
    ! [Za: nat,X622: relati7126052417554554232at_nat,X612: relati7126052417554554232at_nat] :
      ( ( member_nat @ Za @ ( relati2567137625159299127at_nat @ X622 ) )
     => ( member_nat @ Za @ ( relati2567137625159299127at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(14)
thf(fact_410_fmla_Oset__intros_I13_J,axiom,
    ! [Yy: b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( member_b @ Yy @ ( relati8924981150291758614la_a_b @ X612 ) )
     => ( member_b @ Yy @ ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(13)
thf(fact_411_fmla_Oset__intros_I13_J,axiom,
    ! [Yy: nat,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ( ( member_nat @ Yy @ ( relati2567137625159299127at_nat @ X612 ) )
     => ( member_nat @ Yy @ ( relati2567137625159299127at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) ) ) ) ).

% fmla.set_intros(13)
thf(fact_412_fmla_Osimps_I126_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ( ( relati3071123380395136021la_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = ( relati3071123380395136021la_a_b @ X722 ) ) ).

% fmla.simps(126)
thf(fact_413_fmla_Osimps_I126_J,axiom,
    ! [X712: nat,X722: relati7126052417554554232at_nat] :
      ( ( relati6321887899146193334at_nat @ ( relati524807352525265095at_nat @ X712 @ X722 ) )
      = ( relati6321887899146193334at_nat @ X722 ) ) ).

% fmla.simps(126)
thf(fact_414_fmla_Oset__intros_I8_J,axiom,
    ! [Ym: a,X722: relational_fmla_a_b,X712: nat] :
      ( ( member_a @ Ym @ ( relati3071123380395136021la_a_b @ X722 ) )
     => ( member_a @ Ym @ ( relati3071123380395136021la_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ) ) ).

% fmla.set_intros(8)
thf(fact_415_fmla_Oset__intros_I8_J,axiom,
    ! [Ym: nat,X722: relati7126052417554554232at_nat,X712: nat] :
      ( ( member_nat @ Ym @ ( relati6321887899146193334at_nat @ X722 ) )
     => ( member_nat @ Ym @ ( relati6321887899146193334at_nat @ ( relati524807352525265095at_nat @ X712 @ X722 ) ) ) ) ).

% fmla.set_intros(8)
thf(fact_416_fmla_Osimps_I133_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ( ( relati8924981150291758614la_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = ( relati8924981150291758614la_a_b @ X722 ) ) ).

% fmla.simps(133)
thf(fact_417_fmla_Osimps_I133_J,axiom,
    ! [X712: nat,X722: relati7126052417554554232at_nat] :
      ( ( relati2567137625159299127at_nat @ ( relati524807352525265095at_nat @ X712 @ X722 ) )
      = ( relati2567137625159299127at_nat @ X722 ) ) ).

% fmla.simps(133)
thf(fact_418_fmla_Oset__intros_I15_J,axiom,
    ! [Zc: b,X722: relational_fmla_a_b,X712: nat] :
      ( ( member_b @ Zc @ ( relati8924981150291758614la_a_b @ X722 ) )
     => ( member_b @ Zc @ ( relati8924981150291758614la_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ) ) ).

% fmla.set_intros(15)
thf(fact_419_fmla_Oset__intros_I15_J,axiom,
    ! [Zc: nat,X722: relati7126052417554554232at_nat,X712: nat] :
      ( ( member_nat @ Zc @ ( relati2567137625159299127at_nat @ X722 ) )
     => ( member_nat @ Zc @ ( relati2567137625159299127at_nat @ ( relati524807352525265095at_nat @ X712 @ X722 ) ) ) ) ).

% fmla.set_intros(15)
thf(fact_420_sat_Osimps_I6_J,axiom,
    ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Disj_a_b @ Phi @ Psi ) @ I @ Sigma )
      = ( ( relational_sat_a_b @ Phi @ I @ Sigma )
        | ( relational_sat_a_b @ Psi @ I @ Sigma ) ) ) ).

% sat.simps(6)
thf(fact_421_fmla_Odisc_I41_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] : ( relati5350680195807439568sj_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(41)
thf(fact_422_fmla_Odisc_I34_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati8168519172193746908nj_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(34)
thf(fact_423_fmla_OdiscI_I6_J,axiom,
    ! [Fmla: relational_fmla_a_b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( Fmla
        = ( relational_Disj_a_b @ X612 @ X622 ) )
     => ( relati5350680195807439568sj_a_b @ Fmla ) ) ).

% fmla.discI(6)
thf(fact_424_is__Disj__def,axiom,
    ( relati5350680195807439568sj_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X61: relational_fmla_a_b,X62: relational_fmla_a_b] :
          ( Fmla2
          = ( relational_Disj_a_b @ X61 @ X62 ) ) ) ) ).

% is_Disj_def
thf(fact_425_fmla_Odisc_I42_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relati5350680195807439568sj_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(42)
thf(fact_426_fmla_Odisc_I35_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relati8168519172193746908nj_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(35)
thf(fact_427_fmla_Odisc_I6_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati3644702733014758741ed_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(6)
thf(fact_428_fmla_Odisc_I27_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati4321004860440572638eg_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(27)
thf(fact_429_fmla_Odisc_I20_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relational_is_Eq_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(20)
thf(fact_430_fmla_Odisc_I13_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati6551038146797045342ol_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(13)
thf(fact_431_fmla_Osimps_I55_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = ( F6 @ X612 @ X622 ) ) ).

% fmla.simps(55)
thf(fact_432_fmla_Odisc_I7_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relati3644702733014758741ed_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(7)
thf(fact_433_fmla_Odisc_I28_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relati4321004860440572638eg_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(28)
thf(fact_434_fmla_Odisc_I21_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relational_is_Eq_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(21)
thf(fact_435_fmla_Odisc_I14_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ~ ( relati6551038146797045342ol_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(14)
thf(fact_436_fmla_Osimps_I56_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X712: nat,X722: relational_fmla_a_b] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = ( F7 @ X712 @ X722 ) ) ).

% fmla.simps(56)
thf(fact_437_fmla_Odisc_I48_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.disc(48)
thf(fact_438_fmla_Odisc_I49_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] : ( relati5212983245281121968ts_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.disc(49)
thf(fact_439_fmla_OdiscI_I7_J,axiom,
    ! [Fmla: relational_fmla_a_b,X712: nat,X722: relational_fmla_a_b] :
      ( ( Fmla
        = ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
     => ( relati5212983245281121968ts_a_b @ Fmla ) ) ).

% fmla.discI(7)
thf(fact_440_is__Exists__def,axiom,
    ( relati5212983245281121968ts_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X71: nat,X72: relational_fmla_a_b] :
          ( Fmla2
          = ( relati591517084277583526ts_a_b @ X71 @ X72 ) ) ) ) ).

% is_Exists_def
thf(fact_441_fmla_Osel_I10_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati8930481278502636917j2_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = X622 ) ).

% fmla.sel(10)
thf(fact_442_fmla_Osel_I9_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati3334262663314506228j1_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = X612 ) ).

% fmla.sel(9)
thf(fact_443_fmla_Osel_I12_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ( ( relati5591445451228332309s2_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = X722 ) ).

% fmla.sel(12)
thf(fact_444_fmla_Osel_I11_J,axiom,
    ! [X712: nat,X722: relational_fmla_a_b] :
      ( ( relati9218598872894977428s1_a_b @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) )
      = X712 ) ).

% fmla.sel(11)
thf(fact_445_fmla_Osimps_I125_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati3071123380395136021la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = ( sup_sup_set_a @ ( relati3071123380395136021la_a_b @ X612 ) @ ( relati3071123380395136021la_a_b @ X622 ) ) ) ).

% fmla.simps(125)
thf(fact_446_fmla_Osimps_I125_J,axiom,
    ! [X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ( ( relati6321887899146193334at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) )
      = ( sup_sup_set_nat @ ( relati6321887899146193334at_nat @ X612 ) @ ( relati6321887899146193334at_nat @ X622 ) ) ) ).

% fmla.simps(125)
thf(fact_447_fmla_Osimps_I132_J,axiom,
    ! [X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relati8924981150291758614la_a_b @ ( relational_Disj_a_b @ X612 @ X622 ) )
      = ( sup_sup_set_b @ ( relati8924981150291758614la_a_b @ X612 ) @ ( relati8924981150291758614la_a_b @ X622 ) ) ) ).

% fmla.simps(132)
thf(fact_448_fmla_Osimps_I132_J,axiom,
    ! [X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ( ( relati2567137625159299127at_nat @ ( relati7949253455907248103at_nat @ X612 @ X622 ) )
      = ( sup_sup_set_nat @ ( relati2567137625159299127at_nat @ X612 ) @ ( relati2567137625159299127at_nat @ X622 ) ) ) ).

% fmla.simps(132)
thf(fact_449_fv_Osimps_I6_J,axiom,
    ! [Phi: relational_fmla_a_b,Psi: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relational_Disj_a_b @ Phi @ Psi ) )
      = ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi ) @ ( relational_fv_a_b @ Psi ) ) ) ).

% fv.simps(6)
thf(fact_450_exists__def,axiom,
    ( relati3989891337220013914ts_a_b
    = ( ^ [X: nat,Q2: relational_fmla_a_b] : ( if_Rel1279876242545935705la_a_b @ ( member_nat @ X @ ( relational_fv_a_b @ Q2 ) ) @ ( relati591517084277583526ts_a_b @ X @ Q2 ) @ Q2 ) ) ) ).

% exists_def
thf(fact_451_exists__Exists,axiom,
    ! [X3: nat,Q: relational_fmla_a_b] :
      ( ( member_nat @ X3 @ ( relational_fv_a_b @ Q ) )
     => ( ( relati3989891337220013914ts_a_b @ X3 @ Q )
        = ( relati591517084277583526ts_a_b @ X3 @ Q ) ) ) ).

% exists_Exists
thf(fact_452_un__Bool__def,axiom,
    ( relati2638701775882563405ol_a_b
    = ( relati6637215556741570915_b_a_o
      @ ^ [Uu2: b,Uv2: list_R6823256787227418703term_a] : undefined_o
      @ ^ [X22: $o] : X22
      @ ^ [Uu2: nat,Uv2: relational_term_a] : undefined_o
      @ ^ [Uu2: relational_fmla_a_b] : undefined_o
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_o
      @ ^ [Uu2: relational_fmla_a_b,Uv2: relational_fmla_a_b] : undefined_o
      @ ^ [Uu2: nat,Uv2: relational_fmla_a_b] : undefined_o ) ) ).

% un_Bool_def
thf(fact_453_boolean__algebra__cancel_Osup1,axiom,
    ! [A2: set_nat,K: set_nat,A: set_nat,B2: set_nat] :
      ( ( A2
        = ( sup_sup_set_nat @ K @ A ) )
     => ( ( sup_sup_set_nat @ A2 @ B2 )
        = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_454_boolean__algebra__cancel_Osup1,axiom,
    ! [A2: set_a,K: set_a,A: set_a,B2: set_a] :
      ( ( A2
        = ( sup_sup_set_a @ K @ A ) )
     => ( ( sup_sup_set_a @ A2 @ B2 )
        = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_455_boolean__algebra__cancel_Osup1,axiom,
    ! [A2: set_b,K: set_b,A: set_b,B2: set_b] :
      ( ( A2
        = ( sup_sup_set_b @ K @ A ) )
     => ( ( sup_sup_set_b @ A2 @ B2 )
        = ( sup_sup_set_b @ K @ ( sup_sup_set_b @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_456_boolean__algebra__cancel_Osup1,axiom,
    ! [A2: nat > $o,K: nat > $o,A: nat > $o,B2: nat > $o] :
      ( ( A2
        = ( sup_sup_nat_o @ K @ A ) )
     => ( ( sup_sup_nat_o @ A2 @ B2 )
        = ( sup_sup_nat_o @ K @ ( sup_sup_nat_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup1
thf(fact_457_boolean__algebra__cancel_Osup2,axiom,
    ! [B: set_nat,K: set_nat,B2: set_nat,A: set_nat] :
      ( ( B
        = ( sup_sup_set_nat @ K @ B2 ) )
     => ( ( sup_sup_set_nat @ A @ B )
        = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_458_boolean__algebra__cancel_Osup2,axiom,
    ! [B: set_a,K: set_a,B2: set_a,A: set_a] :
      ( ( B
        = ( sup_sup_set_a @ K @ B2 ) )
     => ( ( sup_sup_set_a @ A @ B )
        = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_459_boolean__algebra__cancel_Osup2,axiom,
    ! [B: set_b,K: set_b,B2: set_b,A: set_b] :
      ( ( B
        = ( sup_sup_set_b @ K @ B2 ) )
     => ( ( sup_sup_set_b @ A @ B )
        = ( sup_sup_set_b @ K @ ( sup_sup_set_b @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_460_boolean__algebra__cancel_Osup2,axiom,
    ! [B: nat > $o,K: nat > $o,B2: nat > $o,A: nat > $o] :
      ( ( B
        = ( sup_sup_nat_o @ K @ B2 ) )
     => ( ( sup_sup_nat_o @ A @ B )
        = ( sup_sup_nat_o @ K @ ( sup_sup_nat_o @ A @ B2 ) ) ) ) ).

% boolean_algebra_cancel.sup2
thf(fact_461_fmla_Omap__sel_I3_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati6551038146797045342ol_a_b @ A )
     => ( ( relati2638701775882563405ol_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati2638701775882563405ol_a_b @ A ) ) ) ).

% fmla.map_sel(3)
thf(fact_462_fmla_Omap__sel_I3_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati6819674536432757887at_nat @ A )
     => ( ( relati6920817008271761646at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati6920817008271761646at_nat @ A ) ) ) ).

% fmla.map_sel(3)
thf(fact_463_fmla_Osplit__sel,axiom,
    ! [P: relational_fmla_a_b > $o,F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,Fmla: relational_fmla_a_b] :
      ( ( P @ ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
      = ( ( ( Fmla
            = ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
         => ( P @ ( F1 @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
         => ( P @ ( F2 @ ( relati2638701775882563405ol_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
         => ( P @ ( F3 @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
         => ( P @ ( F4 @ ( relati5982302313924697647eg_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
         => ( P @ ( F5 @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
         => ( P @ ( F6 @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) ) )
        & ( ( Fmla
            = ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) )
         => ( P @ ( F7 @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ).

% fmla.split_sel
thf(fact_464_fmla_Osplit__sel__asm,axiom,
    ! [P: relational_fmla_a_b > $o,F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,Fmla: relational_fmla_a_b] :
      ( ( P @ ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ Fmla ) )
      = ( ~ ( ( ( Fmla
                = ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
              & ~ ( P @ ( F1 @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
              & ~ ( P @ ( F2 @ ( relati2638701775882563405ol_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
              & ~ ( P @ ( F3 @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
              & ~ ( P @ ( F4 @ ( relati5982302313924697647eg_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
              & ~ ( P @ ( F5 @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
              & ~ ( P @ ( F6 @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) ) )
            | ( ( Fmla
                = ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) )
              & ~ ( P @ ( F7 @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ) ).

% fmla.split_sel_asm
thf(fact_465_fmla_Oexhaust__sel,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( Fmla
       != ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) ) )
     => ( ( Fmla
         != ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) ) )
       => ( ( Fmla
           != ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) ) )
         => ( ( Fmla
             != ( relational_Neg_a_b @ ( relati5982302313924697647eg_a_b @ Fmla ) ) )
           => ( ( Fmla
               != ( relational_Conj_a_b @ ( relati5154284022127734760j1_a_b @ Fmla ) @ ( relati1527130600461089641j2_a_b @ Fmla ) ) )
             => ( ( Fmla
                 != ( relational_Disj_a_b @ ( relati3334262663314506228j1_a_b @ Fmla ) @ ( relati8930481278502636917j2_a_b @ Fmla ) ) )
               => ( Fmla
                  = ( relati591517084277583526ts_a_b @ ( relati9218598872894977428s1_a_b @ Fmla ) @ ( relati5591445451228332309s2_a_b @ Fmla ) ) ) ) ) ) ) ) ) ).

% fmla.exhaust_sel
thf(fact_466_fmla_Oset__cases_I2_J,axiom,
    ! [E: nat,A: relati7126052417554554232at_nat] :
      ( ( member_nat @ E @ ( relati2567137625159299127at_nat @ A ) )
     => ( ! [Z22: list_R114826772386431851rm_nat] :
            ( A
           != ( relati5908763325135257836at_nat @ E @ Z22 ) )
       => ( ! [Z3: relati7126052417554554232at_nat] :
              ( ( A
                = ( relati3679007509795571081at_nat @ Z3 ) )
             => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z3 ) ) )
         => ( ! [Z12: relati7126052417554554232at_nat] :
                ( ? [Z22: relati7126052417554554232at_nat] :
                    ( A
                    = ( relati8628237474745418483at_nat @ Z12 @ Z22 ) )
               => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z12 ) ) )
           => ( ! [Z12: relati7126052417554554232at_nat,Z22: relati7126052417554554232at_nat] :
                  ( ( A
                    = ( relati8628237474745418483at_nat @ Z12 @ Z22 ) )
                 => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z22 ) ) )
             => ( ! [Z12: relati7126052417554554232at_nat] :
                    ( ? [Z22: relati7126052417554554232at_nat] :
                        ( A
                        = ( relati7949253455907248103at_nat @ Z12 @ Z22 ) )
                   => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z12 ) ) )
               => ( ! [Z12: relati7126052417554554232at_nat,Z22: relati7126052417554554232at_nat] :
                      ( ( A
                        = ( relati7949253455907248103at_nat @ Z12 @ Z22 ) )
                     => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z22 ) ) )
                 => ~ ! [Z12: nat,Z22: relati7126052417554554232at_nat] :
                        ( ( A
                          = ( relati524807352525265095at_nat @ Z12 @ Z22 ) )
                       => ~ ( member_nat @ E @ ( relati2567137625159299127at_nat @ Z22 ) ) ) ) ) ) ) ) ) ) ).

% fmla.set_cases(2)
thf(fact_467_fmla_Oset__cases_I2_J,axiom,
    ! [E: b,A: relational_fmla_a_b] :
      ( ( member_b @ E @ ( relati8924981150291758614la_a_b @ A ) )
     => ( ! [Z22: list_R6823256787227418703term_a] :
            ( A
           != ( relational_Pred_b_a @ E @ Z22 ) )
       => ( ! [Z3: relational_fmla_a_b] :
              ( ( A
                = ( relational_Neg_a_b @ Z3 ) )
             => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z3 ) ) )
         => ( ! [Z12: relational_fmla_a_b] :
                ( ? [Z22: relational_fmla_a_b] :
                    ( A
                    = ( relational_Conj_a_b @ Z12 @ Z22 ) )
               => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z12 ) ) )
           => ( ! [Z12: relational_fmla_a_b,Z22: relational_fmla_a_b] :
                  ( ( A
                    = ( relational_Conj_a_b @ Z12 @ Z22 ) )
                 => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) )
             => ( ! [Z12: relational_fmla_a_b] :
                    ( ? [Z22: relational_fmla_a_b] :
                        ( A
                        = ( relational_Disj_a_b @ Z12 @ Z22 ) )
                   => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z12 ) ) )
               => ( ! [Z12: relational_fmla_a_b,Z22: relational_fmla_a_b] :
                      ( ( A
                        = ( relational_Disj_a_b @ Z12 @ Z22 ) )
                     => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) )
                 => ~ ! [Z12: nat,Z22: relational_fmla_a_b] :
                        ( ( A
                          = ( relati591517084277583526ts_a_b @ Z12 @ Z22 ) )
                       => ~ ( member_b @ E @ ( relati8924981150291758614la_a_b @ Z22 ) ) ) ) ) ) ) ) ) ) ).

% fmla.set_cases(2)
thf(fact_468_fmla_Oset__sel_I2_J,axiom,
    ! [A: relational_fmla_a_b,Xb: a] :
      ( ( relational_is_Eq_a_b @ A )
     => ( ( member_a @ Xb @ ( relati2096729434547099208term_a @ ( relati1832481647827092069q2_a_b @ A ) ) )
       => ( member_a @ Xb @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ).

% fmla.set_sel(2)
thf(fact_469_fmla_Oset__sel_I2_J,axiom,
    ! [A: relati7126052417554554232at_nat,Xb: nat] :
      ( ( relati8448989431961727361at_nat @ A )
     => ( ( member_nat @ Xb @ ( relati7416457470477713926rm_nat @ ( relati1351115928714518534at_nat @ A ) ) )
       => ( member_nat @ Xb @ ( relati6321887899146193334at_nat @ A ) ) ) ) ).

% fmla.set_sel(2)
thf(fact_470_fmla_Ocollapse_I3_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relational_is_Eq_a_b @ Fmla )
     => ( ( relational_Eq_a_b @ ( relati5459635069493737188q1_a_b @ Fmla ) @ ( relati1832481647827092069q2_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(3)
thf(fact_471_fmla_Ocollapse_I1_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati3644702733014758741ed_a_b @ Fmla )
     => ( ( relational_Pred_b_a @ ( relati91604085239814319d1_a_b @ Fmla ) @ ( relati5687822700427945008d2_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(1)
thf(fact_472_fmla_Oinject_I1_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,Y11: b,Y12: list_R6823256787227418703term_a] :
      ( ( ( relational_Pred_b_a @ X112 @ X122 )
        = ( relational_Pred_b_a @ Y11 @ Y12 ) )
      = ( ( X112 = Y11 )
        & ( X122 = Y12 ) ) ) ).

% fmla.inject(1)
thf(fact_473_fmla_Oinject_I3_J,axiom,
    ! [X312: nat,X322: relational_term_a,Y31: nat,Y32: relational_term_a] :
      ( ( ( relational_Eq_a_b @ X312 @ X322 )
        = ( relational_Eq_a_b @ Y31 @ Y32 ) )
      = ( ( X312 = Y31 )
        & ( X322 = Y32 ) ) ) ).

% fmla.inject(3)
thf(fact_474_fmla_Oinject_I2_J,axiom,
    ! [X23: $o,Y22: $o] :
      ( ( ( relational_Bool_a_b @ X23 )
        = ( relational_Bool_a_b @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fmla.inject(2)
thf(fact_475_fmla_Ocollapse_I2_J,axiom,
    ! [Fmla: relational_fmla_a_b] :
      ( ( relati6551038146797045342ol_a_b @ Fmla )
     => ( ( relational_Bool_a_b @ ( relati2638701775882563405ol_a_b @ Fmla ) )
        = Fmla ) ) ).

% fmla.collapse(2)
thf(fact_476_fmla_Orel__cases,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,A: relati7126052417554554232at_nat,B2: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ A @ B2 )
     => ( ! [X13: nat,X2a: list_R114826772386431851rm_nat] :
            ( ( A
              = ( relati5908763325135257836at_nat @ X13 @ X2a ) )
           => ! [Y1: nat,Y2a: list_R114826772386431851rm_nat] :
                ( ( B2
                  = ( relati5908763325135257836at_nat @ Y1 @ Y2a ) )
               => ( ( R2 @ X13 @ Y1 )
                 => ~ ( list_a2842054329120570431rm_nat @ ( relati2881564729679077486at_nat @ R1 ) @ X2a @ Y2a ) ) ) )
       => ( ! [X2: $o] :
              ( ( A
                = ( relati4833799250026832501at_nat @ X2 ) )
             => ! [Y3: $o] :
                  ( ( B2
                    = ( relati4833799250026832501at_nat @ Y3 ) )
                 => ( X2 = (~ Y3) ) ) )
         => ( ! [X1a: nat,X2b: relational_term_nat] :
                ( ( A
                  = ( relati8266145252267328119at_nat @ X1a @ X2b ) )
               => ! [Y1a: nat,Y2b: relational_term_nat] :
                    ( ( B2
                      = ( relati8266145252267328119at_nat @ Y1a @ Y2b ) )
                   => ( ( X1a = Y1a )
                     => ~ ( relati2881564729679077486at_nat @ R1 @ X2b @ Y2b ) ) ) )
           => ( ! [Xa2: relati7126052417554554232at_nat] :
                  ( ( A
                    = ( relati3679007509795571081at_nat @ Xa2 ) )
                 => ! [Ya2: relati7126052417554554232at_nat] :
                      ( ( B2
                        = ( relati3679007509795571081at_nat @ Ya2 ) )
                     => ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ Xa2 @ Ya2 ) ) )
             => ( ! [X1b: relati7126052417554554232at_nat,X2c: relati7126052417554554232at_nat] :
                    ( ( A
                      = ( relati8628237474745418483at_nat @ X1b @ X2c ) )
                   => ! [Y1b: relati7126052417554554232at_nat,Y2c: relati7126052417554554232at_nat] :
                        ( ( B2
                          = ( relati8628237474745418483at_nat @ Y1b @ Y2c ) )
                       => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X1b @ Y1b )
                         => ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ X2c @ Y2c ) ) ) )
               => ( ! [X1c: relati7126052417554554232at_nat,X2d: relati7126052417554554232at_nat] :
                      ( ( A
                        = ( relati7949253455907248103at_nat @ X1c @ X2d ) )
                     => ! [Y1c: relati7126052417554554232at_nat,Y2d: relati7126052417554554232at_nat] :
                          ( ( B2
                            = ( relati7949253455907248103at_nat @ Y1c @ Y2d ) )
                         => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X1c @ Y1c )
                           => ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ X2d @ Y2d ) ) ) )
                 => ~ ! [X1d: nat,X2e: relati7126052417554554232at_nat] :
                        ( ( A
                          = ( relati524807352525265095at_nat @ X1d @ X2e ) )
                       => ! [Y1d: nat,Y2e: relati7126052417554554232at_nat] :
                            ( ( B2
                              = ( relati524807352525265095at_nat @ Y1d @ Y2e ) )
                           => ( ( X1d = Y1d )
                             => ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ X2e @ Y2e ) ) ) ) ) ) ) ) ) ) ) ).

% fmla.rel_cases
thf(fact_477_fmla_Orel__cases,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,A: relational_fmla_a_b,B2: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ A @ B2 )
     => ( ! [X13: b,X2a: list_R6823256787227418703term_a] :
            ( ( A
              = ( relational_Pred_b_a @ X13 @ X2a ) )
           => ! [Y1: b,Y2a: list_R6823256787227418703term_a] :
                ( ( B2
                  = ( relational_Pred_b_a @ Y1 @ Y2a ) )
               => ( ( R2 @ X13 @ Y1 )
                 => ~ ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X2a @ Y2a ) ) ) )
       => ( ! [X2: $o] :
              ( ( A
                = ( relational_Bool_a_b @ X2 ) )
             => ! [Y3: $o] :
                  ( ( B2
                    = ( relational_Bool_a_b @ Y3 ) )
                 => ( X2 = (~ Y3) ) ) )
         => ( ! [X1a: nat,X2b: relational_term_a] :
                ( ( A
                  = ( relational_Eq_a_b @ X1a @ X2b ) )
               => ! [Y1a: nat,Y2b: relational_term_a] :
                    ( ( B2
                      = ( relational_Eq_a_b @ Y1a @ Y2b ) )
                   => ( ( X1a = Y1a )
                     => ~ ( relati3163788165526728396rm_a_a @ R1 @ X2b @ Y2b ) ) ) )
           => ( ! [Xa2: relational_fmla_a_b] :
                  ( ( A
                    = ( relational_Neg_a_b @ Xa2 ) )
                 => ! [Ya2: relational_fmla_a_b] :
                      ( ( B2
                        = ( relational_Neg_a_b @ Ya2 ) )
                     => ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ Xa2 @ Ya2 ) ) )
             => ( ! [X1b: relational_fmla_a_b,X2c: relational_fmla_a_b] :
                    ( ( A
                      = ( relational_Conj_a_b @ X1b @ X2c ) )
                   => ! [Y1b: relational_fmla_a_b,Y2c: relational_fmla_a_b] :
                        ( ( B2
                          = ( relational_Conj_a_b @ Y1b @ Y2c ) )
                       => ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X1b @ Y1b )
                         => ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2c @ Y2c ) ) ) )
               => ( ! [X1c: relational_fmla_a_b,X2d: relational_fmla_a_b] :
                      ( ( A
                        = ( relational_Disj_a_b @ X1c @ X2d ) )
                     => ! [Y1c: relational_fmla_a_b,Y2d: relational_fmla_a_b] :
                          ( ( B2
                            = ( relational_Disj_a_b @ Y1c @ Y2d ) )
                         => ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X1c @ Y1c )
                           => ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2d @ Y2d ) ) ) )
                 => ~ ! [X1d: nat,X2e: relational_fmla_a_b] :
                        ( ( A
                          = ( relati591517084277583526ts_a_b @ X1d @ X2e ) )
                       => ! [Y1d: nat,Y2e: relational_fmla_a_b] :
                            ( ( B2
                              = ( relati591517084277583526ts_a_b @ Y1d @ Y2e ) )
                           => ( ( X1d = Y1d )
                             => ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X2e @ Y2e ) ) ) ) ) ) ) ) ) ) ) ).

% fmla.rel_cases
thf(fact_478_fmla_Orel__induct,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X3: relati7126052417554554232at_nat,Y: relati7126052417554554232at_nat,Q: relati7126052417554554232at_nat > relati7126052417554554232at_nat > $o] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X3 @ Y )
     => ( ! [A11: nat,A12: list_R114826772386431851rm_nat,B11: nat,B12: list_R114826772386431851rm_nat] :
            ( ( R2 @ A11 @ B11 )
           => ( ( list_a2842054329120570431rm_nat @ ( relati2881564729679077486at_nat @ R1 ) @ A12 @ B12 )
             => ( Q @ ( relati5908763325135257836at_nat @ A11 @ A12 ) @ ( relati5908763325135257836at_nat @ B11 @ B12 ) ) ) )
       => ( ! [A22: $o,B22: $o] :
              ( ( A22 = B22 )
             => ( Q @ ( relati4833799250026832501at_nat @ A22 ) @ ( relati4833799250026832501at_nat @ B22 ) ) )
         => ( ! [A31: nat,A32: relational_term_nat,B31: nat,B32: relational_term_nat] :
                ( ( A31 = B31 )
               => ( ( relati2881564729679077486at_nat @ R1 @ A32 @ B32 )
                 => ( Q @ ( relati8266145252267328119at_nat @ A31 @ A32 ) @ ( relati8266145252267328119at_nat @ B31 @ B32 ) ) ) )
           => ( ! [A42: relati7126052417554554232at_nat,B42: relati7126052417554554232at_nat] :
                  ( ( Q @ A42 @ B42 )
                 => ( Q @ ( relati3679007509795571081at_nat @ A42 ) @ ( relati3679007509795571081at_nat @ B42 ) ) )
             => ( ! [A51: relati7126052417554554232at_nat,A52: relati7126052417554554232at_nat,B51: relati7126052417554554232at_nat,B52: relati7126052417554554232at_nat] :
                    ( ( Q @ A51 @ B51 )
                   => ( ( Q @ A52 @ B52 )
                     => ( Q @ ( relati8628237474745418483at_nat @ A51 @ A52 ) @ ( relati8628237474745418483at_nat @ B51 @ B52 ) ) ) )
               => ( ! [A61: relati7126052417554554232at_nat,A62: relati7126052417554554232at_nat,B61: relati7126052417554554232at_nat,B62: relati7126052417554554232at_nat] :
                      ( ( Q @ A61 @ B61 )
                     => ( ( Q @ A62 @ B62 )
                       => ( Q @ ( relati7949253455907248103at_nat @ A61 @ A62 ) @ ( relati7949253455907248103at_nat @ B61 @ B62 ) ) ) )
                 => ( ! [A71: nat,A72: relati7126052417554554232at_nat,B71: nat,B72: relati7126052417554554232at_nat] :
                        ( ( A71 = B71 )
                       => ( ( Q @ A72 @ B72 )
                         => ( Q @ ( relati524807352525265095at_nat @ A71 @ A72 ) @ ( relati524807352525265095at_nat @ B71 @ B72 ) ) ) )
                   => ( Q @ X3 @ Y ) ) ) ) ) ) ) ) ) ).

% fmla.rel_induct
thf(fact_479_fmla_Orel__induct,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X3: relational_fmla_a_b,Y: relational_fmla_a_b,Q: relational_fmla_a_b > relational_fmla_a_b > $o] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X3 @ Y )
     => ( ! [A11: b,A12: list_R6823256787227418703term_a,B11: b,B12: list_R6823256787227418703term_a] :
            ( ( R2 @ A11 @ B11 )
           => ( ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ A12 @ B12 )
             => ( Q @ ( relational_Pred_b_a @ A11 @ A12 ) @ ( relational_Pred_b_a @ B11 @ B12 ) ) ) )
       => ( ! [A22: $o,B22: $o] :
              ( ( A22 = B22 )
             => ( Q @ ( relational_Bool_a_b @ A22 ) @ ( relational_Bool_a_b @ B22 ) ) )
         => ( ! [A31: nat,A32: relational_term_a,B31: nat,B32: relational_term_a] :
                ( ( A31 = B31 )
               => ( ( relati3163788165526728396rm_a_a @ R1 @ A32 @ B32 )
                 => ( Q @ ( relational_Eq_a_b @ A31 @ A32 ) @ ( relational_Eq_a_b @ B31 @ B32 ) ) ) )
           => ( ! [A42: relational_fmla_a_b,B42: relational_fmla_a_b] :
                  ( ( Q @ A42 @ B42 )
                 => ( Q @ ( relational_Neg_a_b @ A42 ) @ ( relational_Neg_a_b @ B42 ) ) )
             => ( ! [A51: relational_fmla_a_b,A52: relational_fmla_a_b,B51: relational_fmla_a_b,B52: relational_fmla_a_b] :
                    ( ( Q @ A51 @ B51 )
                   => ( ( Q @ A52 @ B52 )
                     => ( Q @ ( relational_Conj_a_b @ A51 @ A52 ) @ ( relational_Conj_a_b @ B51 @ B52 ) ) ) )
               => ( ! [A61: relational_fmla_a_b,A62: relational_fmla_a_b,B61: relational_fmla_a_b,B62: relational_fmla_a_b] :
                      ( ( Q @ A61 @ B61 )
                     => ( ( Q @ A62 @ B62 )
                       => ( Q @ ( relational_Disj_a_b @ A61 @ A62 ) @ ( relational_Disj_a_b @ B61 @ B62 ) ) ) )
                 => ( ! [A71: nat,A72: relational_fmla_a_b,B71: nat,B72: relational_fmla_a_b] :
                        ( ( A71 = B71 )
                       => ( ( Q @ A72 @ B72 )
                         => ( Q @ ( relati591517084277583526ts_a_b @ A71 @ A72 ) @ ( relati591517084277583526ts_a_b @ B71 @ B72 ) ) ) )
                   => ( Q @ X3 @ Y ) ) ) ) ) ) ) ) ) ).

% fmla.rel_induct
thf(fact_480_fmla_Orel__distinct_I30_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.rel_distinct(30)
thf(fact_481_fmla_Orel__distinct_I30_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X312: nat,X322: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati8266145252267328119at_nat @ X312 @ X322 ) ) ).

% fmla.rel_distinct(30)
thf(fact_482_fmla_Orel__distinct_I29_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(29)
thf(fact_483_fmla_Orel__distinct_I29_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X312: nat,X322: relational_term_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(29)
thf(fact_484_fmla_Orel__distinct_I28_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.rel_distinct(28)
thf(fact_485_fmla_Orel__distinct_I28_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat,X312: nat,X322: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) @ ( relati8266145252267328119at_nat @ X312 @ X322 ) ) ).

% fmla.rel_distinct(28)
thf(fact_486_fmla_Orel__distinct_I27_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(27)
thf(fact_487_fmla_Orel__distinct_I27_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X312: nat,X322: relational_term_nat,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(27)
thf(fact_488_fmla_Orel__distinct_I22_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X23: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.rel_distinct(22)
thf(fact_489_fmla_Orel__distinct_I22_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X23: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.rel_distinct(22)
thf(fact_490_fmla_Orel__distinct_I21_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(21)
thf(fact_491_fmla_Orel__distinct_I21_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(21)
thf(fact_492_fmla_Orel__distinct_I20_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X23: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.rel_distinct(20)
thf(fact_493_fmla_Orel__distinct_I20_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat,X23: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) @ ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.rel_distinct(20)
thf(fact_494_fmla_Orel__distinct_I19_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(19)
thf(fact_495_fmla_Orel__distinct_I19_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(19)
thf(fact_496_fmla_Orel__distinct_I12_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(12)
thf(fact_497_fmla_Orel__distinct_I12_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(12)
thf(fact_498_fmla_Orel__distinct_I11_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(11)
thf(fact_499_fmla_Orel__distinct_I11_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(11)
thf(fact_500_fmla_Orel__distinct_I10_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(10)
thf(fact_501_fmla_Orel__distinct_I10_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(10)
thf(fact_502_fmla_Orel__distinct_I9_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(9)
thf(fact_503_fmla_Orel__distinct_I9_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(9)
thf(fact_504_fmla_Osimps_I122_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ( ( relati3071123380395136021la_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
      = ( relati2096729434547099208term_a @ X322 ) ) ).

% fmla.simps(122)
thf(fact_505_fmla_Osimps_I122_J,axiom,
    ! [X312: nat,X322: relational_term_nat] :
      ( ( relati6321887899146193334at_nat @ ( relati8266145252267328119at_nat @ X312 @ X322 ) )
      = ( relati7416457470477713926rm_nat @ X322 ) ) ).

% fmla.simps(122)
thf(fact_506_fmla_Oset__intros_I2_J,axiom,
    ! [Yb: a,X322: relational_term_a,X312: nat] :
      ( ( member_a @ Yb @ ( relati2096729434547099208term_a @ X322 ) )
     => ( member_a @ Yb @ ( relati3071123380395136021la_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ) ) ).

% fmla.set_intros(2)
thf(fact_507_fmla_Oset__intros_I2_J,axiom,
    ! [Yb: nat,X322: relational_term_nat,X312: nat] :
      ( ( member_nat @ Yb @ ( relati7416457470477713926rm_nat @ X322 ) )
     => ( member_nat @ Yb @ ( relati6321887899146193334at_nat @ ( relati8266145252267328119at_nat @ X312 @ X322 ) ) ) ) ).

% fmla.set_intros(2)
thf(fact_508_term_Orel__refl__strong,axiom,
    ! [X3: relational_term_b,Ra: b > b > $o] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati376332583554052364rm_b_b @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_509_term_Orel__refl__strong,axiom,
    ! [X3: relati5277550215419191316term_a,Ra: relational_term_a > relational_term_a > $o] :
      ( ! [Z3: relational_term_a] :
          ( ( member5466445112152945266term_a @ Z3 @ ( relati2372589673864734099term_a @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati2794329474471028620term_a @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_510_term_Orel__refl__strong,axiom,
    ! [X3: relati383187284260386255list_a,Ra: list_a > list_a > $o] :
      ( ! [Z3: list_a] :
          ( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati8847882339280608716list_a @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_511_term_Orel__refl__strong,axiom,
    ! [X3: relati8250976376238479564at_nat,Ra: product_prod_nat_nat > product_prod_nat_nat > $o] :
      ( ! [Z3: product_prod_nat_nat] :
          ( ( member8440522571783428010at_nat @ Z3 @ ( relati3132094035298600779at_nat @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati8728558461388257676at_nat @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_512_term_Orel__refl__strong,axiom,
    ! [X3: relational_term_a,Ra: a > a > $o] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati3163788165526728396rm_a_a @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_513_term_Orel__refl__strong,axiom,
    ! [X3: relational_term_nat,Ra: nat > nat > $o] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( relati2881564729679077486at_nat @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl_strong
thf(fact_514_term_Orel__mono__strong,axiom,
    ! [R: nat > nat > $o,X3: relational_term_nat,Y: relational_term_nat,Ra: nat > nat > $o] :
      ( ( relati2881564729679077486at_nat @ R @ X3 @ Y )
     => ( ! [Z3: nat,Yb2: nat] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
           => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati2881564729679077486at_nat @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_515_term_Orel__mono__strong,axiom,
    ! [R: b > b > $o,X3: relational_term_b,Y: relational_term_b,Ra: b > b > $o] :
      ( ( relati376332583554052364rm_b_b @ R @ X3 @ Y )
     => ( ! [Z3: b,Yb2: b] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
           => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati376332583554052364rm_b_b @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_516_term_Orel__mono__strong,axiom,
    ! [R: b > nat > $o,X3: relational_term_b,Y: relational_term_nat,Ra: b > nat > $o] :
      ( ( relati4158688736304548995_b_nat @ R @ X3 @ Y )
     => ( ! [Z3: b,Yb2: nat] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
           => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati4158688736304548995_b_nat @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_517_term_Orel__mono__strong,axiom,
    ! [R: b > a > $o,X3: relational_term_b,Y: relational_term_a,Ra: b > a > $o] :
      ( ( relati376332583554052363rm_b_a @ R @ X3 @ Y )
     => ( ! [Z3: b,Yb2: a] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
           => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati376332583554052363rm_b_a @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_518_term_Orel__mono__strong,axiom,
    ! [R: nat > b > $o,X3: relational_term_nat,Y: relational_term_b,Ra: nat > b > $o] :
      ( ( relati6955175908526440929_nat_b @ R @ X3 @ Y )
     => ( ! [Z3: nat,Yb2: b] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
           => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati6955175908526440929_nat_b @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_519_term_Orel__mono__strong,axiom,
    ! [R: nat > a > $o,X3: relational_term_nat,Y: relational_term_a,Ra: nat > a > $o] :
      ( ( relati6955175908526440928_nat_a @ R @ X3 @ Y )
     => ( ! [Z3: nat,Yb2: a] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
           => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati6955175908526440928_nat_a @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_520_term_Orel__mono__strong,axiom,
    ! [R: a > b > $o,X3: relational_term_a,Y: relational_term_b,Ra: a > b > $o] :
      ( ( relati3163788165526728397rm_a_b @ R @ X3 @ Y )
     => ( ! [Z3: a,Yb2: b] :
            ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X3 ) )
           => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati3163788165526728397rm_a_b @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_521_term_Orel__mono__strong,axiom,
    ! [R: a > nat > $o,X3: relational_term_a,Y: relational_term_nat,Ra: a > nat > $o] :
      ( ( relati2923244407348154498_a_nat @ R @ X3 @ Y )
     => ( ! [Z3: a,Yb2: nat] :
            ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X3 ) )
           => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati2923244407348154498_a_nat @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_522_term_Orel__mono__strong,axiom,
    ! [R: a > a > $o,X3: relational_term_a,Y: relational_term_a,Ra: a > a > $o] :
      ( ( relati3163788165526728396rm_a_a @ R @ X3 @ Y )
     => ( ! [Z3: a,Yb2: a] :
            ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X3 ) )
           => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati3163788165526728396rm_a_a @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_523_term_Orel__mono__strong,axiom,
    ! [R: b > relational_term_a > $o,X3: relational_term_b,Y: relati5277550215419191316term_a,Ra: b > relational_term_a > $o] :
      ( ( relati5843166439758153046term_a @ R @ X3 @ Y )
     => ( ! [Z3: b,Yb2: relational_term_a] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
           => ( ( member5466445112152945266term_a @ Yb2 @ ( relati2372589673864734099term_a @ Y ) )
             => ( ( R @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( relati5843166439758153046term_a @ Ra @ X3 @ Y ) ) ) ).

% term.rel_mono_strong
thf(fact_524_term_Orel__refl,axiom,
    ! [Ra: a > a > $o,X3: relational_term_a] :
      ( ! [X2: a] : ( Ra @ X2 @ X2 )
     => ( relati3163788165526728396rm_a_a @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl
thf(fact_525_term_Orel__refl,axiom,
    ! [Ra: nat > nat > $o,X3: relational_term_nat] :
      ( ! [X2: nat] : ( Ra @ X2 @ X2 )
     => ( relati2881564729679077486at_nat @ Ra @ X3 @ X3 ) ) ).

% term.rel_refl
thf(fact_526_term_Orel__cong,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,Y: relational_term_nat,Xa: relational_term_nat,R: nat > nat > $o,Ra: nat > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: nat,Yb2: nat] :
              ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya ) )
             => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati2881564729679077486at_nat @ R @ X3 @ Y )
            = ( relati2881564729679077486at_nat @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_527_term_Orel__cong,axiom,
    ! [X3: relational_term_b,Ya: relational_term_b,Y: relational_term_b,Xa: relational_term_b,R: b > b > $o,Ra: b > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: b,Yb2: b] :
              ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya ) )
             => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati376332583554052364rm_b_b @ R @ X3 @ Y )
            = ( relati376332583554052364rm_b_b @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_528_term_Orel__cong,axiom,
    ! [X3: relational_term_b,Ya: relational_term_b,Y: relational_term_nat,Xa: relational_term_nat,R: b > nat > $o,Ra: b > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: b,Yb2: nat] :
              ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya ) )
             => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati4158688736304548995_b_nat @ R @ X3 @ Y )
            = ( relati4158688736304548995_b_nat @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_529_term_Orel__cong,axiom,
    ! [X3: relational_term_b,Ya: relational_term_b,Y: relational_term_a,Xa: relational_term_a,R: b > a > $o,Ra: b > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: b,Yb2: a] :
              ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya ) )
             => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati376332583554052363rm_b_a @ R @ X3 @ Y )
            = ( relati376332583554052363rm_b_a @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_530_term_Orel__cong,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,Y: relational_term_b,Xa: relational_term_b,R: nat > b > $o,Ra: nat > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: nat,Yb2: b] :
              ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya ) )
             => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati6955175908526440929_nat_b @ R @ X3 @ Y )
            = ( relati6955175908526440929_nat_b @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_531_term_Orel__cong,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,Y: relational_term_a,Xa: relational_term_a,R: nat > a > $o,Ra: nat > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: nat,Yb2: a] :
              ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya ) )
             => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati6955175908526440928_nat_a @ R @ X3 @ Y )
            = ( relati6955175908526440928_nat_a @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_532_term_Orel__cong,axiom,
    ! [X3: relational_term_a,Ya: relational_term_a,Y: relational_term_b,Xa: relational_term_b,R: a > b > $o,Ra: a > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: a,Yb2: b] :
              ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya ) )
             => ( ( member_b @ Yb2 @ ( relati2096729434547099209term_b @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati3163788165526728397rm_a_b @ R @ X3 @ Y )
            = ( relati3163788165526728397rm_a_b @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_533_term_Orel__cong,axiom,
    ! [X3: relational_term_a,Ya: relational_term_a,Y: relational_term_nat,Xa: relational_term_nat,R: a > nat > $o,Ra: a > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: a,Yb2: nat] :
              ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya ) )
             => ( ( member_nat @ Yb2 @ ( relati7416457470477713926rm_nat @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati2923244407348154498_a_nat @ R @ X3 @ Y )
            = ( relati2923244407348154498_a_nat @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_534_term_Orel__cong,axiom,
    ! [X3: relational_term_a,Ya: relational_term_a,Y: relational_term_a,Xa: relational_term_a,R: a > a > $o,Ra: a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: a,Yb2: a] :
              ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya ) )
             => ( ( member_a @ Yb2 @ ( relati2096729434547099208term_a @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati3163788165526728396rm_a_a @ R @ X3 @ Y )
            = ( relati3163788165526728396rm_a_a @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_535_term_Orel__cong,axiom,
    ! [X3: relational_term_b,Ya: relational_term_b,Y: relati5277550215419191316term_a,Xa: relati5277550215419191316term_a,R: b > relational_term_a > $o,Ra: b > relational_term_a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z3: b,Yb2: relational_term_a] :
              ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya ) )
             => ( ( member5466445112152945266term_a @ Yb2 @ ( relati2372589673864734099term_a @ Xa ) )
               => ( ( R @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( relati5843166439758153046term_a @ R @ X3 @ Y )
            = ( relati5843166439758153046term_a @ Ra @ Ya @ Xa ) ) ) ) ) ).

% term.rel_cong
thf(fact_536_fmla_Orel__refl,axiom,
    ! [R1a: a > a > $o,R2a: b > b > $o,X3: relational_fmla_a_b] :
      ( ! [X2: a] : ( R1a @ X2 @ X2 )
     => ( ! [X2: b] : ( R2a @ X2 @ X2 )
       => ( relati8459511609072445516_a_b_b @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl
thf(fact_537_fmla_Orel__refl,axiom,
    ! [R1a: nat > nat > $o,R2a: nat > nat > $o,X3: relati7126052417554554232at_nat] :
      ( ! [X2: nat] : ( R1a @ X2 @ X2 )
     => ( ! [X2: nat] : ( R2a @ X2 @ X2 )
       => ( relati3787705992210192720at_nat @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl
thf(fact_538_term_Orel__eq,axiom,
    ( ( relati3163788165526728396rm_a_a
      @ ^ [Y5: a,Z4: a] : ( Y5 = Z4 ) )
    = ( ^ [Y5: relational_term_a,Z4: relational_term_a] : ( Y5 = Z4 ) ) ) ).

% term.rel_eq
thf(fact_539_term_Orel__eq,axiom,
    ( ( relati2881564729679077486at_nat
      @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
    = ( ^ [Y5: relational_term_nat,Z4: relational_term_nat] : ( Y5 = Z4 ) ) ) ).

% term.rel_eq
thf(fact_540_fmla_Orel__eq,axiom,
    ( ( relati8459511609072445516_a_b_b
      @ ^ [Y5: a,Z4: a] : ( Y5 = Z4 )
      @ ^ [Y5: b,Z4: b] : ( Y5 = Z4 ) )
    = ( ^ [Y5: relational_fmla_a_b,Z4: relational_fmla_a_b] : ( Y5 = Z4 ) ) ) ).

% fmla.rel_eq
thf(fact_541_fmla_Orel__eq,axiom,
    ( ( relati3787705992210192720at_nat
      @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
      @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
    = ( ^ [Y5: relati7126052417554554232at_nat,Z4: relati7126052417554554232at_nat] : ( Y5 = Z4 ) ) ) ).

% fmla.rel_eq
thf(fact_542_fmla_Orel__distinct_I1_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y22: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Bool_a_b @ Y22 ) ) ).

% fmla.rel_distinct(1)
thf(fact_543_fmla_Orel__distinct_I1_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y22: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati4833799250026832501at_nat @ Y22 ) ) ).

% fmla.rel_distinct(1)
thf(fact_544_fmla_Orel__distinct_I2_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y22: $o,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ Y22 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(2)
thf(fact_545_fmla_Orel__distinct_I2_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y22: $o,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ Y22 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(2)
thf(fact_546_fmla_Orel__distinct_I3_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y31: nat,Y32: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ).

% fmla.rel_distinct(3)
thf(fact_547_fmla_Orel__distinct_I3_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y31: nat,Y32: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) ) ).

% fmla.rel_distinct(3)
thf(fact_548_fmla_Orel__distinct_I4_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y31: nat,Y32: relational_term_a,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ Y31 @ Y32 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(4)
thf(fact_549_fmla_Orel__distinct_I4_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y31: nat,Y32: relational_term_nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(4)
thf(fact_550_fmla_Orel__distinct_I13_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y31: nat,Y32: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ).

% fmla.rel_distinct(13)
thf(fact_551_fmla_Orel__distinct_I13_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y31: nat,Y32: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) ) ).

% fmla.rel_distinct(13)
thf(fact_552_fmla_Orel__distinct_I14_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y31: nat,Y32: relational_term_a,X23: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ Y31 @ Y32 ) @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.rel_distinct(14)
thf(fact_553_fmla_Orel__distinct_I14_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y31: nat,Y32: relational_term_nat,X23: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) @ ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.rel_distinct(14)
thf(fact_554_fmla_Orel__intros_I1_J,axiom,
    ! [R2: b > b > $o,X112: b,Y11: b,R1: a > a > $o,X122: list_R6823256787227418703term_a,Y12: list_R6823256787227418703term_a] :
      ( ( R2 @ X112 @ Y11 )
     => ( ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X122 @ Y12 )
       => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Pred_b_a @ Y11 @ Y12 ) ) ) ) ).

% fmla.rel_intros(1)
thf(fact_555_fmla_Orel__intros_I1_J,axiom,
    ! [R2: nat > nat > $o,X112: nat,Y11: nat,R1: nat > nat > $o,X122: list_R114826772386431851rm_nat,Y12: list_R114826772386431851rm_nat] :
      ( ( R2 @ X112 @ Y11 )
     => ( ( list_a2842054329120570431rm_nat @ ( relati2881564729679077486at_nat @ R1 ) @ X122 @ Y12 )
       => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati5908763325135257836at_nat @ Y11 @ Y12 ) ) ) ) ).

% fmla.rel_intros(1)
thf(fact_556_fmla_Orel__intros_I2_J,axiom,
    ! [X23: $o,Y22: $o,R1: a > a > $o,R2: b > b > $o] :
      ( ( X23 = Y22 )
     => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Bool_a_b @ Y22 ) ) ) ).

% fmla.rel_intros(2)
thf(fact_557_fmla_Orel__intros_I2_J,axiom,
    ! [X23: $o,Y22: $o,R1: nat > nat > $o,R2: nat > nat > $o] :
      ( ( X23 = Y22 )
     => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati4833799250026832501at_nat @ Y22 ) ) ) ).

% fmla.rel_intros(2)
thf(fact_558_fmla_Orel__intros_I3_J,axiom,
    ! [X312: nat,Y31: nat,R1: a > a > $o,X322: relational_term_a,Y32: relational_term_a,R2: b > b > $o] :
      ( ( X312 = Y31 )
     => ( ( relati3163788165526728396rm_a_a @ R1 @ X322 @ Y32 )
       => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) ) ) ) ).

% fmla.rel_intros(3)
thf(fact_559_fmla_Orel__intros_I3_J,axiom,
    ! [X312: nat,Y31: nat,R1: nat > nat > $o,X322: relational_term_nat,Y32: relational_term_nat,R2: nat > nat > $o] :
      ( ( X312 = Y31 )
     => ( ( relati2881564729679077486at_nat @ R1 @ X322 @ Y32 )
       => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) ) ) ) ).

% fmla.rel_intros(3)
thf(fact_560_fmla_Orel__inject_I1_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y11: b,Y12: list_R6823256787227418703term_a] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Pred_b_a @ Y11 @ Y12 ) )
      = ( ( R2 @ X112 @ Y11 )
        & ( list_a3533670403825157575term_a @ ( relati3163788165526728396rm_a_a @ R1 ) @ X122 @ Y12 ) ) ) ).

% fmla.rel_inject(1)
thf(fact_561_fmla_Orel__inject_I1_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y11: nat,Y12: list_R114826772386431851rm_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati5908763325135257836at_nat @ Y11 @ Y12 ) )
      = ( ( R2 @ X112 @ Y11 )
        & ( list_a2842054329120570431rm_nat @ ( relati2881564729679077486at_nat @ R1 ) @ X122 @ Y12 ) ) ) ).

% fmla.rel_inject(1)
thf(fact_562_fmla_Orel__inject_I2_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y22: $o] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Bool_a_b @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fmla.rel_inject(2)
thf(fact_563_fmla_Orel__inject_I2_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y22: $o] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati4833799250026832501at_nat @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% fmla.rel_inject(2)
thf(fact_564_fmla_Orel__inject_I3_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y31: nat,Y32: relational_term_a] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Eq_a_b @ Y31 @ Y32 ) )
      = ( ( X312 = Y31 )
        & ( relati3163788165526728396rm_a_a @ R1 @ X322 @ Y32 ) ) ) ).

% fmla.rel_inject(3)
thf(fact_565_fmla_Orel__inject_I3_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X312: nat,X322: relational_term_nat,Y31: nat,Y32: relational_term_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati8266145252267328119at_nat @ Y31 @ Y32 ) )
      = ( ( X312 = Y31 )
        & ( relati2881564729679077486at_nat @ R1 @ X322 @ Y32 ) ) ) ).

% fmla.rel_inject(3)
thf(fact_566_fmla_Odistinct_I1_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X23: $o] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relational_Bool_a_b @ X23 ) ) ).

% fmla.distinct(1)
thf(fact_567_fmla_Odistinct_I3_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X312: nat,X322: relational_term_a] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.distinct(3)
thf(fact_568_fmla_Odistinct_I13_J,axiom,
    ! [X23: $o,X312: nat,X322: relational_term_a] :
      ( ( relational_Bool_a_b @ X23 )
     != ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.distinct(13)
thf(fact_569_fmla_Orel__distinct_I17_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(17)
thf(fact_570_fmla_Orel__distinct_I17_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(17)
thf(fact_571_fmla_Orel__distinct_I18_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X23: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.rel_distinct(18)
thf(fact_572_fmla_Orel__distinct_I18_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat,X23: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) @ ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.rel_distinct(18)
thf(fact_573_fmla_Orel__distinct_I25_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(25)
thf(fact_574_fmla_Orel__distinct_I25_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X312: nat,X322: relational_term_nat,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(25)
thf(fact_575_fmla_Orel__distinct_I26_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.rel_distinct(26)
thf(fact_576_fmla_Orel__distinct_I26_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat,X312: nat,X322: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) @ ( relati8266145252267328119at_nat @ X312 @ X322 ) ) ).

% fmla.rel_distinct(26)
thf(fact_577_fmla_Orel__distinct_I7_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(7)
thf(fact_578_fmla_Orel__distinct_I7_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(7)
thf(fact_579_fmla_Orel__distinct_I8_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(8)
thf(fact_580_fmla_Orel__distinct_I8_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(8)
thf(fact_581_fmla_Orel__distinct_I24_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.rel_distinct(24)
thf(fact_582_fmla_Orel__distinct_I24_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y4: relati7126052417554554232at_nat,X312: nat,X322: relational_term_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ Y4 ) @ ( relati8266145252267328119at_nat @ X312 @ X322 ) ) ).

% fmla.rel_distinct(24)
thf(fact_583_fmla_Orel__distinct_I23_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X312: nat,X322: relational_term_a,Y4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Eq_a_b @ X312 @ X322 ) @ ( relational_Neg_a_b @ Y4 ) ) ).

% fmla.rel_distinct(23)
thf(fact_584_fmla_Orel__distinct_I23_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X312: nat,X322: relational_term_nat,Y4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) @ ( relati3679007509795571081at_nat @ Y4 ) ) ).

% fmla.rel_distinct(23)
thf(fact_585_fmla_Orel__distinct_I16_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X23: $o] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.rel_distinct(16)
thf(fact_586_fmla_Orel__distinct_I16_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y4: relati7126052417554554232at_nat,X23: $o] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ Y4 ) @ ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.rel_distinct(16)
thf(fact_587_fmla_Orel__distinct_I15_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X23: $o,Y4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Bool_a_b @ X23 ) @ ( relational_Neg_a_b @ Y4 ) ) ).

% fmla.rel_distinct(15)
thf(fact_588_fmla_Orel__distinct_I15_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X23: $o,Y4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati4833799250026832501at_nat @ X23 ) @ ( relati3679007509795571081at_nat @ Y4 ) ) ).

% fmla.rel_distinct(15)
thf(fact_589_fmla_Orel__distinct_I6_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y4: relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ Y4 ) @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.rel_distinct(6)
thf(fact_590_fmla_Orel__distinct_I6_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y4: relati7126052417554554232at_nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ Y4 ) @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ).

% fmla.rel_distinct(6)
thf(fact_591_fmla_Orel__distinct_I5_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X112: b,X122: list_R6823256787227418703term_a,Y4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Pred_b_a @ X112 @ X122 ) @ ( relational_Neg_a_b @ Y4 ) ) ).

% fmla.rel_distinct(5)
thf(fact_592_fmla_Orel__distinct_I5_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X112: nat,X122: list_R114826772386431851rm_nat,Y4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) @ ( relati3679007509795571081at_nat @ Y4 ) ) ).

% fmla.rel_distinct(5)
thf(fact_593_fmla_Orel__inject_I5_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ X51 @ X52 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) )
      = ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X51 @ Y51 )
        & ( relati3787705992210192720at_nat @ R1 @ R2 @ X52 @ Y52 ) ) ) ).

% fmla.rel_inject(5)
thf(fact_594_fmla_Orel__inject_I5_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) )
      = ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X51 @ Y51 )
        & ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X52 @ Y52 ) ) ) ).

% fmla.rel_inject(5)
thf(fact_595_fmla_Orel__intros_I5_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X51: relati7126052417554554232at_nat,Y51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X51 @ Y51 )
     => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X52 @ Y52 )
       => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ X51 @ X52 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) ) ) ) ).

% fmla.rel_intros(5)
thf(fact_596_fmla_Orel__intros_I5_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,Y51: relational_fmla_a_b,X52: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X51 @ Y51 )
     => ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X52 @ Y52 )
       => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ) ) ).

% fmla.rel_intros(5)
thf(fact_597_fmla_Orel__intros_I6_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X612: relational_fmla_a_b,Y61: relational_fmla_a_b,X622: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X612 @ Y61 )
     => ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X622 @ Y62 )
       => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X612 @ X622 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ) ) ).

% fmla.rel_intros(6)
thf(fact_598_fmla_Orel__intros_I6_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X612: relati7126052417554554232at_nat,Y61: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X612 @ Y61 )
     => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X622 @ Y62 )
       => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ X612 @ X622 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ) ) ).

% fmla.rel_intros(6)
thf(fact_599_fmla_Orel__inject_I6_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X612: relational_fmla_a_b,X622: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X612 @ X622 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) )
      = ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X612 @ Y61 )
        & ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X622 @ Y62 ) ) ) ).

% fmla.rel_inject(6)
thf(fact_600_fmla_Orel__inject_I6_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ X612 @ X622 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) )
      = ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X612 @ Y61 )
        & ( relati3787705992210192720at_nat @ R1 @ R2 @ X622 @ Y62 ) ) ) ).

% fmla.rel_inject(6)
thf(fact_601_fmla_Orel__intros_I7_J,axiom,
    ! [X712: nat,Y71: nat,R1: a > a > $o,R2: b > b > $o,X722: relational_fmla_a_b,Y72: relational_fmla_a_b] :
      ( ( X712 = Y71 )
     => ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X722 @ Y72 )
       => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ) ) ).

% fmla.rel_intros(7)
thf(fact_602_fmla_Orel__intros_I7_J,axiom,
    ! [X712: nat,Y71: nat,R1: nat > nat > $o,R2: nat > nat > $o,X722: relati7126052417554554232at_nat,Y72: relati7126052417554554232at_nat] :
      ( ( X712 = Y71 )
     => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X722 @ Y72 )
       => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ X712 @ X722 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ) ) ).

% fmla.rel_intros(7)
thf(fact_603_fmla_Orel__inject_I7_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X712: nat,X722: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ X712 @ X722 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) )
      = ( ( X712 = Y71 )
        & ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X722 @ Y72 ) ) ) ).

% fmla.rel_inject(7)
thf(fact_604_fmla_Orel__inject_I7_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X712: nat,X722: relati7126052417554554232at_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ X712 @ X722 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) )
      = ( ( X712 = Y71 )
        & ( relati3787705992210192720at_nat @ R1 @ R2 @ X722 @ Y72 ) ) ) ).

% fmla.rel_inject(7)
thf(fact_605_fmla_Orel__intros_I4_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X4 @ Y4 )
     => ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Neg_a_b @ Y4 ) ) ) ).

% fmla.rel_intros(4)
thf(fact_606_fmla_Orel__intros_I4_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X4: relati7126052417554554232at_nat,Y4: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X4 @ Y4 )
     => ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ X4 ) @ ( relati3679007509795571081at_nat @ Y4 ) ) ) ).

% fmla.rel_intros(4)
thf(fact_607_fmla_Orel__inject_I4_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y4: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Neg_a_b @ Y4 ) )
      = ( relati8459511609072445516_a_b_b @ R1 @ R2 @ X4 @ Y4 ) ) ).

% fmla.rel_inject(4)
thf(fact_608_fmla_Orel__inject_I4_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X4: relati7126052417554554232at_nat,Y4: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ X4 ) @ ( relati3679007509795571081at_nat @ Y4 ) )
      = ( relati3787705992210192720at_nat @ R1 @ R2 @ X4 @ Y4 ) ) ).

% fmla.rel_inject(4)
thf(fact_609_fmla_Odistinct_I7_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.distinct(7)
thf(fact_610_fmla_Odistinct_I9_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.distinct(9)
thf(fact_611_fmla_Odistinct_I11_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(11)
thf(fact_612_fmla_Odistinct_I5_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a,X4: relational_fmla_a_b] :
      ( ( relational_Pred_b_a @ X112 @ X122 )
     != ( relational_Neg_a_b @ X4 ) ) ).

% fmla.distinct(5)
thf(fact_613_fmla_Odistinct_I25_J,axiom,
    ! [X312: nat,X322: relational_term_a,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relational_Eq_a_b @ X312 @ X322 )
     != ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.distinct(25)
thf(fact_614_fmla_Odistinct_I27_J,axiom,
    ! [X312: nat,X322: relational_term_a,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relational_Eq_a_b @ X312 @ X322 )
     != ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.distinct(27)
thf(fact_615_fmla_Odistinct_I29_J,axiom,
    ! [X312: nat,X322: relational_term_a,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Eq_a_b @ X312 @ X322 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(29)
thf(fact_616_fmla_Odistinct_I23_J,axiom,
    ! [X312: nat,X322: relational_term_a,X4: relational_fmla_a_b] :
      ( ( relational_Eq_a_b @ X312 @ X322 )
     != ( relational_Neg_a_b @ X4 ) ) ).

% fmla.distinct(23)
thf(fact_617_fmla_Odistinct_I17_J,axiom,
    ! [X23: $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ( ( relational_Bool_a_b @ X23 )
     != ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.distinct(17)
thf(fact_618_fmla_Odistinct_I19_J,axiom,
    ! [X23: $o,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ( ( relational_Bool_a_b @ X23 )
     != ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.distinct(19)
thf(fact_619_fmla_Odistinct_I21_J,axiom,
    ! [X23: $o,X712: nat,X722: relational_fmla_a_b] :
      ( ( relational_Bool_a_b @ X23 )
     != ( relati591517084277583526ts_a_b @ X712 @ X722 ) ) ).

% fmla.distinct(21)
thf(fact_620_fmla_Odistinct_I15_J,axiom,
    ! [X23: $o,X4: relational_fmla_a_b] :
      ( ( relational_Bool_a_b @ X23 )
     != ( relational_Neg_a_b @ X4 ) ) ).

% fmla.distinct(15)
thf(fact_621_fmla_Oset__intros_I9_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] : ( member_b @ X112 @ ( relati8924981150291758614la_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ) ).

% fmla.set_intros(9)
thf(fact_622_fmla_Oset__intros_I9_J,axiom,
    ! [X112: nat,X122: list_R114826772386431851rm_nat] : ( member_nat @ X112 @ ( relati2567137625159299127at_nat @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ) ).

% fmla.set_intros(9)
thf(fact_623_fmla_Osimps_I65_J,axiom,
    ! [F1: a > a,F2: b > b,X23: $o] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Bool_a_b @ X23 ) )
      = ( relational_Bool_a_b @ X23 ) ) ).

% fmla.simps(65)
thf(fact_624_fmla_Osimps_I65_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X23: $o] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati4833799250026832501at_nat @ X23 ) )
      = ( relati4833799250026832501at_nat @ X23 ) ) ).

% fmla.simps(65)
thf(fact_625_sat_Osimps_I2_J,axiom,
    ! [B2: $o,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Bool_a_b @ B2 ) @ I @ Sigma )
      = B2 ) ).

% sat.simps(2)
thf(fact_626_fmla_Odisc_I29_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati8168519172193746908nj_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(29)
thf(fact_627_fmla_Odisc_I36_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati5350680195807439568sj_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(36)
thf(fact_628_is__Pred__def,axiom,
    ( relati3644702733014758741ed_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X11: b,X12: list_R6823256787227418703term_a] :
          ( Fmla2
          = ( relational_Pred_b_a @ X11 @ X12 ) ) ) ) ).

% is_Pred_def
thf(fact_629_fmla_OdiscI_I1_J,axiom,
    ! [Fmla: relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ( ( Fmla
        = ( relational_Pred_b_a @ X112 @ X122 ) )
     => ( relati3644702733014758741ed_a_b @ Fmla ) ) ).

% fmla.discI(1)
thf(fact_630_fmla_Odisc_I1_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] : ( relati3644702733014758741ed_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(1)
thf(fact_631_fmla_Odisc_I31_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati8168519172193746908nj_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(31)
thf(fact_632_fmla_Odisc_I38_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati5350680195807439568sj_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(38)
thf(fact_633_fmla_Osimps_I50_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X112: b,X122: list_R6823256787227418703term_a] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Pred_b_a @ X112 @ X122 ) )
      = ( F1 @ X112 @ X122 ) ) ).

% fmla.simps(50)
thf(fact_634_fmla_Odisc_I8_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati6551038146797045342ol_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(8)
thf(fact_635_fmla_Odisc_I15_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relational_is_Eq_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(15)
thf(fact_636_fmla_Odisc_I22_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati4321004860440572638eg_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(22)
thf(fact_637_fmla_Odisc_I3_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati3644702733014758741ed_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(3)
thf(fact_638_is__Eq__def,axiom,
    ( relational_is_Eq_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X31: nat,X32: relational_term_a] :
          ( Fmla2
          = ( relational_Eq_a_b @ X31 @ X32 ) ) ) ) ).

% is_Eq_def
thf(fact_639_fmla_Osimps_I52_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Eq_a_b @ X312 @ X322 ) )
      = ( F3 @ X312 @ X322 ) ) ).

% fmla.simps(52)
thf(fact_640_fmla_OdiscI_I3_J,axiom,
    ! [Fmla: relational_fmla_a_b,X312: nat,X322: relational_term_a] :
      ( ( Fmla
        = ( relational_Eq_a_b @ X312 @ X322 ) )
     => ( relational_is_Eq_a_b @ Fmla ) ) ).

% fmla.discI(3)
thf(fact_641_fmla_Odisc_I10_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati6551038146797045342ol_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(10)
thf(fact_642_fmla_Odisc_I17_J,axiom,
    ! [X312: nat,X322: relational_term_a] : ( relational_is_Eq_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(17)
thf(fact_643_fmla_Odisc_I24_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati4321004860440572638eg_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(24)
thf(fact_644_fmla_Odisc_I30_J,axiom,
    ! [X23: $o] :
      ~ ( relati8168519172193746908nj_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(30)
thf(fact_645_fmla_Odisc_I37_J,axiom,
    ! [X23: $o] :
      ~ ( relati5350680195807439568sj_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(37)
thf(fact_646_fmla_Odisc_I43_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ).

% fmla.disc(43)
thf(fact_647_fmla_Odisc_I2_J,axiom,
    ! [X23: $o] :
      ~ ( relati3644702733014758741ed_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(2)
thf(fact_648_is__Bool__def,axiom,
    ( relati6551038146797045342ol_a_b
    = ( ^ [Fmla2: relational_fmla_a_b] :
        ? [X22: $o] :
          ( Fmla2
          = ( relational_Bool_a_b @ X22 ) ) ) ) ).

% is_Bool_def
thf(fact_649_fmla_Osimps_I51_J,axiom,
    ! [F1: b > list_R6823256787227418703term_a > relational_fmla_a_b,F2: $o > relational_fmla_a_b,F3: nat > relational_term_a > relational_fmla_a_b,F4: relational_fmla_a_b > relational_fmla_a_b,F5: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F6: relational_fmla_a_b > relational_fmla_a_b > relational_fmla_a_b,F7: nat > relational_fmla_a_b > relational_fmla_a_b,X23: $o] :
      ( ( relati5004271986839035796la_a_b @ F1 @ F2 @ F3 @ F4 @ F5 @ F6 @ F7 @ ( relational_Bool_a_b @ X23 ) )
      = ( F2 @ X23 ) ) ).

% fmla.simps(51)
thf(fact_650_fmla_OdiscI_I2_J,axiom,
    ! [Fmla: relational_fmla_a_b,X23: $o] :
      ( ( Fmla
        = ( relational_Bool_a_b @ X23 ) )
     => ( relati6551038146797045342ol_a_b @ Fmla ) ) ).

% fmla.discI(2)
thf(fact_651_fmla_Odisc_I9_J,axiom,
    ! [X23: $o] : ( relati6551038146797045342ol_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(9)
thf(fact_652_fmla_Odisc_I16_J,axiom,
    ! [X23: $o] :
      ~ ( relational_is_Eq_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(16)
thf(fact_653_fmla_Odisc_I23_J,axiom,
    ! [X23: $o] :
      ~ ( relati4321004860440572638eg_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(23)
thf(fact_654_fmla_Odisc_I45_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) ) ).

% fmla.disc(45)
thf(fact_655_fmla_Odisc_I44_J,axiom,
    ! [X23: $o] :
      ~ ( relati5212983245281121968ts_a_b @ ( relational_Bool_a_b @ X23 ) ) ).

% fmla.disc(44)
thf(fact_656_fmla_Oexhaust,axiom,
    ! [Y: relational_fmla_a_b] :
      ( ! [X113: b,X123: list_R6823256787227418703term_a] :
          ( Y
         != ( relational_Pred_b_a @ X113 @ X123 ) )
     => ( ! [X24: $o] :
            ( Y
           != ( relational_Bool_a_b @ X24 ) )
       => ( ! [X313: nat,X323: relational_term_a] :
              ( Y
             != ( relational_Eq_a_b @ X313 @ X323 ) )
         => ( ! [X43: relational_fmla_a_b] :
                ( Y
               != ( relational_Neg_a_b @ X43 ) )
           => ( ! [X513: relational_fmla_a_b,X523: relational_fmla_a_b] :
                  ( Y
                 != ( relational_Conj_a_b @ X513 @ X523 ) )
             => ( ! [X613: relational_fmla_a_b,X623: relational_fmla_a_b] :
                    ( Y
                   != ( relational_Disj_a_b @ X613 @ X623 ) )
               => ~ ! [X713: nat,X723: relational_fmla_a_b] :
                      ( Y
                     != ( relati591517084277583526ts_a_b @ X713 @ X723 ) ) ) ) ) ) ) ) ).

% fmla.exhaust
thf(fact_657_fv_Ocases,axiom,
    ! [X3: relational_fmla_a_b] :
      ( ! [Uu3: b,Ts: list_R6823256787227418703term_a] :
          ( X3
         != ( relational_Pred_b_a @ Uu3 @ Ts ) )
     => ( ! [B5: $o] :
            ( X3
           != ( relational_Bool_a_b @ B5 ) )
       => ( ! [X2: nat,T2: relational_term_a] :
              ( X3
             != ( relational_Eq_a_b @ X2 @ T2 ) )
         => ( ! [Phi2: relational_fmla_a_b] :
                ( X3
               != ( relational_Neg_a_b @ Phi2 ) )
           => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                  ( X3
                 != ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                    ( X3
                   != ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
               => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                      ( X3
                     != ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) ) ) ) ) ) ) ) ).

% fv.cases
thf(fact_658_fmla_Osel_I1_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ( ( relati91604085239814319d1_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) )
      = X112 ) ).

% fmla.sel(1)
thf(fact_659_fmla_Osel_I2_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ( ( relati5687822700427945008d2_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) )
      = X122 ) ).

% fmla.sel(2)
thf(fact_660_fmla_Osel_I5_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ( ( relati1832481647827092069q2_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
      = X322 ) ).

% fmla.sel(5)
thf(fact_661_fmla_Osel_I4_J,axiom,
    ! [X312: nat,X322: relational_term_a] :
      ( ( relati5459635069493737188q1_a_b @ ( relational_Eq_a_b @ X312 @ X322 ) )
      = X312 ) ).

% fmla.sel(4)
thf(fact_662_fmla_Osel_I3_J,axiom,
    ! [X23: $o] :
      ( ( relati2638701775882563405ol_a_b @ ( relational_Bool_a_b @ X23 ) )
      = X23 ) ).

% fmla.sel(3)
thf(fact_663_fmla_Orel__map_I1_J,axiom,
    ! [S1b: a > a > $o,S2b: b > b > $o,I1: a > a,I2: b > b,X3: relational_fmla_a_b,Y: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ S1b @ S2b @ ( relati4520850492397955663_a_b_b @ I1 @ I2 @ X3 ) @ Y )
      = ( relati8459511609072445516_a_b_b
        @ ^ [X: a] : ( S1b @ ( I1 @ X ) )
        @ ^ [X: b] : ( S2b @ ( I2 @ X ) )
        @ X3
        @ Y ) ) ).

% fmla.rel_map(1)
thf(fact_664_fmla_Orel__map_I1_J,axiom,
    ! [S1b: nat > nat > $o,S2b: nat > nat > $o,I1: nat > nat,I2: nat > nat,X3: relati7126052417554554232at_nat,Y: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ S1b @ S2b @ ( relati9000828793121449555at_nat @ I1 @ I2 @ X3 ) @ Y )
      = ( relati3787705992210192720at_nat
        @ ^ [X: nat] : ( S1b @ ( I1 @ X ) )
        @ ^ [X: nat] : ( S2b @ ( I2 @ X ) )
        @ X3
        @ Y ) ) ).

% fmla.rel_map(1)
thf(fact_665_fmla_Orel__map_I2_J,axiom,
    ! [S1a: a > a > $o,S2a: b > b > $o,X3: relational_fmla_a_b,G1: a > a,G2: b > b,Y: relational_fmla_a_b] :
      ( ( relati8459511609072445516_a_b_b @ S1a @ S2a @ X3 @ ( relati4520850492397955663_a_b_b @ G1 @ G2 @ Y ) )
      = ( relati8459511609072445516_a_b_b
        @ ^ [X: a,Y2: a] : ( S1a @ X @ ( G1 @ Y2 ) )
        @ ^ [X: b,Y2: b] : ( S2a @ X @ ( G2 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% fmla.rel_map(2)
thf(fact_666_fmla_Orel__map_I2_J,axiom,
    ! [S1a: nat > nat > $o,S2a: nat > nat > $o,X3: relati7126052417554554232at_nat,G1: nat > nat,G2: nat > nat,Y: relati7126052417554554232at_nat] :
      ( ( relati3787705992210192720at_nat @ S1a @ S2a @ X3 @ ( relati9000828793121449555at_nat @ G1 @ G2 @ Y ) )
      = ( relati3787705992210192720at_nat
        @ ^ [X: nat,Y2: nat] : ( S1a @ X @ ( G1 @ Y2 ) )
        @ ^ [X: nat,Y2: nat] : ( S2a @ X @ ( G2 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% fmla.rel_map(2)
thf(fact_667_fmla_Orel__distinct_I37_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(37)
thf(fact_668_fmla_Orel__distinct_I37_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ X51 @ X52 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(37)
thf(fact_669_fmla_Orel__distinct_I38_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.rel_distinct(38)
thf(fact_670_fmla_Orel__distinct_I38_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ).

% fmla.rel_distinct(38)
thf(fact_671_fmla_Orel__distinct_I39_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X51: relational_fmla_a_b,X52: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ X51 @ X52 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(39)
thf(fact_672_fmla_Orel__distinct_I39_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ X51 @ X52 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(39)
thf(fact_673_fmla_Orel__distinct_I40_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X51: relational_fmla_a_b,X52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Conj_a_b @ X51 @ X52 ) ) ).

% fmla.rel_distinct(40)
thf(fact_674_fmla_Orel__distinct_I40_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X51: relati7126052417554554232at_nat,X52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati8628237474745418483at_nat @ X51 @ X52 ) ) ).

% fmla.rel_distinct(40)
thf(fact_675_fmla_Orel__distinct_I41_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X612: relational_fmla_a_b,X622: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ X612 @ X622 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(41)
thf(fact_676_fmla_Orel__distinct_I41_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ X612 @ X622 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(41)
thf(fact_677_fmla_Orel__distinct_I42_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X612: relational_fmla_a_b,X622: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Disj_a_b @ X612 @ X622 ) ) ).

% fmla.rel_distinct(42)
thf(fact_678_fmla_Orel__distinct_I42_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X612: relati7126052417554554232at_nat,X622: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati7949253455907248103at_nat @ X612 @ X622 ) ) ).

% fmla.rel_distinct(42)
thf(fact_679_fmla_Orel__distinct_I32_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b,X4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Conj_a_b @ Y51 @ Y52 ) @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.rel_distinct(32)
thf(fact_680_fmla_Orel__distinct_I32_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat,X4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) @ ( relati3679007509795571081at_nat @ X4 ) ) ).

% fmla.rel_distinct(32)
thf(fact_681_fmla_Orel__distinct_I31_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y51: relational_fmla_a_b,Y52: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Conj_a_b @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(31)
thf(fact_682_fmla_Orel__distinct_I31_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X4: relati7126052417554554232at_nat,Y51: relati7126052417554554232at_nat,Y52: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ X4 ) @ ( relati8628237474745418483at_nat @ Y51 @ Y52 ) ) ).

% fmla.rel_distinct(31)
thf(fact_683_fmla_Orel__distinct_I34_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b,X4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Disj_a_b @ Y61 @ Y62 ) @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.rel_distinct(34)
thf(fact_684_fmla_Orel__distinct_I34_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat,X4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) @ ( relati3679007509795571081at_nat @ X4 ) ) ).

% fmla.rel_distinct(34)
thf(fact_685_fmla_Orel__distinct_I33_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y61: relational_fmla_a_b,Y62: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relational_Disj_a_b @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(33)
thf(fact_686_fmla_Orel__distinct_I33_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X4: relati7126052417554554232at_nat,Y61: relati7126052417554554232at_nat,Y62: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ X4 ) @ ( relati7949253455907248103at_nat @ Y61 @ Y62 ) ) ).

% fmla.rel_distinct(33)
thf(fact_687_fmla_Orel__distinct_I36_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,Y71: nat,Y72: relational_fmla_a_b,X4: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) @ ( relational_Neg_a_b @ X4 ) ) ).

% fmla.rel_distinct(36)
thf(fact_688_fmla_Orel__distinct_I36_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,Y71: nat,Y72: relati7126052417554554232at_nat,X4: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) @ ( relati3679007509795571081at_nat @ X4 ) ) ).

% fmla.rel_distinct(36)
thf(fact_689_fmla_Orel__distinct_I35_J,axiom,
    ! [R1: a > a > $o,R2: b > b > $o,X4: relational_fmla_a_b,Y71: nat,Y72: relational_fmla_a_b] :
      ~ ( relati8459511609072445516_a_b_b @ R1 @ R2 @ ( relational_Neg_a_b @ X4 ) @ ( relati591517084277583526ts_a_b @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(35)
thf(fact_690_fmla_Orel__distinct_I35_J,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X4: relati7126052417554554232at_nat,Y71: nat,Y72: relati7126052417554554232at_nat] :
      ~ ( relati3787705992210192720at_nat @ R1 @ R2 @ ( relati3679007509795571081at_nat @ X4 ) @ ( relati524807352525265095at_nat @ Y71 @ Y72 ) ) ).

% fmla.rel_distinct(35)
thf(fact_691_fmla_Orel__refl__strong,axiom,
    ! [X3: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: nat > nat > $o] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati3787705992210192720at_nat @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_692_fmla_Orel__refl__strong,axiom,
    ! [X3: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: b > b > $o] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati4008535345494810862at_b_b @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_693_fmla_Orel__refl__strong,axiom,
    ! [X3: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: a > a > $o] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati6795990927467486894at_a_a @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_694_fmla_Orel__refl__strong,axiom,
    ! [X3: relati1059154107580485063_b_nat,R1a: b > b > $o,R2a: nat > nat > $o] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati700162154543277371_b_nat @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati6837777949408058618_b_nat @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati6801122105465879022at_nat @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_695_fmla_Orel__refl__strong,axiom,
    ! [X3: relational_fmla_b_b,R1a: b > b > $o,R2a: b > b > $o] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati283667798422459988la_b_b @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati6137525568319082581la_b_b @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati6320320224700598924_b_b_b @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_696_fmla_Orel__refl__strong,axiom,
    ! [X3: relational_fmla_b_a,R1a: b > b > $o,R2a: a > a > $o] :
      ( ! [Z12: b] :
          ( ( member_b @ Z12 @ ( relati283667798422459987la_b_a @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati6137525568319082580la_b_a @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati9107775806673274956_b_a_a @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_697_fmla_Orel__refl__strong,axiom,
    ! [X3: relati9047081815478866374_a_nat,R1a: a > a > $o,R2a: nat > nat > $o] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati8688089862441658682_a_nat @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: nat] :
            ( ( member_nat @ Z22 @ ( relati5602333620451664121_a_nat @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati1061155776830437294at_nat @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_698_fmla_Orel__refl__strong,axiom,
    ! [X3: relational_fmla_a_a,R1a: a > a > $o,R2a: a > a > $o] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136020la_a_a @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: a] :
            ( ( member_a @ Z22 @ ( relati8924981150291758613la_a_a @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati2023595154190345740_a_a_a @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_699_fmla_Orel__refl__strong,axiom,
    ! [X3: relational_fmla_a_b,R1a: a > a > $o,R2a: b > b > $o] :
      ( ! [Z12: a] :
          ( ( member_a @ Z12 @ ( relati3071123380395136021la_a_b @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: b] :
            ( ( member_b @ Z22 @ ( relati8924981150291758614la_a_b @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati8459511609072445516_a_b_b @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_700_fmla_Orel__refl__strong,axiom,
    ! [X3: relati4454658568062418871term_a,R1a: nat > nat > $o,R2a: relational_term_a > relational_term_a > $o] :
      ( ! [Z12: nat] :
          ( ( member_nat @ Z12 @ ( relati5193166848434641379term_a @ X3 ) )
         => ( R1a @ Z12 @ Z12 ) )
     => ( ! [Z22: relational_term_a] :
            ( ( member5466445112152945266term_a @ Z22 @ ( relati172813024183515810term_a @ X3 ) )
           => ( R2a @ Z22 @ Z22 ) )
       => ( relati682952617693115246term_a @ R1a @ R2a @ X3 @ X3 ) ) ) ).

% fmla.rel_refl_strong
thf(fact_701_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > nat > $o,R2: nat > nat > $o,X3: relati7126052417554554232at_nat,Y: relati7126052417554554232at_nat,R1a: nat > nat > $o,R2a: nat > nat > $o] :
      ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: nat] :
            ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ X3 ) )
           => ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: nat,Y23: nat] :
              ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ X3 ) )
             => ( ( member_nat @ Y23 @ ( relati2567137625159299127at_nat @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati3787705992210192720at_nat @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_702_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > nat > $o,R2: b > b > $o,X3: relati3061873246650996333_nat_b,Y: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: b > b > $o] :
      ( ( relati4008535345494810862at_b_b @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: b,Y23: b] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( member_b @ Y23 @ ( relati410893084775174744_nat_b @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati4008535345494810862at_b_b @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_703_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > nat > $o,R2: b > a > $o,X3: relati3061873246650996333_nat_b,Y: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: b > a > $o] :
      ( ( relati4008535345494810861at_b_a @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: b,Y23: a] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( member_a @ Y23 @ ( relati410893084775174743_nat_a @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati4008535345494810861at_b_a @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_704_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > nat > $o,R2: a > b > $o,X3: relati3061873242347767532_nat_a,Y: relati3061873246650996333_nat_b,R1a: nat > nat > $o,R2a: a > b > $o] :
      ( ( relati6795990927467486895at_a_b @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
           => ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: a,Y23: b] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
             => ( ( member_b @ Y23 @ ( relati410893084775174744_nat_b @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati6795990927467486895at_a_b @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_705_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > nat > $o,R2: a > a > $o,X3: relati3061873242347767532_nat_a,Y: relati3061873242347767532_nat_a,R1a: nat > nat > $o,R2a: a > a > $o] :
      ( ( relati6795990927467486894at_a_a @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: nat] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
           => ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: a,Y23: a] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
             => ( ( member_a @ Y23 @ ( relati410893084775174743_nat_a @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati6795990927467486894at_a_a @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_706_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > b > $o,R2: b > nat > $o,X3: relati3061873246650996333_nat_b,Y: relati1059154107580485063_b_nat,R1a: nat > b > $o,R2a: b > nat > $o] :
      ( ( relati4939769195162127726_b_nat @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: b] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: b,Y23: nat] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( member_nat @ Y23 @ ( relati6837777949408058618_b_nat @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati4939769195162127726_b_nat @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_707_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > b > $o,R2: b > b > $o,X3: relati3061873246650996333_nat_b,Y: relational_fmla_b_b,R1a: nat > b > $o,R2a: b > b > $o] :
      ( ( relati7633695832249111777_b_b_b @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: b] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( member_b @ Y1 @ ( relati283667798422459988la_b_b @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: b,Y23: b] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( member_b @ Y23 @ ( relati6137525568319082581la_b_b @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati7633695832249111777_b_b_b @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_708_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > b > $o,R2: b > a > $o,X3: relati3061873246650996333_nat_b,Y: relational_fmla_b_a,R1a: nat > b > $o,R2a: b > a > $o] :
      ( ( relati7633695832249111776_b_b_a @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: b] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ X3 ) )
           => ( ( member_b @ Y1 @ ( relati283667798422459987la_b_a @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: b,Y23: a] :
              ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ X3 ) )
             => ( ( member_a @ Y23 @ ( relati6137525568319082580la_b_a @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati7633695832249111776_b_b_a @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_709_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > b > $o,R2: a > nat > $o,X3: relati3061873242347767532_nat_a,Y: relati1059154107580485063_b_nat,R1a: nat > b > $o,R2a: a > nat > $o] :
      ( ( relati3704324866205733229_a_nat @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: b] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
           => ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: a,Y23: nat] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
             => ( ( member_nat @ Y23 @ ( relati6837777949408058618_b_nat @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati3704324866205733229_a_nat @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_710_fmla_Orel__mono__strong,axiom,
    ! [R1: nat > b > $o,R2: a > b > $o,X3: relati3061873242347767532_nat_a,Y: relational_fmla_b_b,R1a: nat > b > $o,R2a: a > b > $o] :
      ( ( relati1197779377367012002_b_a_b @ R1 @ R2 @ X3 @ Y )
     => ( ! [Z12: nat,Y1: b] :
            ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ X3 ) )
           => ( ( member_b @ Y1 @ ( relati283667798422459988la_b_b @ Y ) )
             => ( ( R1 @ Z12 @ Y1 )
               => ( R1a @ Z12 @ Y1 ) ) ) )
       => ( ! [Z22: a,Y23: b] :
              ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ X3 ) )
             => ( ( member_b @ Y23 @ ( relati6137525568319082581la_b_b @ Y ) )
               => ( ( R2 @ Z22 @ Y23 )
                 => ( R2a @ Z22 @ Y23 ) ) ) )
         => ( relati1197779377367012002_b_a_b @ R1a @ R2a @ X3 @ Y ) ) ) ) ).

% fmla.rel_mono_strong
thf(fact_711_fmla_Orel__cong,axiom,
    ! [X3: relati7126052417554554232at_nat,Ya: relati7126052417554554232at_nat,Y: relati7126052417554554232at_nat,Xa: relati7126052417554554232at_nat,R1: nat > nat > $o,R1a: nat > nat > $o,R2: nat > nat > $o,R2a: nat > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: nat] :
              ( ( member_nat @ Z12 @ ( relati6321887899146193334at_nat @ Ya ) )
             => ( ( member_nat @ Y1 @ ( relati6321887899146193334at_nat @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: nat,Y23: nat] :
                ( ( member_nat @ Z22 @ ( relati2567137625159299127at_nat @ Ya ) )
               => ( ( member_nat @ Y23 @ ( relati2567137625159299127at_nat @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati3787705992210192720at_nat @ R1 @ R2 @ X3 @ Y )
              = ( relati3787705992210192720at_nat @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_712_fmla_Orel__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,Y: relati3061873246650996333_nat_b,Xa: relati3061873246650996333_nat_b,R1: nat > nat > $o,R1a: nat > nat > $o,R2: b > b > $o,R2a: b > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: nat] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
             => ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: b,Y23: b] :
                ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
               => ( ( member_b @ Y23 @ ( relati410893084775174744_nat_b @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati4008535345494810862at_b_b @ R1 @ R2 @ X3 @ Y )
              = ( relati4008535345494810862at_b_b @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_713_fmla_Orel__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,Y: relati3061873242347767532_nat_a,Xa: relati3061873242347767532_nat_a,R1: nat > nat > $o,R1a: nat > nat > $o,R2: b > a > $o,R2a: b > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: nat] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
             => ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: b,Y23: a] :
                ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
               => ( ( member_a @ Y23 @ ( relati410893084775174743_nat_a @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati4008535345494810861at_b_a @ R1 @ R2 @ X3 @ Y )
              = ( relati4008535345494810861at_b_a @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_714_fmla_Orel__cong,axiom,
    ! [X3: relati3061873242347767532_nat_a,Ya: relati3061873242347767532_nat_a,Y: relati3061873246650996333_nat_b,Xa: relati3061873246650996333_nat_b,R1: nat > nat > $o,R1a: nat > nat > $o,R2: a > b > $o,R2a: a > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: nat] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ Ya ) )
             => ( ( member_nat @ Y1 @ ( relati3496649326765169305_nat_b @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: a,Y23: b] :
                ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya ) )
               => ( ( member_b @ Y23 @ ( relati410893084775174744_nat_b @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati6795990927467486895at_a_b @ R1 @ R2 @ X3 @ Y )
              = ( relati6795990927467486895at_a_b @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_715_fmla_Orel__cong,axiom,
    ! [X3: relati3061873242347767532_nat_a,Ya: relati3061873242347767532_nat_a,Y: relati3061873242347767532_nat_a,Xa: relati3061873242347767532_nat_a,R1: nat > nat > $o,R1a: nat > nat > $o,R2: a > a > $o,R2a: a > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: nat] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ Ya ) )
             => ( ( member_nat @ Y1 @ ( relati3496649326765169304_nat_a @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: a,Y23: a] :
                ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya ) )
               => ( ( member_a @ Y23 @ ( relati410893084775174743_nat_a @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati6795990927467486894at_a_a @ R1 @ R2 @ X3 @ Y )
              = ( relati6795990927467486894at_a_a @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_716_fmla_Orel__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,Y: relati1059154107580485063_b_nat,Xa: relati1059154107580485063_b_nat,R1: nat > b > $o,R1a: nat > b > $o,R2: b > nat > $o,R2a: b > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: b] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
             => ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: b,Y23: nat] :
                ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
               => ( ( member_nat @ Y23 @ ( relati6837777949408058618_b_nat @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati4939769195162127726_b_nat @ R1 @ R2 @ X3 @ Y )
              = ( relati4939769195162127726_b_nat @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_717_fmla_Orel__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,Y: relational_fmla_b_b,Xa: relational_fmla_b_b,R1: nat > b > $o,R1a: nat > b > $o,R2: b > b > $o,R2a: b > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: b] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
             => ( ( member_b @ Y1 @ ( relati283667798422459988la_b_b @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: b,Y23: b] :
                ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
               => ( ( member_b @ Y23 @ ( relati6137525568319082581la_b_b @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati7633695832249111777_b_b_b @ R1 @ R2 @ X3 @ Y )
              = ( relati7633695832249111777_b_b_b @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_718_fmla_Orel__cong,axiom,
    ! [X3: relati3061873246650996333_nat_b,Ya: relati3061873246650996333_nat_b,Y: relational_fmla_b_a,Xa: relational_fmla_b_a,R1: nat > b > $o,R1a: nat > b > $o,R2: b > a > $o,R2a: b > a > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: b] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169305_nat_b @ Ya ) )
             => ( ( member_b @ Y1 @ ( relati283667798422459987la_b_a @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: b,Y23: a] :
                ( ( member_b @ Z22 @ ( relati410893084775174744_nat_b @ Ya ) )
               => ( ( member_a @ Y23 @ ( relati6137525568319082580la_b_a @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati7633695832249111776_b_b_a @ R1 @ R2 @ X3 @ Y )
              = ( relati7633695832249111776_b_b_a @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_719_fmla_Orel__cong,axiom,
    ! [X3: relati3061873242347767532_nat_a,Ya: relati3061873242347767532_nat_a,Y: relati1059154107580485063_b_nat,Xa: relati1059154107580485063_b_nat,R1: nat > b > $o,R1a: nat > b > $o,R2: a > nat > $o,R2a: a > nat > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: b] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ Ya ) )
             => ( ( member_b @ Y1 @ ( relati700162154543277371_b_nat @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: a,Y23: nat] :
                ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya ) )
               => ( ( member_nat @ Y23 @ ( relati6837777949408058618_b_nat @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati3704324866205733229_a_nat @ R1 @ R2 @ X3 @ Y )
              = ( relati3704324866205733229_a_nat @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_720_fmla_Orel__cong,axiom,
    ! [X3: relati3061873242347767532_nat_a,Ya: relati3061873242347767532_nat_a,Y: relational_fmla_b_b,Xa: relational_fmla_b_b,R1: nat > b > $o,R1a: nat > b > $o,R2: a > b > $o,R2a: a > b > $o] :
      ( ( X3 = Ya )
     => ( ( Y = Xa )
       => ( ! [Z12: nat,Y1: b] :
              ( ( member_nat @ Z12 @ ( relati3496649326765169304_nat_a @ Ya ) )
             => ( ( member_b @ Y1 @ ( relati283667798422459988la_b_b @ Xa ) )
               => ( ( R1 @ Z12 @ Y1 )
                  = ( R1a @ Z12 @ Y1 ) ) ) )
         => ( ! [Z22: a,Y23: b] :
                ( ( member_a @ Z22 @ ( relati410893084775174743_nat_a @ Ya ) )
               => ( ( member_b @ Y23 @ ( relati6137525568319082581la_b_b @ Xa ) )
                 => ( ( R2 @ Z22 @ Y23 )
                    = ( R2a @ Z22 @ Y23 ) ) ) )
           => ( ( relati1197779377367012002_b_a_b @ R1 @ R2 @ X3 @ Y )
              = ( relati1197779377367012002_b_a_b @ R1a @ R2a @ Ya @ Xa ) ) ) ) ) ) ).

% fmla.rel_cong
thf(fact_721_fmla_Oset__cases_I1_J,axiom,
    ! [E: nat,A: relati7126052417554554232at_nat] :
      ( ( member_nat @ E @ ( relati6321887899146193334at_nat @ A ) )
     => ( ! [Z12: nat,Z22: list_R114826772386431851rm_nat] :
            ( ( A
              = ( relati5908763325135257836at_nat @ Z12 @ Z22 ) )
           => ! [X2: relational_term_nat] :
                ( ( member5011674626906061938rm_nat @ X2 @ ( set_Re212469413022677766rm_nat @ Z22 ) )
               => ~ ( member_nat @ E @ ( relati7416457470477713926rm_nat @ X2 ) ) ) )
       => ( ! [Z12: nat,Z22: relational_term_nat] :
              ( ( A
                = ( relati8266145252267328119at_nat @ Z12 @ Z22 ) )
             => ~ ( member_nat @ E @ ( relati7416457470477713926rm_nat @ Z22 ) ) )
         => ( ! [Z3: relati7126052417554554232at_nat] :
                ( ( A
                  = ( relati3679007509795571081at_nat @ Z3 ) )
               => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z3 ) ) )
           => ( ! [Z12: relati7126052417554554232at_nat] :
                  ( ? [Z22: relati7126052417554554232at_nat] :
                      ( A
                      = ( relati8628237474745418483at_nat @ Z12 @ Z22 ) )
                 => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z12 ) ) )
             => ( ! [Z12: relati7126052417554554232at_nat,Z22: relati7126052417554554232at_nat] :
                    ( ( A
                      = ( relati8628237474745418483at_nat @ Z12 @ Z22 ) )
                   => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z22 ) ) )
               => ( ! [Z12: relati7126052417554554232at_nat] :
                      ( ? [Z22: relati7126052417554554232at_nat] :
                          ( A
                          = ( relati7949253455907248103at_nat @ Z12 @ Z22 ) )
                     => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z12 ) ) )
                 => ( ! [Z12: relati7126052417554554232at_nat,Z22: relati7126052417554554232at_nat] :
                        ( ( A
                          = ( relati7949253455907248103at_nat @ Z12 @ Z22 ) )
                       => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z22 ) ) )
                   => ~ ! [Z12: nat,Z22: relati7126052417554554232at_nat] :
                          ( ( A
                            = ( relati524807352525265095at_nat @ Z12 @ Z22 ) )
                         => ~ ( member_nat @ E @ ( relati6321887899146193334at_nat @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fmla.set_cases(1)
thf(fact_722_fmla_Oset__cases_I1_J,axiom,
    ! [E: a,A: relational_fmla_a_b] :
      ( ( member_a @ E @ ( relati3071123380395136021la_a_b @ A ) )
     => ( ! [Z12: b,Z22: list_R6823256787227418703term_a] :
            ( ( A
              = ( relational_Pred_b_a @ Z12 @ Z22 ) )
           => ! [X2: relational_term_a] :
                ( ( member5466445112152945266term_a @ X2 @ ( set_Re3569617851344498910term_a @ Z22 ) )
               => ~ ( member_a @ E @ ( relati2096729434547099208term_a @ X2 ) ) ) )
       => ( ! [Z12: nat,Z22: relational_term_a] :
              ( ( A
                = ( relational_Eq_a_b @ Z12 @ Z22 ) )
             => ~ ( member_a @ E @ ( relati2096729434547099208term_a @ Z22 ) ) )
         => ( ! [Z3: relational_fmla_a_b] :
                ( ( A
                  = ( relational_Neg_a_b @ Z3 ) )
               => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z3 ) ) )
           => ( ! [Z12: relational_fmla_a_b] :
                  ( ? [Z22: relational_fmla_a_b] :
                      ( A
                      = ( relational_Conj_a_b @ Z12 @ Z22 ) )
                 => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z12 ) ) )
             => ( ! [Z12: relational_fmla_a_b,Z22: relational_fmla_a_b] :
                    ( ( A
                      = ( relational_Conj_a_b @ Z12 @ Z22 ) )
                   => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) )
               => ( ! [Z12: relational_fmla_a_b] :
                      ( ? [Z22: relational_fmla_a_b] :
                          ( A
                          = ( relational_Disj_a_b @ Z12 @ Z22 ) )
                     => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z12 ) ) )
                 => ( ! [Z12: relational_fmla_a_b,Z22: relational_fmla_a_b] :
                        ( ( A
                          = ( relational_Disj_a_b @ Z12 @ Z22 ) )
                       => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) )
                   => ~ ! [Z12: nat,Z22: relational_fmla_a_b] :
                          ( ( A
                            = ( relati591517084277583526ts_a_b @ Z12 @ Z22 ) )
                         => ~ ( member_a @ E @ ( relati3071123380395136021la_a_b @ Z22 ) ) ) ) ) ) ) ) ) ) ) ).

% fmla.set_cases(1)
thf(fact_723_fmla_Oset__sel_I1_J,axiom,
    ! [A: relational_fmla_a_b,X3: relational_term_a,Xa: a] :
      ( ( relati3644702733014758741ed_a_b @ A )
     => ( ( member5466445112152945266term_a @ X3 @ ( set_Re3569617851344498910term_a @ ( relati5687822700427945008d2_a_b @ A ) ) )
       => ( ( member_a @ Xa @ ( relati2096729434547099208term_a @ X3 ) )
         => ( member_a @ Xa @ ( relati3071123380395136021la_a_b @ A ) ) ) ) ) ).

% fmla.set_sel(1)
thf(fact_724_fmla_Oset__sel_I1_J,axiom,
    ! [A: relati7126052417554554232at_nat,X3: relational_term_nat,Xa: nat] :
      ( ( relati7894638611541183222at_nat @ A )
     => ( ( member5011674626906061938rm_nat @ X3 @ ( set_Re212469413022677766rm_nat @ ( relati4630500915990367057at_nat @ A ) ) )
       => ( ( member_nat @ Xa @ ( relati7416457470477713926rm_nat @ X3 ) )
         => ( member_nat @ Xa @ ( relati6321887899146193334at_nat @ A ) ) ) ) ) ).

% fmla.set_sel(1)
thf(fact_725_fmla_Opred__inject_I3_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: nat,Aa: relational_term_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati8266145252267328119at_nat @ A @ Aa ) )
      = ( relati2679609588974042615rm_nat @ P1 @ Aa ) ) ).

% fmla.pred_inject(3)
thf(fact_726_fmla_Opred__inject_I3_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: nat,Aa: relational_term_a] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Eq_a_b @ A @ Aa ) )
      = ( relati6920953664156333207term_a @ P1 @ Aa ) ) ).

% fmla.pred_inject(3)
thf(fact_727_fv_Osimps_I1_J,axiom,
    ! [Uu4: b,Ts2: list_R6823256787227418703term_a] :
      ( ( relational_fv_a_b @ ( relational_Pred_b_a @ Uu4 @ Ts2 ) )
      = ( relati4569515538964159125_set_a @ Ts2 ) ) ).

% fv.simps(1)
thf(fact_728_fmla_Omap__sel_I5_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relational_is_Eq_a_b @ A )
     => ( ( relati1832481647827092069q2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( relati3585320759856631375rm_a_a @ F1 @ ( relati1832481647827092069q2_a_b @ A ) ) ) ) ).

% fmla.map_sel(5)
thf(fact_729_fmla_Omap__sel_I5_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati8448989431961727361at_nat @ A )
     => ( ( relati1351115928714518534at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( relati2575597170284168561at_nat @ F1 @ ( relati1351115928714518534at_nat @ A ) ) ) ) ).

% fmla.map_sel(5)
thf(fact_730_sat_Ocases,axiom,
    ! [X3: produc1132964494702330949_nat_a] :
      ( ! [R3: b,Ts: list_R6823256787227418703term_a,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
          ( X3
         != ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
     => ( ! [B5: $o,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
            ( X3
           != ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B5 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
       => ( ! [X2: nat,T2: relational_term_a,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
              ( X3
             != ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X2 @ T2 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
         => ( ! [Phi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
                ( X3
               != ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi2 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
           => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
                  ( X3
                 != ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
                    ( X3
                   != ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) )
               => ~ ! [Z3: nat,Phi2: relational_fmla_a_b,I3: product_prod_b_nat > set_list_a,Sigma3: nat > a] :
                      ( X3
                     != ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) @ ( produc2895298938842563487_nat_a @ I3 @ Sigma3 ) ) ) ) ) ) ) ) ) ).

% sat.cases
thf(fact_731_term_Opred__True,axiom,
    ( ( relati6920953664156333207term_a
      @ ^ [Uu: a] : $true )
    = ( ^ [Uu: relational_term_a] : $true ) ) ).

% term.pred_True
thf(fact_732_term_Opred__True,axiom,
    ( ( relati2679609588974042615rm_nat
      @ ^ [Uu: nat] : $true )
    = ( ^ [Uu: relational_term_nat] : $true ) ) ).

% term.pred_True
thf(fact_733_sup__Un__eq2,axiom,
    ! [R: set_Pr5230901268616262395_nat_a,S: set_Pr5230901268616262395_nat_a] :
      ( ( sup_su4853332313885595128at_a_o
        @ ^ [X: relational_fmla_a_b,Y2: produc5835360497134304175_nat_a] : ( member6570610415612139612_nat_a @ ( produc6598558901832717687_nat_a @ X @ Y2 ) @ R )
        @ ^ [X: relational_fmla_a_b,Y2: produc5835360497134304175_nat_a] : ( member6570610415612139612_nat_a @ ( produc6598558901832717687_nat_a @ X @ Y2 ) @ S ) )
      = ( ^ [X: relational_fmla_a_b,Y2: produc5835360497134304175_nat_a] : ( member6570610415612139612_nat_a @ ( produc6598558901832717687_nat_a @ X @ Y2 ) @ ( sup_su1345088743400656423_nat_a @ R @ S ) ) ) ) ).

% sup_Un_eq2
thf(fact_734_sup__Un__eq2,axiom,
    ! [R: set_Pr6389665502131816719_nat_a,S: set_Pr6389665502131816719_nat_a] :
      ( ( sup_su9031902984018088378at_a_o
        @ ^ [X: product_prod_b_nat > set_list_a,Y2: nat > a] : ( member9198066416134578520_nat_a @ ( produc2895298938842563487_nat_a @ X @ Y2 ) @ R )
        @ ^ [X: product_prod_b_nat > set_list_a,Y2: nat > a] : ( member9198066416134578520_nat_a @ ( produc2895298938842563487_nat_a @ X @ Y2 ) @ S ) )
      = ( ^ [X: product_prod_b_nat > set_list_a,Y2: nat > a] : ( member9198066416134578520_nat_a @ ( produc2895298938842563487_nat_a @ X @ Y2 ) @ ( sup_su4018038469549967587_nat_a @ R @ S ) ) ) ) ).

% sup_Un_eq2
thf(fact_735_sup__Un__eq2,axiom,
    ! [R: set_Pr1307281990691478580_b_nat,S: set_Pr1307281990691478580_b_nat] :
      ( ( sup_sup_b_nat_o
        @ ^ [X: b,Y2: nat] : ( member6959632917342813205_b_nat @ ( product_Pair_b_nat @ X @ Y2 ) @ R )
        @ ^ [X: b,Y2: nat] : ( member6959632917342813205_b_nat @ ( product_Pair_b_nat @ X @ Y2 ) @ S ) )
      = ( ^ [X: b,Y2: nat] : ( member6959632917342813205_b_nat @ ( product_Pair_b_nat @ X @ Y2 ) @ ( sup_su6056130500584125792_b_nat @ R @ S ) ) ) ) ).

% sup_Un_eq2
thf(fact_736_sup__Un__eq2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
      ( ( sup_sup_nat_nat_o
        @ ^ [X: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
        @ ^ [X: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ S ) )
      = ( ^ [X: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ ( sup_su6327502436637775413at_nat @ R @ S ) ) ) ) ).

% sup_Un_eq2
thf(fact_737_pred__equals__eq2,axiom,
    ! [R: set_Pr5230901268616262395_nat_a,S: set_Pr5230901268616262395_nat_a] :
      ( ( ( ^ [X: relational_fmla_a_b,Y2: produc5835360497134304175_nat_a] : ( member6570610415612139612_nat_a @ ( produc6598558901832717687_nat_a @ X @ Y2 ) @ R ) )
        = ( ^ [X: relational_fmla_a_b,Y2: produc5835360497134304175_nat_a] : ( member6570610415612139612_nat_a @ ( produc6598558901832717687_nat_a @ X @ Y2 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_738_pred__equals__eq2,axiom,
    ! [R: set_Pr6389665502131816719_nat_a,S: set_Pr6389665502131816719_nat_a] :
      ( ( ( ^ [X: product_prod_b_nat > set_list_a,Y2: nat > a] : ( member9198066416134578520_nat_a @ ( produc2895298938842563487_nat_a @ X @ Y2 ) @ R ) )
        = ( ^ [X: product_prod_b_nat > set_list_a,Y2: nat > a] : ( member9198066416134578520_nat_a @ ( produc2895298938842563487_nat_a @ X @ Y2 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_739_pred__equals__eq2,axiom,
    ! [R: set_Pr1307281990691478580_b_nat,S: set_Pr1307281990691478580_b_nat] :
      ( ( ( ^ [X: b,Y2: nat] : ( member6959632917342813205_b_nat @ ( product_Pair_b_nat @ X @ Y2 ) @ R ) )
        = ( ^ [X: b,Y2: nat] : ( member6959632917342813205_b_nat @ ( product_Pair_b_nat @ X @ Y2 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_740_pred__equals__eq2,axiom,
    ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
      ( ( ( ^ [X: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R ) )
        = ( ^ [X: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_741_term_Omap__ident,axiom,
    ! [T: relational_term_nat] :
      ( ( relati2575597170284168561at_nat
        @ ^ [X: nat] : X
        @ T )
      = T ) ).

% term.map_ident
thf(fact_742_term_Omap__cong__pred,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,F8: nat > nat,G3: nat > nat] :
      ( ( X3 = Ya )
     => ( ( relati2679609588974042615rm_nat
          @ ^ [Z5: nat] :
              ( ( F8 @ Z5 )
              = ( G3 @ Z5 ) )
          @ Ya )
       => ( ( relati2575597170284168561at_nat @ F8 @ X3 )
          = ( relati2575597170284168561at_nat @ G3 @ Ya ) ) ) ) ).

% term.map_cong_pred
thf(fact_743_term_Omap__cong,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,F8: nat > nat,G3: nat > nat] :
      ( ( X3 = Ya )
     => ( ! [Z3: nat] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya ) )
           => ( ( F8 @ Z3 )
              = ( G3 @ Z3 ) ) )
       => ( ( relati2575597170284168561at_nat @ F8 @ X3 )
          = ( relati2575597170284168561at_nat @ G3 @ Ya ) ) ) ) ).

% term.map_cong
thf(fact_744_term_Omap__cong0,axiom,
    ! [X3: relational_term_nat,F8: nat > nat,G3: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
         => ( ( F8 @ Z3 )
            = ( G3 @ Z3 ) ) )
     => ( ( relati2575597170284168561at_nat @ F8 @ X3 )
        = ( relati2575597170284168561at_nat @ G3 @ X3 ) ) ) ).

% term.map_cong0
thf(fact_745_term_Oinj__map__strong,axiom,
    ! [X3: relational_term_nat,Xa: relational_term_nat,F8: nat > nat,Fa: nat > nat] :
      ( ! [Z3: nat,Za2: nat] :
          ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
         => ( ( member_nat @ Za2 @ ( relati7416457470477713926rm_nat @ Xa ) )
           => ( ( ( F8 @ Z3 )
                = ( Fa @ Za2 ) )
             => ( Z3 = Za2 ) ) ) )
     => ( ( ( relati2575597170284168561at_nat @ F8 @ X3 )
          = ( relati2575597170284168561at_nat @ Fa @ Xa ) )
       => ( X3 = Xa ) ) ) ).

% term.inj_map_strong
thf(fact_746_term_Omap__ident__strong,axiom,
    ! [T: relational_term_b,F8: b > b] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati797865177883955343rm_b_b @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_747_term_Omap__ident__strong,axiom,
    ! [T: relati5277550215419191316term_a,F8: relational_term_a > relational_term_a] :
      ( ! [Z3: relational_term_a] :
          ( ( member5466445112152945266term_a @ Z3 @ ( relati2372589673864734099term_a @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati3034611374901186831term_a @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_748_term_Omap__ident__strong,axiom,
    ! [T: relati383187284260386255list_a,F8: list_a > list_a] :
      ( ! [Z3: list_a] :
          ( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati6186803337415672399list_a @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_749_term_Omap__ident__strong,axiom,
    ! [T: relati8250976376238479564at_nat,F8: product_prod_nat_nat > product_prod_nat_nat] :
      ( ! [Z3: product_prod_nat_nat] :
          ( ( member8440522571783428010at_nat @ Z3 @ ( relati3132094035298600779at_nat @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati505408293679640079at_nat @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_750_term_Omap__ident__strong,axiom,
    ! [T: relational_term_a,F8: a > a] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati3585320759856631375rm_a_a @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_751_term_Omap__ident__strong,axiom,
    ! [T: relational_term_nat,F8: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ T ) )
         => ( ( F8 @ Z3 )
            = Z3 ) )
     => ( ( relati2575597170284168561at_nat @ F8 @ T )
        = T ) ) ).

% term.map_ident_strong
thf(fact_752_term_Opred__cong,axiom,
    ! [X3: relational_term_b,Ya: relational_term_b,P: b > $o,Pa: b > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: b] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati6920953664156333208term_b @ P @ X3 )
          = ( relati6920953664156333208term_b @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_753_term_Opred__cong,axiom,
    ! [X3: relati5277550215419191316term_a,Ya: relati5277550215419191316term_a,P: relational_term_a > $o,Pa: relational_term_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: relational_term_a] :
            ( ( member5466445112152945266term_a @ Z3 @ ( relati2372589673864734099term_a @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati9185991753150389474term_a @ P @ X3 )
          = ( relati9185991753150389474term_a @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_754_term_Opred__cong,axiom,
    ! [X3: relati383187284260386255list_a,Ya: relati383187284260386255list_a,P: list_a > $o,Pa: list_a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: list_a] :
            ( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati4353722553127530653list_a @ P @ X3 )
          = ( relati4353722553127530653list_a @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_755_term_Opred__cong,axiom,
    ! [X3: relati8250976376238479564at_nat,Ya: relati8250976376238479564at_nat,P: product_prod_nat_nat > $o,Pa: product_prod_nat_nat > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: product_prod_nat_nat] :
            ( ( member8440522571783428010at_nat @ Z3 @ ( relati3132094035298600779at_nat @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati751324514532473370at_nat @ P @ X3 )
          = ( relati751324514532473370at_nat @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_756_term_Opred__cong,axiom,
    ! [X3: relational_term_a,Ya: relational_term_a,P: a > $o,Pa: a > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: a] :
            ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati6920953664156333207term_a @ P @ X3 )
          = ( relati6920953664156333207term_a @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_757_term_Opred__cong,axiom,
    ! [X3: relational_term_nat,Ya: relational_term_nat,P: nat > $o,Pa: nat > $o] :
      ( ( X3 = Ya )
     => ( ! [Z3: nat] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ Ya ) )
           => ( ( P @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( relati2679609588974042615rm_nat @ P @ X3 )
          = ( relati2679609588974042615rm_nat @ Pa @ Ya ) ) ) ) ).

% term.pred_cong
thf(fact_758_term_Opred__mono__strong,axiom,
    ! [P: b > $o,X3: relational_term_b,Pa: b > $o] :
      ( ( relati6920953664156333208term_b @ P @ X3 )
     => ( ! [Z3: b] :
            ( ( member_b @ Z3 @ ( relati2096729434547099209term_b @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati6920953664156333208term_b @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_759_term_Opred__mono__strong,axiom,
    ! [P: relational_term_a > $o,X3: relati5277550215419191316term_a,Pa: relational_term_a > $o] :
      ( ( relati9185991753150389474term_a @ P @ X3 )
     => ( ! [Z3: relational_term_a] :
            ( ( member5466445112152945266term_a @ Z3 @ ( relati2372589673864734099term_a @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati9185991753150389474term_a @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_760_term_Opred__mono__strong,axiom,
    ! [P: list_a > $o,X3: relati383187284260386255list_a,Pa: list_a > $o] :
      ( ( relati4353722553127530653list_a @ P @ X3 )
     => ( ! [Z3: list_a] :
            ( ( member_list_a @ Z3 @ ( relati1115505217504806350list_a @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati4353722553127530653list_a @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_761_term_Opred__mono__strong,axiom,
    ! [P: product_prod_nat_nat > $o,X3: relati8250976376238479564at_nat,Pa: product_prod_nat_nat > $o] :
      ( ( relati751324514532473370at_nat @ P @ X3 )
     => ( ! [Z3: product_prod_nat_nat] :
            ( ( member8440522571783428010at_nat @ Z3 @ ( relati3132094035298600779at_nat @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati751324514532473370at_nat @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_762_term_Opred__mono__strong,axiom,
    ! [P: a > $o,X3: relational_term_a,Pa: a > $o] :
      ( ( relati6920953664156333207term_a @ P @ X3 )
     => ( ! [Z3: a] :
            ( ( member_a @ Z3 @ ( relati2096729434547099208term_a @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati6920953664156333207term_a @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_763_term_Opred__mono__strong,axiom,
    ! [P: nat > $o,X3: relational_term_nat,Pa: nat > $o] :
      ( ( relati2679609588974042615rm_nat @ P @ X3 )
     => ( ! [Z3: nat] :
            ( ( member_nat @ Z3 @ ( relati7416457470477713926rm_nat @ X3 ) )
           => ( ( P @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( relati2679609588974042615rm_nat @ Pa @ X3 ) ) ) ).

% term.pred_mono_strong
thf(fact_764_term_Orel__map_I2_J,axiom,
    ! [Sa: a > a > $o,X3: relational_term_a,G3: a > a,Y: relational_term_a] :
      ( ( relati3163788165526728396rm_a_a @ Sa @ X3 @ ( relati3585320759856631375rm_a_a @ G3 @ Y ) )
      = ( relati3163788165526728396rm_a_a
        @ ^ [X: a,Y2: a] : ( Sa @ X @ ( G3 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% term.rel_map(2)
thf(fact_765_term_Orel__map_I2_J,axiom,
    ! [Sa: nat > nat > $o,X3: relational_term_nat,G3: nat > nat,Y: relational_term_nat] :
      ( ( relati2881564729679077486at_nat @ Sa @ X3 @ ( relati2575597170284168561at_nat @ G3 @ Y ) )
      = ( relati2881564729679077486at_nat
        @ ^ [X: nat,Y2: nat] : ( Sa @ X @ ( G3 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% term.rel_map(2)
thf(fact_766_term_Orel__map_I1_J,axiom,
    ! [Sb: a > a > $o,I4: a > a,X3: relational_term_a,Y: relational_term_a] :
      ( ( relati3163788165526728396rm_a_a @ Sb @ ( relati3585320759856631375rm_a_a @ I4 @ X3 ) @ Y )
      = ( relati3163788165526728396rm_a_a
        @ ^ [X: a] : ( Sb @ ( I4 @ X ) )
        @ X3
        @ Y ) ) ).

% term.rel_map(1)
thf(fact_767_term_Orel__map_I1_J,axiom,
    ! [Sb: nat > nat > $o,I4: nat > nat,X3: relational_term_nat,Y: relational_term_nat] :
      ( ( relati2881564729679077486at_nat @ Sb @ ( relati2575597170284168561at_nat @ I4 @ X3 ) @ Y )
      = ( relati2881564729679077486at_nat
        @ ^ [X: nat] : ( Sb @ ( I4 @ X ) )
        @ X3
        @ Y ) ) ).

% term.rel_map(1)
thf(fact_768_sat_Osimps_I7_J,axiom,
    ! [Z: nat,Phi: relational_fmla_a_b,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relati591517084277583526ts_a_b @ Z @ Phi ) @ I @ Sigma )
      = ( ? [X: a] : ( relational_sat_a_b @ Phi @ I @ ( fun_upd_nat_a @ Sigma @ Z @ X ) ) ) ) ).

% sat.simps(7)
thf(fact_769_fmla_Osimps_I66_J,axiom,
    ! [F1: a > a,F2: b > b,X312: nat,X322: relational_term_a] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Eq_a_b @ X312 @ X322 ) )
      = ( relational_Eq_a_b @ X312 @ ( relati3585320759856631375rm_a_a @ F1 @ X322 ) ) ) ).

% fmla.simps(66)
thf(fact_770_fmla_Osimps_I66_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X312: nat,X322: relational_term_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati8266145252267328119at_nat @ X312 @ X322 ) )
      = ( relati8266145252267328119at_nat @ X312 @ ( relati2575597170284168561at_nat @ F1 @ X322 ) ) ) ).

% fmla.simps(66)
thf(fact_771_fmla_Oset__intros_I1_J,axiom,
    ! [Y: relational_term_a,X122: list_R6823256787227418703term_a,Ya: a,X112: b] :
      ( ( member5466445112152945266term_a @ Y @ ( set_Re3569617851344498910term_a @ X122 ) )
     => ( ( member_a @ Ya @ ( relati2096729434547099208term_a @ Y ) )
       => ( member_a @ Ya @ ( relati3071123380395136021la_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) ) ) ) ) ).

% fmla.set_intros(1)
thf(fact_772_fmla_Oset__intros_I1_J,axiom,
    ! [Y: relational_term_nat,X122: list_R114826772386431851rm_nat,Ya: nat,X112: nat] :
      ( ( member5011674626906061938rm_nat @ Y @ ( set_Re212469413022677766rm_nat @ X122 ) )
     => ( ( member_nat @ Ya @ ( relati7416457470477713926rm_nat @ Y ) )
       => ( member_nat @ Ya @ ( relati6321887899146193334at_nat @ ( relati5908763325135257836at_nat @ X112 @ X122 ) ) ) ) ) ).

% fmla.set_intros(1)
thf(fact_773_fmla_Opred__inject_I1_J,axiom,
    ! [P1: nat > $o,P2: nat > $o,A: nat,Aa: list_R114826772386431851rm_nat] :
      ( ( relati6725209092851823240at_nat @ P1 @ P2 @ ( relati5908763325135257836at_nat @ A @ Aa ) )
      = ( ( P2 @ A )
        & ( list_a4621116280679065895rm_nat @ ( relati2679609588974042615rm_nat @ P1 ) @ Aa ) ) ) ).

% fmla.pred_inject(1)
thf(fact_774_fmla_Opred__inject_I1_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: b,Aa: list_R6823256787227418703term_a] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Pred_b_a @ A @ Aa ) )
      = ( ( P2 @ A )
        & ( list_a1394079704683284733term_a @ ( relati6920953664156333207term_a @ P1 ) @ Aa ) ) ) ).

% fmla.pred_inject(1)
thf(fact_775_fmla_Omap__sel_I2_J,axiom,
    ! [A: relational_fmla_a_b,F1: a > a,F2: b > b] :
      ( ( relati3644702733014758741ed_a_b @ A )
     => ( ( relati5687822700427945008d2_a_b @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ A ) )
        = ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F1 ) @ ( relati5687822700427945008d2_a_b @ A ) ) ) ) ).

% fmla.map_sel(2)
thf(fact_776_fmla_Omap__sel_I2_J,axiom,
    ! [A: relati7126052417554554232at_nat,F1: nat > nat,F2: nat > nat] :
      ( ( relati7894638611541183222at_nat @ A )
     => ( ( relati4630500915990367057at_nat @ ( relati9000828793121449555at_nat @ F1 @ F2 @ A ) )
        = ( map_Re5644085056688888188rm_nat @ ( relati2575597170284168561at_nat @ F1 ) @ ( relati4630500915990367057at_nat @ A ) ) ) ) ).

% fmla.map_sel(2)
thf(fact_777_set__union,axiom,
    ! [Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a] :
      ( ( set_Re3569617851344498910term_a @ ( union_2615200886310307395term_a @ Xs @ Ys ) )
      = ( sup_su8474575085660790013term_a @ ( set_Re3569617851344498910term_a @ Xs ) @ ( set_Re3569617851344498910term_a @ Ys ) ) ) ).

% set_union
thf(fact_778_set__union,axiom,
    ! [Xs: list_list_nat,Ys: list_list_nat] :
      ( ( set_list_nat2 @ ( union_list_nat @ Xs @ Ys ) )
      = ( sup_sup_set_list_nat @ ( set_list_nat2 @ Xs ) @ ( set_list_nat2 @ Ys ) ) ) ).

% set_union
thf(fact_779_set__union,axiom,
    ! [Xs: list_nat,Ys: list_nat] :
      ( ( set_nat2 @ ( union_nat @ Xs @ Ys ) )
      = ( sup_sup_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ Ys ) ) ) ).

% set_union
thf(fact_780_set__union,axiom,
    ! [Xs: list_a,Ys: list_a] :
      ( ( set_a2 @ ( union_a @ Xs @ Ys ) )
      = ( sup_sup_set_a @ ( set_a2 @ Xs ) @ ( set_a2 @ Ys ) ) ) ).

% set_union
thf(fact_781_set__union,axiom,
    ! [Xs: list_b,Ys: list_b] :
      ( ( set_b2 @ ( union_b @ Xs @ Ys ) )
      = ( sup_sup_set_b @ ( set_b2 @ Xs ) @ ( set_b2 @ Ys ) ) ) ).

% set_union
thf(fact_782_sat_Osimps_I3_J,axiom,
    ! [X3: nat,T3: relational_term_a,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Eq_a_b @ X3 @ T3 ) @ I @ Sigma )
      = ( ( Sigma @ X3 )
        = ( relati1177013128715261720term_a @ Sigma @ T3 ) ) ) ).

% sat.simps(3)
thf(fact_783_fmla_Opred__set,axiom,
    ( relati6725209092851823240at_nat
    = ( ^ [P12: nat > $o,P22: nat > $o,X: relati7126052417554554232at_nat] :
          ( ! [Y2: nat] :
              ( ( member_nat @ Y2 @ ( relati6321887899146193334at_nat @ X ) )
             => ( P12 @ Y2 ) )
          & ! [Y2: nat] :
              ( ( member_nat @ Y2 @ ( relati2567137625159299127at_nat @ X ) )
             => ( P22 @ Y2 ) ) ) ) ) ).

% fmla.pred_set
thf(fact_784_fmla_Opred__set,axiom,
    ( relati3660035184769383399la_a_b
    = ( ^ [P12: a > $o,P22: b > $o,X: relational_fmla_a_b] :
          ( ! [Y2: a] :
              ( ( member_a @ Y2 @ ( relati3071123380395136021la_a_b @ X ) )
             => ( P12 @ Y2 ) )
          & ! [Y2: b] :
              ( ( member_b @ Y2 @ ( relati8924981150291758614la_a_b @ X ) )
             => ( P22 @ Y2 ) ) ) ) ) ).

% fmla.pred_set
thf(fact_785_Ball__def,axiom,
    ( ball_b
    = ( ^ [A3: set_b,P3: b > $o] :
        ! [X: b] :
          ( ( member_b @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_786_Ball__def,axiom,
    ( ball_a
    = ( ^ [A3: set_a,P3: a > $o] :
        ! [X: a] :
          ( ( member_a @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_787_Ball__def,axiom,
    ( ball_R4883633954770375667term_a
    = ( ^ [A3: set_Re5178783185447174953term_a,P3: relational_term_a > $o] :
        ! [X: relational_term_a] :
          ( ( member5466445112152945266term_a @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_788_Ball__def,axiom,
    ( ball_list_a
    = ( ^ [A3: set_list_a,P3: list_a > $o] :
        ! [X: list_a] :
          ( ( member_list_a @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_789_Ball__def,axiom,
    ( ball_P8096063237992195499at_nat
    = ( ^ [A3: set_Pr1261947904930325089at_nat,P3: product_prod_nat_nat > $o] :
        ! [X: product_prod_nat_nat] :
          ( ( member8440522571783428010at_nat @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_790_Ball__def,axiom,
    ( ball_nat
    = ( ^ [A3: set_nat,P3: nat > $o] :
        ! [X: nat] :
          ( ( member_nat @ X @ A3 )
         => ( P3 @ X ) ) ) ) ).

% Ball_def
thf(fact_791_list_Opred__True,axiom,
    ( ( list_a1394079704683284733term_a
      @ ^ [Uu: relational_term_a] : $true )
    = ( ^ [Uu: list_R6823256787227418703term_a] : $true ) ) ).

% list.pred_True
thf(fact_792_list_Orel__map_I2_J,axiom,
    ! [Sa: relational_term_a > relational_term_a > $o,X3: list_R6823256787227418703term_a,G3: relational_term_a > relational_term_a,Y: list_R6823256787227418703term_a] :
      ( ( list_a3533670403825157575term_a @ Sa @ X3 @ ( map_Re5736185711816362116term_a @ G3 @ Y ) )
      = ( list_a3533670403825157575term_a
        @ ^ [X: relational_term_a,Y2: relational_term_a] : ( Sa @ X @ ( G3 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% list.rel_map(2)
thf(fact_793_list_Orel__map_I2_J,axiom,
    ! [Sa: nat > list_nat > $o,X3: list_nat,G3: list_nat > list_nat,Y: list_list_nat] :
      ( ( list_a5155878676884504761st_nat @ Sa @ X3 @ ( map_li7225945977422193158st_nat @ G3 @ Y ) )
      = ( list_a5155878676884504761st_nat
        @ ^ [X: nat,Y2: list_nat] : ( Sa @ X @ ( G3 @ Y2 ) )
        @ X3
        @ Y ) ) ).

% list.rel_map(2)
thf(fact_794_list_Orel__map_I1_J,axiom,
    ! [Sb: relational_term_a > relational_term_a > $o,I4: relational_term_a > relational_term_a,X3: list_R6823256787227418703term_a,Y: list_R6823256787227418703term_a] :
      ( ( list_a3533670403825157575term_a @ Sb @ ( map_Re5736185711816362116term_a @ I4 @ X3 ) @ Y )
      = ( list_a3533670403825157575term_a
        @ ^ [X: relational_term_a] : ( Sb @ ( I4 @ X ) )
        @ X3
        @ Y ) ) ).

% list.rel_map(1)
thf(fact_795_list_Orel__map_I1_J,axiom,
    ! [Sb: nat > list_nat > $o,I4: nat > nat,X3: list_nat,Y: list_list_nat] :
      ( ( list_a5155878676884504761st_nat @ Sb @ ( map_nat_nat @ I4 @ X3 ) @ Y )
      = ( list_a5155878676884504761st_nat
        @ ^ [X: nat] : ( Sb @ ( I4 @ X ) )
        @ X3
        @ Y ) ) ).

% list.rel_map(1)
thf(fact_796_list__all2__map1,axiom,
    ! [P: relational_term_a > relational_term_a > $o,F8: relational_term_a > relational_term_a,As: list_R6823256787227418703term_a,Bs: list_R6823256787227418703term_a] :
      ( ( list_a3533670403825157575term_a @ P @ ( map_Re5736185711816362116term_a @ F8 @ As ) @ Bs )
      = ( list_a3533670403825157575term_a
        @ ^ [X: relational_term_a] : ( P @ ( F8 @ X ) )
        @ As
        @ Bs ) ) ).

% list_all2_map1
thf(fact_797_list__all2__map1,axiom,
    ! [P: nat > list_nat > $o,F8: nat > nat,As: list_nat,Bs: list_list_nat] :
      ( ( list_a5155878676884504761st_nat @ P @ ( map_nat_nat @ F8 @ As ) @ Bs )
      = ( list_a5155878676884504761st_nat
        @ ^ [X: nat] : ( P @ ( F8 @ X ) )
        @ As
        @ Bs ) ) ).

% list_all2_map1
thf(fact_798_list__all2__map2,axiom,
    ! [P: relational_term_a > relational_term_a > $o,As: list_R6823256787227418703term_a,F8: relational_term_a > relational_term_a,Bs: list_R6823256787227418703term_a] :
      ( ( list_a3533670403825157575term_a @ P @ As @ ( map_Re5736185711816362116term_a @ F8 @ Bs ) )
      = ( list_a3533670403825157575term_a
        @ ^ [X: relational_term_a,Y2: relational_term_a] : ( P @ X @ ( F8 @ Y2 ) )
        @ As
        @ Bs ) ) ).

% list_all2_map2
thf(fact_799_list__all2__map2,axiom,
    ! [P: nat > list_nat > $o,As: list_nat,F8: list_nat > list_nat,Bs: list_list_nat] :
      ( ( list_a5155878676884504761st_nat @ P @ As @ ( map_li7225945977422193158st_nat @ F8 @ Bs ) )
      = ( list_a5155878676884504761st_nat
        @ ^ [X: nat,Y2: list_nat] : ( P @ X @ ( F8 @ Y2 ) )
        @ As
        @ Bs ) ) ).

% list_all2_map2
thf(fact_800_term_Opred__set,axiom,
    ( relati6920953664156333207term_a
    = ( ^ [P3: a > $o,X: relational_term_a] :
        ! [Y2: a] :
          ( ( member_a @ Y2 @ ( relati2096729434547099208term_a @ X ) )
         => ( P3 @ Y2 ) ) ) ) ).

% term.pred_set
thf(fact_801_term_Opred__set,axiom,
    ( relati2679609588974042615rm_nat
    = ( ^ [P3: nat > $o,X: relational_term_nat] :
        ! [Y2: nat] :
          ( ( member_nat @ Y2 @ ( relati7416457470477713926rm_nat @ X ) )
         => ( P3 @ Y2 ) ) ) ) ).

% term.pred_set
thf(fact_802_fv__terms__set__cong,axiom,
    ! [F8: a > a] :
      ( relati4569515538964159125_set_a
      = ( ^ [Ts3: list_R6823256787227418703term_a] : ( relati4569515538964159125_set_a @ ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F8 ) @ Ts3 ) ) ) ) ).

% fv_terms_set_cong
thf(fact_803_fv__terms__set__cong,axiom,
    ! [F8: nat > nat] :
      ( relati1372350980941296761et_nat
      = ( ^ [Ts3: list_R114826772386431851rm_nat] : ( relati1372350980941296761et_nat @ ( map_Re5644085056688888188rm_nat @ ( relati2575597170284168561at_nat @ F8 ) @ Ts3 ) ) ) ) ).

% fv_terms_set_cong
thf(fact_804_fmla_Osimps_I64_J,axiom,
    ! [F1: a > a,F2: b > b,X112: b,X122: list_R6823256787227418703term_a] :
      ( ( relati4520850492397955663_a_b_b @ F1 @ F2 @ ( relational_Pred_b_a @ X112 @ X122 ) )
      = ( relational_Pred_b_a @ ( F2 @ X112 ) @ ( map_Re5736185711816362116term_a @ ( relati3585320759856631375rm_a_a @ F1 ) @ X122 ) ) ) ).

% fmla.simps(64)
thf(fact_805_fmla_Osimps_I64_J,axiom,
    ! [F1: nat > nat,F2: nat > nat,X112: nat,X122: list_R114826772386431851rm_nat] :
      ( ( relati9000828793121449555at_nat @ F1 @ F2 @ ( relati5908763325135257836at_nat @ X112 @ X122 ) )
      = ( relati5908763325135257836at_nat @ ( F2 @ X112 ) @ ( map_Re5644085056688888188rm_nat @ ( relati2575597170284168561at_nat @ F1 ) @ X122 ) ) ) ).

% fmla.simps(64)
thf(fact_806_sat_Oelims_I3_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a] :
      ( ~ ( relational_sat_a_nat @ X3 @ Xa @ Xb )
     => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
           => ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relati9034565498597818939_a_nat @ B5 ) )
             => B5 )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_nat @ X2 @ T2 ) )
               => ( ( Xb @ X2 )
                  = ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
           => ( ! [Phi2: relati9047081815478866374_a_nat] :
                  ( ( X3
                    = ( relational_Neg_a_nat @ Phi2 ) )
                 => ~ ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                   => ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                      & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                     => ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                        | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
                 => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                       => ? [X5: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(3)
thf(fact_807_sat_Oelims_I3_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a] :
      ( ~ ( relational_sat_a_b @ X3 @ Xa @ Xb )
     => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relational_Pred_b_a @ R3 @ Ts ) )
           => ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relational_Bool_a_b @ B5 ) )
             => B5 )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_b @ X2 @ T2 ) )
               => ( ( Xb @ X2 )
                  = ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
           => ( ! [Phi2: relational_fmla_a_b] :
                  ( ( X3
                    = ( relational_Neg_a_b @ Phi2 ) )
                 => ~ ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                   => ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                      & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                     => ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                        | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
                 => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                       => ? [X5: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(3)
thf(fact_808_sat_Oelims_I2_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a] :
      ( ( relational_sat_a_nat @ X3 @ Xa @ Xb )
     => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
           => ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relati9034565498597818939_a_nat @ B5 ) )
             => ~ B5 )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_nat @ X2 @ T2 ) )
               => ( ( Xb @ X2 )
                 != ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
           => ( ! [Phi2: relati9047081815478866374_a_nat] :
                  ( ( X3
                    = ( relational_Neg_a_nat @ Phi2 ) )
                 => ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                   => ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                        & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                     => ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                          | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
                 => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                       => ~ ? [X2: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X2 ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(2)
thf(fact_809_sat_Oelims_I2_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a] :
      ( ( relational_sat_a_b @ X3 @ Xa @ Xb )
     => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relational_Pred_b_a @ R3 @ Ts ) )
           => ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relational_Bool_a_b @ B5 ) )
             => ~ B5 )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_b @ X2 @ T2 ) )
               => ( ( Xb @ X2 )
                 != ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
           => ( ! [Phi2: relational_fmla_a_b] :
                  ( ( X3
                    = ( relational_Neg_a_b @ Phi2 ) )
                 => ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                   => ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                        & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                     => ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                          | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
                 => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                       => ~ ? [X2: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X2 ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(2)
thf(fact_810_sat_Oelims_I1_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a,Y: $o] :
      ( ( ( relational_sat_a_nat @ X3 @ Xa @ Xb )
        = Y )
     => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
           => ( Y
              = ( ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relati9034565498597818939_a_nat @ B5 ) )
             => ( Y = (~ B5) ) )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_nat @ X2 @ T2 ) )
               => ( Y
                  = ( ( Xb @ X2 )
                   != ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
           => ( ! [Phi2: relati9047081815478866374_a_nat] :
                  ( ( X3
                    = ( relational_Neg_a_nat @ Phi2 ) )
                 => ( Y
                    = ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                   => ( Y
                      = ( ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                     => ( Y
                        = ( ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) ) )
                 => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                       => ( Y
                          = ( ~ ? [X: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(1)
thf(fact_811_sat_Oelims_I1_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a,Y: $o] :
      ( ( ( relational_sat_a_b @ X3 @ Xa @ Xb )
        = Y )
     => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relational_Pred_b_a @ R3 @ Ts ) )
           => ( Y
              = ( ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) ) )
       => ( ! [B5: $o] :
              ( ( X3
                = ( relational_Bool_a_b @ B5 ) )
             => ( Y = (~ B5) ) )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_b @ X2 @ T2 ) )
               => ( Y
                  = ( ( Xb @ X2 )
                   != ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
           => ( ! [Phi2: relational_fmla_a_b] :
                  ( ( X3
                    = ( relational_Neg_a_b @ Phi2 ) )
                 => ( Y
                    = ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                   => ( Y
                      = ( ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                     => ( Y
                        = ( ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) ) )
                 => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                       => ( Y
                          = ( ~ ? [X: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.elims(1)
thf(fact_812_eval__terms__def,axiom,
    ( relati4772805863405912879erms_a
    = ( ^ [Sigma4: nat > a] : ( map_Re419313091343012409rm_a_a @ ( relati1177013128715261720term_a @ Sigma4 ) ) ) ) ).

% eval_terms_def
thf(fact_813_fmla_Omap__comp,axiom,
    ! [G1: a > $o,G2: a > $o,F1: a > a,F2: a > a,V: relational_fmla_a_a] :
      ( ( relati2737375947961860675_o_a_o @ G1 @ G2 @ ( relati7308306074370631695_a_a_a @ F1 @ F2 @ V ) )
      = ( relati2737375947961860675_o_a_o @ ( comp_a_o_a @ G1 @ F1 ) @ ( comp_a_o_a @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_814_fmla_Omap__comp,axiom,
    ! [G1: b > $o,G2: a > $o,F1: b > b,F2: a > a,V: relational_fmla_b_a] :
      ( ( relati9075677475533109250_o_a_o @ G1 @ G2 @ ( relati5169114689998785103_b_a_a @ F1 @ F2 @ V ) )
      = ( relati9075677475533109250_o_a_o @ ( comp_b_o_b @ G1 @ F1 ) @ ( comp_a_o_a @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_815_fmla_Omap__comp,axiom,
    ! [G1: b > $o,G2: b > $o,F1: b > b,F2: b > b,V: relational_fmla_b_b] :
      ( ( relati6176455076068714945_o_b_o @ G1 @ G2 @ ( relati2381659108026109071_b_b_b @ F1 @ F2 @ V ) )
      = ( relati6176455076068714945_o_b_o @ ( comp_b_o_b @ G1 @ F1 ) @ ( comp_b_o_b @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_816_fmla_Omap__comp,axiom,
    ! [G1: a > $o,G2: b > $o,F1: a > a,F2: b > b,V: relational_fmla_a_b] :
      ( ( relati9061525585352242178_o_b_o @ G1 @ G2 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ V ) )
      = ( relati9061525585352242178_o_b_o @ ( comp_a_o_a @ G1 @ F1 ) @ ( comp_b_o_b @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_817_fmla_Omap__comp,axiom,
    ! [G1: a > a,G2: b > b,F1: a > a,F2: b > b,V: relational_fmla_a_b] :
      ( ( relati4520850492397955663_a_b_b @ G1 @ G2 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ V ) )
      = ( relati4520850492397955663_a_b_b @ ( comp_a_a_a @ G1 @ F1 ) @ ( comp_b_b_b @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_818_fmla_Omap__comp,axiom,
    ! [G1: nat > nat,G2: nat > nat,F1: nat > nat,F2: nat > nat,V: relati7126052417554554232at_nat] :
      ( ( relati9000828793121449555at_nat @ G1 @ G2 @ ( relati9000828793121449555at_nat @ F1 @ F2 @ V ) )
      = ( relati9000828793121449555at_nat @ ( comp_nat_nat_nat @ G1 @ F1 ) @ ( comp_nat_nat_nat @ G2 @ F2 ) @ V ) ) ).

% fmla.map_comp
thf(fact_819_term_Omap__comp,axiom,
    ! [G3: a > $o,F8: a > a,V: relational_term_a] :
      ( ( relati632880486827351913rm_a_o @ G3 @ ( relati3585320759856631375rm_a_a @ F8 @ V ) )
      = ( relati632880486827351913rm_a_o @ ( comp_a_o_a @ G3 @ F8 ) @ V ) ) ).

% term.map_comp
thf(fact_820_term_Omap__comp,axiom,
    ! [G3: b > $o,F8: b > b,V: relational_term_b] :
      ( ( relati6957030124217733416rm_b_o @ G3 @ ( relati797865177883955343rm_b_b @ F8 @ V ) )
      = ( relati6957030124217733416rm_b_o @ ( comp_b_o_b @ G3 @ F8 ) @ V ) ) ).

% term.map_comp
thf(fact_821_term_Omap__comp,axiom,
    ! [G3: nat > nat,F8: nat > nat,V: relational_term_nat] :
      ( ( relati2575597170284168561at_nat @ G3 @ ( relati2575597170284168561at_nat @ F8 @ V ) )
      = ( relati2575597170284168561at_nat @ ( comp_nat_nat_nat @ G3 @ F8 ) @ V ) ) ).

% term.map_comp
thf(fact_822_sat_Osimps_I1_J,axiom,
    ! [R4: nat,Ts2: list_R6823256787227418703term_a,I: product_prod_nat_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_nat @ ( relati6362048942677509346_nat_a @ R4 @ Ts2 ) @ I @ Sigma )
      = ( member_list_a @ ( relati4772805863405912879erms_a @ Sigma @ Ts2 ) @ ( I @ ( product_Pair_nat_nat @ R4 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) ).

% sat.simps(1)
thf(fact_823_sat_Osimps_I1_J,axiom,
    ! [R4: b,Ts2: list_R6823256787227418703term_a,I: product_prod_b_nat > set_list_a,Sigma: nat > a] :
      ( ( relational_sat_a_b @ ( relational_Pred_b_a @ R4 @ Ts2 ) @ I @ Sigma )
      = ( member_list_a @ ( relati4772805863405912879erms_a @ Sigma @ Ts2 ) @ ( I @ ( product_Pair_b_nat @ R4 @ ( size_s88622898042387131term_a @ Ts2 ) ) ) ) ) ).

% sat.simps(1)
thf(fact_824_eval__terms__cong,axiom,
    ! [Ts2: list_R6823256787227418703term_a,Sigma: nat > a,Sigma2: nat > a] :
      ( ! [N: nat] :
          ( ( member_nat @ N @ ( relati4569515538964159125_set_a @ Ts2 ) )
         => ( ( Sigma @ N )
            = ( Sigma2 @ N ) ) )
     => ( ( relati4772805863405912879erms_a @ Sigma @ Ts2 )
        = ( relati4772805863405912879erms_a @ Sigma2 @ Ts2 ) ) ) ).

% eval_terms_cong
thf(fact_825_eval__terms__fv__terms__set,axiom,
    ! [Sigma: nat > a,Ts2: list_R6823256787227418703term_a,Sigma2: nat > a,N2: nat] :
      ( ( ( relati4772805863405912879erms_a @ Sigma @ Ts2 )
        = ( relati4772805863405912879erms_a @ Sigma2 @ Ts2 ) )
     => ( ( member_nat @ N2 @ ( relati4569515538964159125_set_a @ Ts2 ) )
       => ( ( Sigma @ N2 )
          = ( Sigma2 @ N2 ) ) ) ) ).

% eval_terms_fv_terms_set
thf(fact_826_sat_Opelims_I1_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a,Y: $o] :
      ( ( ( relational_sat_a_nat @ X3 @ Xa @ Xb )
        = Y )
     => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X3 @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
             => ( ( Y
                  = ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
               => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relati9034565498597818939_a_nat @ B5 ) )
               => ( ( Y = B5 )
                 => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B5 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_nat @ X2 @ T2 ) )
                 => ( ( Y
                      = ( ( Xb @ X2 )
                        = ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
                   => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X2 @ T2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relational_Neg_a_nat @ Phi2 ) )
                   => ( ( Y
                        = ( ~ ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) ) )
                     => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                     => ( ( Y
                          = ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
                       => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
                 => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                       => ( ( Y
                            = ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) )
                         => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                          ( ( X3
                            = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                         => ( ( Y
                              = ( ? [X: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X ) ) ) )
                           => ~ ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(1)
thf(fact_827_sat_Opelims_I1_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a,Y: $o] :
      ( ( ( relational_sat_a_b @ X3 @ Xa @ Xb )
        = Y )
     => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X3 @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relational_Pred_b_a @ R3 @ Ts ) )
             => ( ( Y
                  = ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) )
               => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relational_Bool_a_b @ B5 ) )
               => ( ( Y = B5 )
                 => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B5 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_b @ X2 @ T2 ) )
                 => ( ( Y
                      = ( ( Xb @ X2 )
                        = ( relati1177013128715261720term_a @ Xb @ T2 ) ) )
                   => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X2 @ T2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
             => ( ! [Phi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Neg_a_b @ Phi2 ) )
                   => ( ( Y
                        = ( ~ ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) ) )
                     => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                     => ( ( Y
                          = ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
                       => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
                 => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                       => ( ( Y
                            = ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) )
                         => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                          ( ( X3
                            = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                         => ( ( Y
                              = ( ? [X: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X ) ) ) )
                           => ~ ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(1)
thf(fact_828_sat_Opelims_I2_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a] :
      ( ( relational_sat_a_nat @ X3 @ Xa @ Xb )
     => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X3 @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
             => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
               => ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relati9034565498597818939_a_nat @ B5 ) )
               => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B5 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                 => ~ B5 ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_nat @ X2 @ T2 ) )
                 => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X2 @ T2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                   => ( ( Xb @ X2 )
                     != ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relational_Neg_a_nat @ Phi2 ) )
                   => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                     => ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                     => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                       => ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) )
                 => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                       => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                         => ~ ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                          ( ( X3
                            = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                         => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                           => ~ ? [X2: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(2)
thf(fact_829_sat_Opelims_I2_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a] :
      ( ( relational_sat_a_b @ X3 @ Xa @ Xb )
     => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X3 @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relational_Pred_b_a @ R3 @ Ts ) )
             => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
               => ~ ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relational_Bool_a_b @ B5 ) )
               => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B5 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                 => ~ B5 ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_b @ X2 @ T2 ) )
                 => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X2 @ T2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                   => ( ( Xb @ X2 )
                     != ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
             => ( ! [Phi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Neg_a_b @ Phi2 ) )
                   => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                     => ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                     => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                       => ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                            & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) )
                 => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                       => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                         => ~ ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                              | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                          ( ( X3
                            = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                         => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                           => ~ ? [X2: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(2)
thf(fact_830_sat_Opelims_I3_J,axiom,
    ! [X3: relati9047081815478866374_a_nat,Xa: product_prod_nat_nat > set_list_a,Xb: nat > a] :
      ( ~ ( relational_sat_a_nat @ X3 @ Xa @ Xb )
     => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ X3 @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: nat,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relati6362048942677509346_nat_a @ R3 @ Ts ) )
             => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6362048942677509346_nat_a @ R3 @ Ts ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
               => ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_nat_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relati9034565498597818939_a_nat @ B5 ) )
               => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9034565498597818939_a_nat @ B5 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                 => B5 ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_nat @ X2 @ T2 ) )
                 => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Eq_a_nat @ X2 @ T2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                   => ( ( Xb @ X2 )
                      = ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
             => ( ! [Phi2: relati9047081815478866374_a_nat] :
                    ( ( X3
                      = ( relational_Neg_a_nat @ Phi2 ) )
                   => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relational_Neg_a_nat @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                     => ~ ( relational_sat_a_nat @ Phi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                      ( ( X3
                        = ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) )
                     => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati2542520632142267709_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                       => ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                          & ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) )
                 => ( ! [Phi2: relati9047081815478866374_a_nat,Psi2: relati9047081815478866374_a_nat] :
                        ( ( X3
                          = ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) )
                       => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati9106205213788308809_a_nat @ Phi2 @ Psi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                         => ( ( relational_sat_a_nat @ Phi2 @ Xa @ Xb )
                            | ( relational_sat_a_nat @ Psi2 @ Xa @ Xb ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relati9047081815478866374_a_nat] :
                          ( ( X3
                            = ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) )
                         => ( ( accp_P3115975753873020414_nat_a @ relati9040413291598363742_a_nat @ ( produc2574091134533170497_nat_a @ ( relati6314223733442460777_a_nat @ Z3 @ Phi2 ) @ ( produc4953239424914856836_nat_a @ Xa @ Xb ) ) )
                           => ? [X5: a] : ( relational_sat_a_nat @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(3)
thf(fact_831_sat_Opelims_I3_J,axiom,
    ! [X3: relational_fmla_a_b,Xa: product_prod_b_nat > set_list_a,Xb: nat > a] :
      ( ~ ( relational_sat_a_b @ X3 @ Xa @ Xb )
     => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ X3 @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
       => ( ! [R3: b,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relational_Pred_b_a @ R3 @ Ts ) )
             => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Pred_b_a @ R3 @ Ts ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
               => ( member_list_a @ ( relati4772805863405912879erms_a @ Xb @ Ts ) @ ( Xa @ ( product_Pair_b_nat @ R3 @ ( size_s88622898042387131term_a @ Ts ) ) ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relational_Bool_a_b @ B5 ) )
               => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Bool_a_b @ B5 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                 => B5 ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_b @ X2 @ T2 ) )
                 => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Eq_a_b @ X2 @ T2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                   => ( ( Xb @ X2 )
                      = ( relati1177013128715261720term_a @ Xb @ T2 ) ) ) )
             => ( ! [Phi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Neg_a_b @ Phi2 ) )
                   => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Neg_a_b @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                     => ~ ( relational_sat_a_b @ Phi2 @ Xa @ Xb ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                     => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                       => ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                          & ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) )
                 => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                       => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                         => ( ( relational_sat_a_b @ Phi2 @ Xa @ Xb )
                            | ( relational_sat_a_b @ Psi2 @ Xa @ Xb ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                          ( ( X3
                            = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                         => ( ( accp_P6721201822162371452_nat_a @ relati4321809963887231473el_a_b @ ( produc6598558901832717687_nat_a @ ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) @ ( produc2895298938842563487_nat_a @ Xa @ Xb ) ) )
                           => ? [X5: a] : ( relational_sat_a_b @ Phi2 @ Xa @ ( fun_upd_nat_a @ Xb @ Z3 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ).

% sat.pelims(3)
thf(fact_832_K__record__comp,axiom,
    ! [C: $o,F8: a > a] :
      ( ( comp_a_o_a
        @ ^ [X: a] : C
        @ F8 )
      = ( ^ [X: a] : C ) ) ).

% K_record_comp
thf(fact_833_K__record__comp,axiom,
    ! [C: $o,F8: b > b] :
      ( ( comp_b_o_b
        @ ^ [X: b] : C
        @ F8 )
      = ( ^ [X: b] : C ) ) ).

% K_record_comp
thf(fact_834_fmla_Opred__map,axiom,
    ! [Q1: a > $o,Q22: a > $o,F1: a > a,F2: a > a,X3: relational_fmla_a_a] :
      ( ( relati3660035184769383398la_a_a @ Q1 @ Q22 @ ( relati7308306074370631695_a_a_a @ F1 @ F2 @ X3 ) )
      = ( relati3660035184769383398la_a_a @ ( comp_a_o_a @ Q1 @ F1 ) @ ( comp_a_o_a @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_835_fmla_Opred__map,axiom,
    ! [Q1: b > $o,Q22: a > $o,F1: b > b,F2: a > a,X3: relational_fmla_b_a] :
      ( ( relati872579602796707365la_b_a @ Q1 @ Q22 @ ( relati5169114689998785103_b_a_a @ F1 @ F2 @ X3 ) )
      = ( relati872579602796707365la_b_a @ ( comp_b_o_b @ Q1 @ F1 ) @ ( comp_a_o_a @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_836_fmla_Opred__map,axiom,
    ! [Q1: b > $o,Q22: b > $o,F1: b > b,F2: b > b,X3: relational_fmla_b_b] :
      ( ( relati872579602796707366la_b_b @ Q1 @ Q22 @ ( relati2381659108026109071_b_b_b @ F1 @ F2 @ X3 ) )
      = ( relati872579602796707366la_b_b @ ( comp_b_o_b @ Q1 @ F1 ) @ ( comp_b_o_b @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_837_fmla_Opred__map,axiom,
    ! [Q1: a > $o,Q22: b > $o,F1: nat > a,F2: nat > b,X3: relati7126052417554554232at_nat] :
      ( ( relati3660035184769383399la_a_b @ Q1 @ Q22 @ ( relati6662804208382264336_nat_b @ F1 @ F2 @ X3 ) )
      = ( relati6725209092851823240at_nat @ ( comp_a_o_nat @ Q1 @ F1 ) @ ( comp_b_o_nat @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_838_fmla_Opred__map,axiom,
    ! [Q1: nat > $o,Q22: nat > $o,F1: a > nat,F2: b > nat,X3: relational_fmla_a_b] :
      ( ( relati6725209092851823240at_nat @ Q1 @ Q22 @ ( relati4067908648865739920_b_nat @ F1 @ F2 @ X3 ) )
      = ( relati3660035184769383399la_a_b @ ( comp_nat_o_a @ Q1 @ F1 ) @ ( comp_nat_o_b @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_839_fmla_Opred__map,axiom,
    ! [Q1: nat > $o,Q22: nat > $o,F1: nat > nat,F2: nat > nat,X3: relati7126052417554554232at_nat] :
      ( ( relati6725209092851823240at_nat @ Q1 @ Q22 @ ( relati9000828793121449555at_nat @ F1 @ F2 @ X3 ) )
      = ( relati6725209092851823240at_nat @ ( comp_nat_o_nat @ Q1 @ F1 ) @ ( comp_nat_o_nat @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_840_fmla_Opred__map,axiom,
    ! [Q1: a > $o,Q22: b > $o,F1: a > a,F2: b > b,X3: relational_fmla_a_b] :
      ( ( relati3660035184769383399la_a_b @ Q1 @ Q22 @ ( relati4520850492397955663_a_b_b @ F1 @ F2 @ X3 ) )
      = ( relati3660035184769383399la_a_b @ ( comp_a_o_a @ Q1 @ F1 ) @ ( comp_b_o_b @ Q22 @ F2 ) @ X3 ) ) ).

% fmla.pred_map
thf(fact_841_term_Opred__map,axiom,
    ! [Q: b > $o,F8: b > b,X3: relational_term_b] :
      ( ( relati6920953664156333208term_b @ Q @ ( relati797865177883955343rm_b_b @ F8 @ X3 ) )
      = ( relati6920953664156333208term_b @ ( comp_b_o_b @ Q @ F8 ) @ X3 ) ) ).

% term.pred_map
thf(fact_842_term_Opred__map,axiom,
    ! [Q: a > $o,F8: a > a,X3: relational_term_a] :
      ( ( relati6920953664156333207term_a @ Q @ ( relati3585320759856631375rm_a_a @ F8 @ X3 ) )
      = ( relati6920953664156333207term_a @ ( comp_a_o_a @ Q @ F8 ) @ X3 ) ) ).

% term.pred_map
thf(fact_843_term_Opred__map,axiom,
    ! [Q: a > $o,F8: nat > a,X3: relational_term_nat] :
      ( ( relati6920953664156333207term_a @ Q @ ( relati8433428048552826781_nat_a @ F8 @ X3 ) )
      = ( relati2679609588974042615rm_nat @ ( comp_a_o_nat @ Q @ F8 ) @ X3 ) ) ).

% term.pred_map
thf(fact_844_term_Opred__map,axiom,
    ! [Q: nat > $o,F8: a > nat,X3: relational_term_a] :
      ( ( relati2679609588974042615rm_nat @ Q @ ( relati4401496547374540351_a_nat @ F8 @ X3 ) )
      = ( relati6920953664156333207term_a @ ( comp_nat_o_a @ Q @ F8 ) @ X3 ) ) ).

% term.pred_map
thf(fact_845_term_Opred__map,axiom,
    ! [Q: nat > $o,F8: nat > nat,X3: relational_term_nat] :
      ( ( relati2679609588974042615rm_nat @ Q @ ( relati2575597170284168561at_nat @ F8 @ X3 ) )
      = ( relati2679609588974042615rm_nat @ ( comp_nat_o_nat @ Q @ F8 ) @ X3 ) ) ).

% term.pred_map
thf(fact_846_partition__set,axiom,
    ! [P: relational_term_a > $o,Xs: list_R6823256787227418703term_a,Yes: list_R6823256787227418703term_a,No: list_R6823256787227418703term_a] :
      ( ( ( partit3301487080212054984term_a @ P @ Xs )
        = ( produc3676283718292092247term_a @ Yes @ No ) )
     => ( ( sup_su8474575085660790013term_a @ ( set_Re3569617851344498910term_a @ Yes ) @ ( set_Re3569617851344498910term_a @ No ) )
        = ( set_Re3569617851344498910term_a @ Xs ) ) ) ).

% partition_set
thf(fact_847_partition__set,axiom,
    ! [P: list_nat > $o,Xs: list_list_nat,Yes: list_list_nat,No: list_list_nat] :
      ( ( ( partition_list_nat @ P @ Xs )
        = ( produc7129799990162260089st_nat @ Yes @ No ) )
     => ( ( sup_sup_set_list_nat @ ( set_list_nat2 @ Yes ) @ ( set_list_nat2 @ No ) )
        = ( set_list_nat2 @ Xs ) ) ) ).

% partition_set
thf(fact_848_partition__set,axiom,
    ! [P: nat > $o,Xs: list_nat,Yes: list_nat,No: list_nat] :
      ( ( ( partition_nat @ P @ Xs )
        = ( produc2694037385005941721st_nat @ Yes @ No ) )
     => ( ( sup_sup_set_nat @ ( set_nat2 @ Yes ) @ ( set_nat2 @ No ) )
        = ( set_nat2 @ Xs ) ) ) ).

% partition_set
thf(fact_849_partition__set,axiom,
    ! [P: a > $o,Xs: list_a,Yes: list_a,No: list_a] :
      ( ( ( partition_a @ P @ Xs )
        = ( produc6837034575241423639list_a @ Yes @ No ) )
     => ( ( sup_sup_set_a @ ( set_a2 @ Yes ) @ ( set_a2 @ No ) )
        = ( set_a2 @ Xs ) ) ) ).

% partition_set
thf(fact_850_partition__set,axiom,
    ! [P: b > $o,Xs: list_b,Yes: list_b,No: list_b] :
      ( ( ( partition_b @ P @ Xs )
        = ( produc1564554178308465111list_b @ Yes @ No ) )
     => ( ( sup_sup_set_b @ ( set_b2 @ Yes ) @ ( set_b2 @ No ) )
        = ( set_b2 @ Xs ) ) ) ).

% partition_set
thf(fact_851_conj__comp__iff,axiom,
    ! [P: a > $o,Q: a > $o,G3: a > a] :
      ( ( comp_a_o_a
        @ ^ [X: a] :
            ( ( P @ X )
            & ( Q @ X ) )
        @ G3 )
      = ( ^ [X: a] :
            ( ( comp_a_o_a @ P @ G3 @ X )
            & ( comp_a_o_a @ Q @ G3 @ X ) ) ) ) ).

% conj_comp_iff
thf(fact_852_conj__comp__iff,axiom,
    ! [P: b > $o,Q: b > $o,G3: b > b] :
      ( ( comp_b_o_b
        @ ^ [X: b] :
            ( ( P @ X )
            & ( Q @ X ) )
        @ G3 )
      = ( ^ [X: b] :
            ( ( comp_b_o_b @ P @ G3 @ X )
            & ( comp_b_o_b @ Q @ G3 @ X ) ) ) ) ).

% conj_comp_iff
thf(fact_853_fun_Opred__map,axiom,
    ! [Q: $o > $o,F8: a > $o,X3: a > a] :
      ( ( basic_pred_fun_a_o
        @ ^ [Uu: a] : $true
        @ Q
        @ ( comp_a_o_a @ F8 @ X3 ) )
      = ( basic_pred_fun_a_a
        @ ^ [Uu: a] : $true
        @ ( comp_o_o_a @ Q @ F8 )
        @ X3 ) ) ).

% fun.pred_map
thf(fact_854_fun_Opred__map,axiom,
    ! [Q: $o > $o,F8: b > $o,X3: b > b] :
      ( ( basic_pred_fun_b_o
        @ ^ [Uu: b] : $true
        @ Q
        @ ( comp_b_o_b @ F8 @ X3 ) )
      = ( basic_pred_fun_b_b
        @ ^ [Uu: b] : $true
        @ ( comp_o_o_b @ Q @ F8 )
        @ X3 ) ) ).

% fun.pred_map
thf(fact_855_Id__on__set,axiom,
    ! [Xs: list_R6823256787227418703term_a] :
      ( ( id_on_2009952563750624742term_a @ ( set_Re3569617851344498910term_a @ Xs ) )
      = ( set_Pr5711402074887782140term_a
        @ ( map_Re1021565884873730722term_a
          @ ^ [X: relational_term_a] : ( produc5718452834064904663term_a @ X @ X )
          @ Xs ) ) ) ).

% Id_on_set
thf(fact_856_Id__on__set,axiom,
    ! [Xs: list_list_nat] :
      ( ( id_on_list_nat @ ( set_list_nat2 @ Xs ) )
      = ( set_Pr3842133991353686454st_nat
        @ ( map_li6665866383299509243st_nat
          @ ^ [X: list_nat] : ( produc2694037385005941721st_nat @ X @ X )
          @ Xs ) ) ) ).

% Id_on_set
thf(fact_857_Id__on__set,axiom,
    ! [Xs: list_nat] :
      ( ( id_on_nat @ ( set_nat2 @ Xs ) )
      = ( set_Pr5648618587558075414at_nat
        @ ( map_na7298421622053143531at_nat
          @ ^ [X: nat] : ( product_Pair_nat_nat @ X @ X )
          @ Xs ) ) ) ).

% Id_on_set
thf(fact_858_fv__terms__setD,axiom,
    ! [M: nat,Ts2: list_R6823256787227418703term_a] :
      ( ( member_nat @ M @ ( relati4569515538964159125_set_a @ Ts2 ) )
     => ( member5466445112152945266term_a @ ( relational_Var_a @ M ) @ ( set_Re3569617851344498910term_a @ Ts2 ) ) ) ).

% fv_terms_setD
thf(fact_859_fv__terms__setI,axiom,
    ! [M: nat,Ts2: list_R6823256787227418703term_a] :
      ( ( member5466445112152945266term_a @ ( relational_Var_a @ M ) @ ( set_Re3569617851344498910term_a @ Ts2 ) )
     => ( member_nat @ M @ ( relati4569515538964159125_set_a @ Ts2 ) ) ) ).

% fv_terms_setI
thf(fact_860_Id__onI,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ( member7862447936710763792od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( id_on_b @ A2 ) ) ) ).

% Id_onI
thf(fact_861_Id__onI,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ A ) @ ( id_on_a @ A2 ) ) ) ).

% Id_onI
thf(fact_862_Id__onI,axiom,
    ! [A: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ A2 )
     => ( member5548800708997798032term_a @ ( produc5718452834064904663term_a @ A @ A ) @ ( id_on_2009952563750624742term_a @ A2 ) ) ) ).

% Id_onI
thf(fact_863_Id__onI,axiom,
    ! [A: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ A2 )
     => ( member8191768239178080336list_a @ ( produc6837034575241423639list_a @ A @ A ) @ ( id_on_list_a @ A2 ) ) ) ).

% Id_onI
thf(fact_864_Id__onI,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ A2 )
     => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ).

% Id_onI
thf(fact_865_Id__onI,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A2 ) ) ) ).

% Id_onI
thf(fact_866_term_Orel__intros_I2_J,axiom,
    ! [X23: nat,Y22: nat,R: a > a > $o] :
      ( ( X23 = Y22 )
     => ( relati3163788165526728396rm_a_a @ R @ ( relational_Var_a @ X23 ) @ ( relational_Var_a @ Y22 ) ) ) ).

% term.rel_intros(2)
thf(fact_867_term_Orel__intros_I2_J,axiom,
    ! [X23: nat,Y22: nat,R: nat > nat > $o] :
      ( ( X23 = Y22 )
     => ( relati2881564729679077486at_nat @ R @ ( relational_Var_nat @ X23 ) @ ( relational_Var_nat @ Y22 ) ) ) ).

% term.rel_intros(2)
thf(fact_868_term_Orel__inject_I2_J,axiom,
    ! [R: a > a > $o,X23: nat,Y22: nat] :
      ( ( relati3163788165526728396rm_a_a @ R @ ( relational_Var_a @ X23 ) @ ( relational_Var_a @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% term.rel_inject(2)
thf(fact_869_term_Orel__inject_I2_J,axiom,
    ! [R: nat > nat > $o,X23: nat,Y22: nat] :
      ( ( relati2881564729679077486at_nat @ R @ ( relational_Var_nat @ X23 ) @ ( relational_Var_nat @ Y22 ) )
      = ( X23 = Y22 ) ) ).

% term.rel_inject(2)
thf(fact_870_Relational__Calculus_Oterm_Osimps_I10_J,axiom,
    ! [F8: nat > nat,X23: nat] :
      ( ( relati2575597170284168561at_nat @ F8 @ ( relational_Var_nat @ X23 ) )
      = ( relational_Var_nat @ X23 ) ) ).

% Relational_Calculus.term.simps(10)
thf(fact_871_Id__onE,axiom,
    ! [C: product_prod_b_b,A2: set_b] :
      ( ( member7862447936710763792od_b_b @ C @ ( id_on_b @ A2 ) )
     => ~ ! [X2: b] :
            ( ( member_b @ X2 @ A2 )
           => ( C
             != ( product_Pair_b_b @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_872_Id__onE,axiom,
    ! [C: product_prod_a_a,A2: set_a] :
      ( ( member1426531477525435216od_a_a @ C @ ( id_on_a @ A2 ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ A2 )
           => ( C
             != ( product_Pair_a_a @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_873_Id__onE,axiom,
    ! [C: produc2716692642101138535term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5548800708997798032term_a @ C @ ( id_on_2009952563750624742term_a @ A2 ) )
     => ~ ! [X2: relational_term_a] :
            ( ( member5466445112152945266term_a @ X2 @ A2 )
           => ( C
             != ( produc5718452834064904663term_a @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_874_Id__onE,axiom,
    ! [C: produc9164743771328383783list_a,A2: set_list_a] :
      ( ( member8191768239178080336list_a @ C @ ( id_on_list_a @ A2 ) )
     => ~ ! [X2: list_a] :
            ( ( member_list_a @ X2 @ A2 )
           => ( C
             != ( produc6837034575241423639list_a @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_875_Id__onE,axiom,
    ! [C: produc859450856879609959at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8206827879206165904at_nat @ C @ ( id_on_2554058798563519774at_nat @ A2 ) )
     => ~ ! [X2: product_prod_nat_nat] :
            ( ( member8440522571783428010at_nat @ X2 @ A2 )
           => ( C
             != ( produc6161850002892822231at_nat @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_876_Id__onE,axiom,
    ! [C: product_prod_nat_nat,A2: set_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A2 ) )
     => ~ ! [X2: nat] :
            ( ( member_nat @ X2 @ A2 )
           => ( C
             != ( product_Pair_nat_nat @ X2 @ X2 ) ) ) ) ).

% Id_onE
thf(fact_877_Id__on__eqI,axiom,
    ! [A: b,B2: b,A2: set_b] :
      ( ( A = B2 )
     => ( ( member_b @ A @ A2 )
       => ( member7862447936710763792od_b_b @ ( product_Pair_b_b @ A @ B2 ) @ ( id_on_b @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_878_Id__on__eqI,axiom,
    ! [A: a,B2: a,A2: set_a] :
      ( ( A = B2 )
     => ( ( member_a @ A @ A2 )
       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( id_on_a @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_879_Id__on__eqI,axiom,
    ! [A: relational_term_a,B2: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( A = B2 )
     => ( ( member5466445112152945266term_a @ A @ A2 )
       => ( member5548800708997798032term_a @ ( produc5718452834064904663term_a @ A @ B2 ) @ ( id_on_2009952563750624742term_a @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_880_Id__on__eqI,axiom,
    ! [A: list_a,B2: list_a,A2: set_list_a] :
      ( ( A = B2 )
     => ( ( member_list_a @ A @ A2 )
       => ( member8191768239178080336list_a @ ( produc6837034575241423639list_a @ A @ B2 ) @ ( id_on_list_a @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_881_Id__on__eqI,axiom,
    ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( A = B2 )
     => ( ( member8440522571783428010at_nat @ A @ A2 )
       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B2 ) @ ( id_on_2554058798563519774at_nat @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_882_Id__on__eqI,axiom,
    ! [A: nat,B2: nat,A2: set_nat] :
      ( ( A = B2 )
     => ( ( member_nat @ A @ A2 )
       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B2 ) @ ( id_on_nat @ A2 ) ) ) ) ).

% Id_on_eqI
thf(fact_883_Id__on__iff,axiom,
    ! [X3: b,Y: b,A2: set_b] :
      ( ( member7862447936710763792od_b_b @ ( product_Pair_b_b @ X3 @ Y ) @ ( id_on_b @ A2 ) )
      = ( ( X3 = Y )
        & ( member_b @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_884_Id__on__iff,axiom,
    ! [X3: a,Y: a,A2: set_a] :
      ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y ) @ ( id_on_a @ A2 ) )
      = ( ( X3 = Y )
        & ( member_a @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_885_Id__on__iff,axiom,
    ! [X3: relational_term_a,Y: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5548800708997798032term_a @ ( produc5718452834064904663term_a @ X3 @ Y ) @ ( id_on_2009952563750624742term_a @ A2 ) )
      = ( ( X3 = Y )
        & ( member5466445112152945266term_a @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_886_Id__on__iff,axiom,
    ! [X3: list_a,Y: list_a,A2: set_list_a] :
      ( ( member8191768239178080336list_a @ ( produc6837034575241423639list_a @ X3 @ Y ) @ ( id_on_list_a @ A2 ) )
      = ( ( X3 = Y )
        & ( member_list_a @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_887_Id__on__iff,axiom,
    ! [X3: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y ) @ ( id_on_2554058798563519774at_nat @ A2 ) )
      = ( ( X3 = Y )
        & ( member8440522571783428010at_nat @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_888_Id__on__iff,axiom,
    ! [X3: nat,Y: nat,A2: set_nat] :
      ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ ( id_on_nat @ A2 ) )
      = ( ( X3 = Y )
        & ( member_nat @ X3 @ A2 ) ) ) ).

% Id_on_iff
thf(fact_889_eval__term_Osimps_I2_J,axiom,
    ! [Sigma: nat > a,N2: nat] :
      ( ( relati1177013128715261720term_a @ Sigma @ ( relational_Var_a @ N2 ) )
      = ( Sigma @ N2 ) ) ).

% eval_term.simps(2)
thf(fact_890_fun_Omap__cong__pred,axiom,
    ! [X3: a > a,Ya: a > a,F8: a > $o,G3: a > $o] :
      ( ( X3 = Ya )
     => ( ( basic_pred_fun_a_a
          @ ^ [Uu: a] : $true
          @ ^ [Z5: a] :
              ( ( F8 @ Z5 )
              = ( G3 @ Z5 ) )
          @ Ya )
       => ( ( comp_a_o_a @ F8 @ X3 )
          = ( comp_a_o_a @ G3 @ Ya ) ) ) ) ).

% fun.map_cong_pred
thf(fact_891_fun_Omap__cong__pred,axiom,
    ! [X3: b > b,Ya: b > b,F8: b > $o,G3: b > $o] :
      ( ( X3 = Ya )
     => ( ( basic_pred_fun_b_b
          @ ^ [Uu: b] : $true
          @ ^ [Z5: b] :
              ( ( F8 @ Z5 )
              = ( G3 @ Z5 ) )
          @ Ya )
       => ( ( comp_b_o_b @ F8 @ X3 )
          = ( comp_b_o_b @ G3 @ Ya ) ) ) ) ).

% fun.map_cong_pred
thf(fact_892_product__code,axiom,
    ! [Xs: list_b,Ys: list_nat] :
      ( ( produc7267454701016561149_b_nat @ ( set_b2 @ Xs ) @ ( set_nat2 @ Ys ) )
      = ( set_Pr2160427703459429033_b_nat
        @ ( concat8173426066143602685_b_nat
          @ ( map_b_599084904809770697_b_nat
            @ ^ [X: b] : ( map_na5915426433201511956_b_nat @ ( product_Pair_b_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_893_product__code,axiom,
    ! [Xs: list_nat,Ys: list_nat] :
      ( ( produc929334515565554804at_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ Ys ) )
      = ( set_Pr5648618587558075414at_nat
        @ ( concat7691415812945658306at_nat
          @ ( map_na4561905831291441265at_nat
            @ ^ [X: nat] : ( map_na7298421622053143531at_nat @ ( product_Pair_nat_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_894_product__code,axiom,
    ! [Xs: list_R6823256787227418703term_a,Ys: list_nat] :
      ( ( produc7419292362220167751_a_nat @ ( set_Re3569617851344498910term_a @ Xs ) @ ( set_nat2 @ Ys ) )
      = ( set_Pr7330506493327882739_a_nat
        @ ( concat921187893273162567_a_nat
          @ ( map_Re2296423716969871709_a_nat
            @ ^ [X: relational_term_a] : ( map_na8727431924180384350_a_nat @ ( produc7406852975468742850_a_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_895_product__code,axiom,
    ! [Xs: list_list_nat,Ys: list_nat] :
      ( ( produc3452567005806842372at_nat @ ( set_list_nat2 @ Xs ) @ ( set_nat2 @ Ys ) )
      = ( set_Pr7715406932454250534at_nat
        @ ( concat2287713305843873746at_nat
          @ ( map_li978161544836236273at_nat
            @ ^ [X: list_nat] : ( map_na91578518272332155at_nat @ ( produc1298395424260782409at_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_896_product__code,axiom,
    ! [Xs: list_nat,Ys: list_R6823256787227418703term_a] :
      ( ( produc1855389550465800357term_a @ ( set_nat2 @ Xs ) @ ( set_Re3569617851344498910term_a @ Ys ) )
      = ( set_Pr7861135356763781785term_a
        @ ( concat1451816756709061613term_a
          @ ( map_na7892716985596332564term_a
            @ ^ [X: nat] : ( map_Re7545003512584125299term_a @ ( produc1842950163714375456term_a @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_897_product__code,axiom,
    ! [Xs: list_nat,Ys: list_list_nat] :
      ( ( produc1213609958644557188st_nat @ ( set_nat2 @ Xs ) @ ( set_list_nat2 @ Ys ) )
      = ( set_Pr1526418413117253030st_nat
        @ ( concat5322096823361652050st_nat
          @ ( map_na3788553780025637377st_nat
            @ ^ [X: nat] : ( map_li4248376968112746091st_nat @ ( produc8282810413953273033st_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_898_product__code,axiom,
    ! [Xs: list_R6823256787227418703term_a,Ys: list_R6823256787227418703term_a] :
      ( ( produc4551712939481758866term_a @ ( set_Re3569617851344498910term_a @ Xs ) @ ( set_Re3569617851344498910term_a @ Ys ) )
      = ( set_Pr5711402074887782140term_a
        @ ( concat7580753900580267688term_a
          @ ( map_Re4862523635040833576term_a
            @ ^ [X: relational_term_a] : ( map_Re1021565884873730722term_a @ ( produc5718452834064904663term_a @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_899_product__code,axiom,
    ! [Xs: list_R6823256787227418703term_a,Ys: list_list_nat] :
      ( ( produc4144661845707822551st_nat @ ( set_Re3569617851344498910term_a @ Xs ) @ ( set_list_nat2 @ Ys ) )
      = ( set_Pr7234668156827496707st_nat
        @ ( concat4557919794027884631st_nat
          @ ( map_Re1576213583866461421st_nat
            @ ^ [X: relational_term_a] : ( map_li9072881189266824318st_nat @ ( produc8752702772314489554st_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_900_product__code,axiom,
    ! [Xs: list_list_nat,Ys: list_R6823256787227418703term_a] :
      ( ( produc6328962015167006485term_a @ ( set_list_nat2 @ Xs ) @ ( set_Re3569617851344498910term_a @ Ys ) )
      = ( set_Pr1016787399942107785term_a
        @ ( concat7563411073997271517term_a
          @ ( map_li705091637597845140term_a
            @ ^ [X: list_nat] : ( map_Re2358163980262620771term_a @ ( produc1713630904918897680term_a @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_901_product__code,axiom,
    ! [Xs: list_list_nat,Ys: list_list_nat] :
      ( ( produc8400933694960370452st_nat @ ( set_list_nat2 @ Xs ) @ ( set_list_nat2 @ Ys ) )
      = ( set_Pr3842133991353686454st_nat
        @ ( concat1372613522848609122st_nat
          @ ( map_li5408149218522361217st_nat
            @ ^ [X: list_nat] : ( map_li6665866383299509243st_nat @ ( produc2694037385005941721st_nat @ X ) @ Ys )
            @ Xs ) ) ) ) ).

% product_code
thf(fact_902_fv_Oelims,axiom,
    ! [X3: relational_fmla_a_b,Y: set_nat] :
      ( ( ( relational_fv_a_b @ X3 )
        = Y )
     => ( ! [Uu3: b,Ts: list_R6823256787227418703term_a] :
            ( ( X3
              = ( relational_Pred_b_a @ Uu3 @ Ts ) )
           => ( Y
             != ( relati4569515538964159125_set_a @ Ts ) ) )
       => ( ( ? [B5: $o] :
                ( X3
                = ( relational_Bool_a_b @ B5 ) )
           => ( Y != bot_bot_set_nat ) )
         => ( ! [X2: nat,T2: relational_term_a] :
                ( ( X3
                  = ( relational_Eq_a_b @ X2 @ T2 ) )
               => ( Y
                 != ( sup_sup_set_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T2 ) ) ) )
           => ( ! [Phi2: relational_fmla_a_b] :
                  ( ( X3
                    = ( relational_Neg_a_b @ Phi2 ) )
                 => ( Y
                   != ( relational_fv_a_b @ Phi2 ) ) )
             => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                   => ( Y
                     != ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                     => ( Y
                       != ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) ) )
                 => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                       => ( Y
                         != ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( insert_nat @ Z3 @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ) ) ).

% fv.elims
thf(fact_903_product__lists__set,axiom,
    ! [Xss: list_list_b] :
      ( ( set_list_b2 @ ( product_lists_b @ Xss ) )
      = ( collect_list_b
        @ ^ [Xs2: list_b] :
            ( list_all2_b_list_b
            @ ^ [X: b,Ys2: list_b] : ( member_b @ X @ ( set_b2 @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_904_product__lists__set,axiom,
    ! [Xss: list_list_a] :
      ( ( set_list_a2 @ ( product_lists_a @ Xss ) )
      = ( collect_list_a
        @ ^ [Xs2: list_a] :
            ( list_all2_a_list_a
            @ ^ [X: a,Ys2: list_a] : ( member_a @ X @ ( set_a2 @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_905_product__lists__set,axiom,
    ! [Xss: list_list_list_a] :
      ( ( set_list_list_a2 @ ( product_lists_list_a @ Xss ) )
      = ( collect_list_list_a
        @ ^ [Xs2: list_list_a] :
            ( list_a1787013445579514253list_a
            @ ^ [X: list_a,Ys2: list_list_a] : ( member_list_a @ X @ ( set_list_a2 @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_906_product__lists__set,axiom,
    ! [Xss: list_l3264859301627795341at_nat] :
      ( ( set_li2962362208618583836at_nat @ ( produc8746550462604311920at_nat @ Xss ) )
      = ( collec3343600615725829874at_nat
        @ ^ [Xs2: list_P6011104703257516679at_nat] :
            ( list_a6131682974029072717at_nat
            @ ^ [X: product_prod_nat_nat,Ys2: list_P6011104703257516679at_nat] : ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_907_product__lists__set,axiom,
    ! [Xss: list_l929788865687709653term_a] :
      ( ( set_li1177193810238305892term_a @ ( produc708360400047254840term_a @ Xss ) )
      = ( collec8200894614646537018term_a
        @ ^ [Xs2: list_R6823256787227418703term_a] :
            ( list_a3044844760545493709term_a
            @ ^ [X: relational_term_a,Ys2: list_R6823256787227418703term_a] : ( member5466445112152945266term_a @ X @ ( set_Re3569617851344498910term_a @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_908_product__lists__set,axiom,
    ! [Xss: list_list_list_nat] :
      ( ( set_list_list_nat2 @ ( produc6783906451316923569st_nat @ Xss ) )
      = ( collec5989764272469232197st_nat
        @ ^ [Xs2: list_list_nat] :
            ( list_a6876179990855209945st_nat
            @ ^ [X: list_nat,Ys2: list_list_nat] : ( member_list_nat @ X @ ( set_list_nat2 @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_909_product__lists__set,axiom,
    ! [Xss: list_list_nat] :
      ( ( set_list_nat2 @ ( product_lists_nat @ Xss ) )
      = ( collect_list_nat
        @ ^ [Xs2: list_nat] :
            ( list_a5155878676884504761st_nat
            @ ^ [X: nat,Ys2: list_nat] : ( member_nat @ X @ ( set_nat2 @ Ys2 ) )
            @ Xs2
            @ Xss ) ) ) ).

% product_lists_set
thf(fact_910_minus__apply,axiom,
    ( minus_minus_nat_o
    = ( ^ [A3: nat > $o,B3: nat > $o,X: nat] : ( minus_minus_o @ ( A3 @ X ) @ ( B3 @ X ) ) ) ) ).

% minus_apply
thf(fact_911_empty__Collect__eq,axiom,
    ! [P: list_nat > $o] :
      ( ( bot_bot_set_list_nat
        = ( collect_list_nat @ P ) )
      = ( ! [X: list_nat] :
            ~ ( P @ X ) ) ) ).

% empty_Collect_eq
thf(fact_912_empty__Collect__eq,axiom,
    ! [P: nat > $o] :
      ( ( bot_bot_set_nat
        = ( collect_nat @ P ) )
      = ( ! [X: nat] :
            ~ ( P @ X ) ) ) ).

% empty_Collect_eq
thf(fact_913_Collect__empty__eq,axiom,
    ! [P: list_nat > $o] :
      ( ( ( collect_list_nat @ P )
        = bot_bot_set_list_nat )
      = ( ! [X: list_nat] :
            ~ ( P @ X ) ) ) ).

% Collect_empty_eq
thf(fact_914_Collect__empty__eq,axiom,
    ! [P: nat > $o] :
      ( ( ( collect_nat @ P )
        = bot_bot_set_nat )
      = ( ! [X: nat] :
            ~ ( P @ X ) ) ) ).

% Collect_empty_eq
thf(fact_915_all__not__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ! [X: b] :
            ~ ( member_b @ X @ A2 ) )
      = ( A2 = bot_bot_set_b ) ) ).

% all_not_in_conv
thf(fact_916_all__not__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ! [X: a] :
            ~ ( member_a @ X @ A2 ) )
      = ( A2 = bot_bot_set_a ) ) ).

% all_not_in_conv
thf(fact_917_all__not__in__conv,axiom,
    ! [A2: set_Re5178783185447174953term_a] :
      ( ( ! [X: relational_term_a] :
            ~ ( member5466445112152945266term_a @ X @ A2 ) )
      = ( A2 = bot_bo8783692591515826581term_a ) ) ).

% all_not_in_conv
thf(fact_918_all__not__in__conv,axiom,
    ! [A2: set_list_a] :
      ( ( ! [X: list_a] :
            ~ ( member_list_a @ X @ A2 ) )
      = ( A2 = bot_bot_set_list_a ) ) ).

% all_not_in_conv
thf(fact_919_all__not__in__conv,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] :
      ( ( ! [X: product_prod_nat_nat] :
            ~ ( member8440522571783428010at_nat @ X @ A2 ) )
      = ( A2 = bot_bo2099793752762293965at_nat ) ) ).

% all_not_in_conv
thf(fact_920_all__not__in__conv,axiom,
    ! [A2: set_nat] :
      ( ( ! [X: nat] :
            ~ ( member_nat @ X @ A2 ) )
      = ( A2 = bot_bot_set_nat ) ) ).

% all_not_in_conv
thf(fact_921_empty__iff,axiom,
    ! [C: b] :
      ~ ( member_b @ C @ bot_bot_set_b ) ).

% empty_iff
thf(fact_922_empty__iff,axiom,
    ! [C: a] :
      ~ ( member_a @ C @ bot_bot_set_a ) ).

% empty_iff
thf(fact_923_empty__iff,axiom,
    ! [C: relational_term_a] :
      ~ ( member5466445112152945266term_a @ C @ bot_bo8783692591515826581term_a ) ).

% empty_iff
thf(fact_924_empty__iff,axiom,
    ! [C: list_a] :
      ~ ( member_list_a @ C @ bot_bot_set_list_a ) ).

% empty_iff
thf(fact_925_empty__iff,axiom,
    ! [C: product_prod_nat_nat] :
      ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).

% empty_iff
thf(fact_926_empty__iff,axiom,
    ! [C: nat] :
      ~ ( member_nat @ C @ bot_bot_set_nat ) ).

% empty_iff
thf(fact_927_insert__absorb2,axiom,
    ! [X3: nat,A2: set_nat] :
      ( ( insert_nat @ X3 @ ( insert_nat @ X3 @ A2 ) )
      = ( insert_nat @ X3 @ A2 ) ) ).

% insert_absorb2
thf(fact_928_insert__iff,axiom,
    ! [A: b,B2: b,A2: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_929_insert__iff,axiom,
    ! [A: a,B2: a,A2: set_a] :
      ( ( member_a @ A @ ( insert_a @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_930_insert__iff,axiom,
    ! [A: relational_term_a,B2: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member5466445112152945266term_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_931_insert__iff,axiom,
    ! [A: list_a,B2: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ ( insert_list_a @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_list_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_932_insert__iff,axiom,
    ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member8440522571783428010at_nat @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_933_insert__iff,axiom,
    ! [A: nat,B2: nat,A2: set_nat] :
      ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_nat @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_934_insertCI,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( ~ ( member_b @ A @ B )
       => ( A = B2 ) )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertCI
thf(fact_935_insertCI,axiom,
    ! [A: a,B: set_a,B2: a] :
      ( ( ~ ( member_a @ A @ B )
       => ( A = B2 ) )
     => ( member_a @ A @ ( insert_a @ B2 @ B ) ) ) ).

% insertCI
thf(fact_936_insertCI,axiom,
    ! [A: relational_term_a,B: set_Re5178783185447174953term_a,B2: relational_term_a] :
      ( ( ~ ( member5466445112152945266term_a @ A @ B )
       => ( A = B2 ) )
     => ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ B2 @ B ) ) ) ).

% insertCI
thf(fact_937_insertCI,axiom,
    ! [A: list_a,B: set_list_a,B2: list_a] :
      ( ( ~ ( member_list_a @ A @ B )
       => ( A = B2 ) )
     => ( member_list_a @ A @ ( insert_list_a @ B2 @ B ) ) ) ).

% insertCI
thf(fact_938_insertCI,axiom,
    ! [A: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
      ( ( ~ ( member8440522571783428010at_nat @ A @ B )
       => ( A = B2 ) )
     => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ B ) ) ) ).

% insertCI
thf(fact_939_insertCI,axiom,
    ! [A: nat,B: set_nat,B2: nat] :
      ( ( ~ ( member_nat @ A @ B )
       => ( A = B2 ) )
     => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).

% insertCI
thf(fact_940_Diff__idemp,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ B )
      = ( minus_minus_set_nat @ A2 @ B ) ) ).

% Diff_idemp
thf(fact_941_Diff__iff,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B ) )
      = ( ( member_b @ C @ A2 )
        & ~ ( member_b @ C @ B ) ) ) ).

% Diff_iff
thf(fact_942_Diff__iff,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B ) )
      = ( ( member_a @ C @ A2 )
        & ~ ( member_a @ C @ B ) ) ) ).

% Diff_iff
thf(fact_943_Diff__iff,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( minus_3019981187013541264term_a @ A2 @ B ) )
      = ( ( member5466445112152945266term_a @ C @ A2 )
        & ~ ( member5466445112152945266term_a @ C @ B ) ) ) ).

% Diff_iff
thf(fact_944_Diff__iff,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( minus_646659088055828811list_a @ A2 @ B ) )
      = ( ( member_list_a @ C @ A2 )
        & ~ ( member_list_a @ C @ B ) ) ) ).

% Diff_iff
thf(fact_945_Diff__iff,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B ) )
      = ( ( member8440522571783428010at_nat @ C @ A2 )
        & ~ ( member8440522571783428010at_nat @ C @ B ) ) ) ).

% Diff_iff
thf(fact_946_Diff__iff,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
      = ( ( member_nat @ C @ A2 )
        & ~ ( member_nat @ C @ B ) ) ) ).

% Diff_iff
thf(fact_947_DiffI,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ A2 )
     => ( ~ ( member_b @ C @ B )
       => ( member_b @ C @ ( minus_minus_set_b @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_948_DiffI,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ A2 )
     => ( ~ ( member_a @ C @ B )
       => ( member_a @ C @ ( minus_minus_set_a @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_949_DiffI,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ A2 )
     => ( ~ ( member5466445112152945266term_a @ C @ B )
       => ( member5466445112152945266term_a @ C @ ( minus_3019981187013541264term_a @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_950_DiffI,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ A2 )
     => ( ~ ( member_list_a @ C @ B )
       => ( member_list_a @ C @ ( minus_646659088055828811list_a @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_951_DiffI,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ A2 )
     => ( ~ ( member8440522571783428010at_nat @ C @ B )
       => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_952_DiffI,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ A2 )
     => ( ~ ( member_nat @ C @ B )
       => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) ) ) ) ).

% DiffI
thf(fact_953_singletonI,axiom,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ) ).

% singletonI
thf(fact_954_singletonI,axiom,
    ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).

% singletonI
thf(fact_955_singletonI,axiom,
    ! [A: relational_term_a] : ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ A @ bot_bo8783692591515826581term_a ) ) ).

% singletonI
thf(fact_956_singletonI,axiom,
    ! [A: list_a] : ( member_list_a @ A @ ( insert_list_a @ A @ bot_bot_set_list_a ) ) ).

% singletonI
thf(fact_957_singletonI,axiom,
    ! [A: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).

% singletonI
thf(fact_958_singletonI,axiom,
    ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singletonI
thf(fact_959_sup__bot__left,axiom,
    ! [X3: set_a] :
      ( ( sup_sup_set_a @ bot_bot_set_a @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_960_sup__bot__left,axiom,
    ! [X3: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_961_sup__bot__left,axiom,
    ! [X3: set_nat] :
      ( ( sup_sup_set_nat @ bot_bot_set_nat @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_962_sup__bot__left,axiom,
    ! [X3: nat > $o] :
      ( ( sup_sup_nat_o @ bot_bot_nat_o @ X3 )
      = X3 ) ).

% sup_bot_left
thf(fact_963_sup__bot__right,axiom,
    ! [X3: set_a] :
      ( ( sup_sup_set_a @ X3 @ bot_bot_set_a )
      = X3 ) ).

% sup_bot_right
thf(fact_964_sup__bot__right,axiom,
    ! [X3: set_b] :
      ( ( sup_sup_set_b @ X3 @ bot_bot_set_b )
      = X3 ) ).

% sup_bot_right
thf(fact_965_sup__bot__right,axiom,
    ! [X3: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ bot_bot_set_nat )
      = X3 ) ).

% sup_bot_right
thf(fact_966_sup__bot__right,axiom,
    ! [X3: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ bot_bot_nat_o )
      = X3 ) ).

% sup_bot_right
thf(fact_967_bot__eq__sup__iff,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( bot_bot_set_a
        = ( sup_sup_set_a @ X3 @ Y ) )
      = ( ( X3 = bot_bot_set_a )
        & ( Y = bot_bot_set_a ) ) ) ).

% bot_eq_sup_iff
thf(fact_968_bot__eq__sup__iff,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( bot_bot_set_b
        = ( sup_sup_set_b @ X3 @ Y ) )
      = ( ( X3 = bot_bot_set_b )
        & ( Y = bot_bot_set_b ) ) ) ).

% bot_eq_sup_iff
thf(fact_969_bot__eq__sup__iff,axiom,
    ! [X3: set_nat,Y: set_nat] :
      ( ( bot_bot_set_nat
        = ( sup_sup_set_nat @ X3 @ Y ) )
      = ( ( X3 = bot_bot_set_nat )
        & ( Y = bot_bot_set_nat ) ) ) ).

% bot_eq_sup_iff
thf(fact_970_bot__eq__sup__iff,axiom,
    ! [X3: nat > $o,Y: nat > $o] :
      ( ( bot_bot_nat_o
        = ( sup_sup_nat_o @ X3 @ Y ) )
      = ( ( X3 = bot_bot_nat_o )
        & ( Y = bot_bot_nat_o ) ) ) ).

% bot_eq_sup_iff
thf(fact_971_sup__eq__bot__iff,axiom,
    ! [X3: set_a,Y: set_a] :
      ( ( ( sup_sup_set_a @ X3 @ Y )
        = bot_bot_set_a )
      = ( ( X3 = bot_bot_set_a )
        & ( Y = bot_bot_set_a ) ) ) ).

% sup_eq_bot_iff
thf(fact_972_sup__eq__bot__iff,axiom,
    ! [X3: set_b,Y: set_b] :
      ( ( ( sup_sup_set_b @ X3 @ Y )
        = bot_bot_set_b )
      = ( ( X3 = bot_bot_set_b )
        & ( Y = bot_bot_set_b ) ) ) ).

% sup_eq_bot_iff
thf(fact_973_sup__eq__bot__iff,axiom,
    ! [X3: set_nat,Y: set_nat] :
      ( ( ( sup_sup_set_nat @ X3 @ Y )
        = bot_bot_set_nat )
      = ( ( X3 = bot_bot_set_nat )
        & ( Y = bot_bot_set_nat ) ) ) ).

% sup_eq_bot_iff
thf(fact_974_sup__eq__bot__iff,axiom,
    ! [X3: nat > $o,Y: nat > $o] :
      ( ( ( sup_sup_nat_o @ X3 @ Y )
        = bot_bot_nat_o )
      = ( ( X3 = bot_bot_nat_o )
        & ( Y = bot_bot_nat_o ) ) ) ).

% sup_eq_bot_iff
thf(fact_975_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( ( sup_sup_set_a @ A @ B2 )
        = bot_bot_set_a )
      = ( ( A = bot_bot_set_a )
        & ( B2 = bot_bot_set_a ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_976_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( ( sup_sup_set_b @ A @ B2 )
        = bot_bot_set_b )
      = ( ( A = bot_bot_set_b )
        & ( B2 = bot_bot_set_b ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_977_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( ( sup_sup_set_nat @ A @ B2 )
        = bot_bot_set_nat )
      = ( ( A = bot_bot_set_nat )
        & ( B2 = bot_bot_set_nat ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_978_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: nat > $o,B2: nat > $o] :
      ( ( ( sup_sup_nat_o @ A @ B2 )
        = bot_bot_nat_o )
      = ( ( A = bot_bot_nat_o )
        & ( B2 = bot_bot_nat_o ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_979_sup__bot_Oleft__neutral,axiom,
    ! [A: set_a] :
      ( ( sup_sup_set_a @ bot_bot_set_a @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_980_sup__bot_Oleft__neutral,axiom,
    ! [A: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_981_sup__bot_Oleft__neutral,axiom,
    ! [A: set_nat] :
      ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_982_sup__bot_Oleft__neutral,axiom,
    ! [A: nat > $o] :
      ( ( sup_sup_nat_o @ bot_bot_nat_o @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_983_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( bot_bot_set_a
        = ( sup_sup_set_a @ A @ B2 ) )
      = ( ( A = bot_bot_set_a )
        & ( B2 = bot_bot_set_a ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_984_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( bot_bot_set_b
        = ( sup_sup_set_b @ A @ B2 ) )
      = ( ( A = bot_bot_set_b )
        & ( B2 = bot_bot_set_b ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_985_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_nat,B2: set_nat] :
      ( ( bot_bot_set_nat
        = ( sup_sup_set_nat @ A @ B2 ) )
      = ( ( A = bot_bot_set_nat )
        & ( B2 = bot_bot_set_nat ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_986_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: nat > $o,B2: nat > $o] :
      ( ( bot_bot_nat_o
        = ( sup_sup_nat_o @ A @ B2 ) )
      = ( ( A = bot_bot_nat_o )
        & ( B2 = bot_bot_nat_o ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_987_sup__bot_Oright__neutral,axiom,
    ! [A: set_a] :
      ( ( sup_sup_set_a @ A @ bot_bot_set_a )
      = A ) ).

% sup_bot.right_neutral
thf(fact_988_sup__bot_Oright__neutral,axiom,
    ! [A: set_b] :
      ( ( sup_sup_set_b @ A @ bot_bot_set_b )
      = A ) ).

% sup_bot.right_neutral
thf(fact_989_sup__bot_Oright__neutral,axiom,
    ! [A: set_nat] :
      ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
      = A ) ).

% sup_bot.right_neutral
thf(fact_990_sup__bot_Oright__neutral,axiom,
    ! [A: nat > $o] :
      ( ( sup_sup_nat_o @ A @ bot_bot_nat_o )
      = A ) ).

% sup_bot.right_neutral
thf(fact_991_ball__empty,axiom,
    ! [P: nat > $o,X5: nat] :
      ( ( member_nat @ X5 @ bot_bot_set_nat )
     => ( P @ X5 ) ) ).

% ball_empty
thf(fact_992_Un__empty,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ( sup_sup_set_a @ A2 @ B )
        = bot_bot_set_a )
      = ( ( A2 = bot_bot_set_a )
        & ( B = bot_bot_set_a ) ) ) ).

% Un_empty
thf(fact_993_Un__empty,axiom,
    ! [A2: set_b,B: set_b] :
      ( ( ( sup_sup_set_b @ A2 @ B )
        = bot_bot_set_b )
      = ( ( A2 = bot_bot_set_b )
        & ( B = bot_bot_set_b ) ) ) ).

% Un_empty
thf(fact_994_Un__empty,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ( ( sup_sup_set_nat @ A2 @ B )
        = bot_bot_set_nat )
      = ( ( A2 = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ) ).

% Un_empty
thf(fact_995_Diff__cancel,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ A2 )
      = bot_bot_set_nat ) ).

% Diff_cancel
thf(fact_996_empty__Diff,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
      = bot_bot_set_nat ) ).

% empty_Diff
thf(fact_997_Diff__empty,axiom,
    ! [A2: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
      = A2 ) ).

% Diff_empty
thf(fact_998_Un__insert__left,axiom,
    ! [A: nat,B: set_nat,C2: set_nat] :
      ( ( sup_sup_set_nat @ ( insert_nat @ A @ B ) @ C2 )
      = ( insert_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).

% Un_insert_left
thf(fact_999_Un__insert__left,axiom,
    ! [A: a,B: set_a,C2: set_a] :
      ( ( sup_sup_set_a @ ( insert_a @ A @ B ) @ C2 )
      = ( insert_a @ A @ ( sup_sup_set_a @ B @ C2 ) ) ) ).

% Un_insert_left
thf(fact_1000_Un__insert__left,axiom,
    ! [A: b,B: set_b,C2: set_b] :
      ( ( sup_sup_set_b @ ( insert_b @ A @ B ) @ C2 )
      = ( insert_b @ A @ ( sup_sup_set_b @ B @ C2 ) ) ) ).

% Un_insert_left
thf(fact_1001_Un__insert__right,axiom,
    ! [A2: set_nat,A: nat,B: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( insert_nat @ A @ B ) )
      = ( insert_nat @ A @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).

% Un_insert_right
thf(fact_1002_Un__insert__right,axiom,
    ! [A2: set_a,A: a,B: set_a] :
      ( ( sup_sup_set_a @ A2 @ ( insert_a @ A @ B ) )
      = ( insert_a @ A @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% Un_insert_right
thf(fact_1003_Un__insert__right,axiom,
    ! [A2: set_b,A: b,B: set_b] :
      ( ( sup_sup_set_b @ A2 @ ( insert_b @ A @ B ) )
      = ( insert_b @ A @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% Un_insert_right
thf(fact_1004_insert__Diff1,axiom,
    ! [X3: b,B: set_b,A2: set_b] :
      ( ( member_b @ X3 @ B )
     => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A2 ) @ B )
        = ( minus_minus_set_b @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1005_insert__Diff1,axiom,
    ! [X3: a,B: set_a,A2: set_a] :
      ( ( member_a @ X3 @ B )
     => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A2 ) @ B )
        = ( minus_minus_set_a @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1006_insert__Diff1,axiom,
    ! [X3: relational_term_a,B: set_Re5178783185447174953term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ X3 @ B )
     => ( ( minus_3019981187013541264term_a @ ( insert8574850016668666393term_a @ X3 @ A2 ) @ B )
        = ( minus_3019981187013541264term_a @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1007_insert__Diff1,axiom,
    ! [X3: list_a,B: set_list_a,A2: set_list_a] :
      ( ( member_list_a @ X3 @ B )
     => ( ( minus_646659088055828811list_a @ ( insert_list_a @ X3 @ A2 ) @ B )
        = ( minus_646659088055828811list_a @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1008_insert__Diff1,axiom,
    ! [X3: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ X3 @ B )
     => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X3 @ A2 ) @ B )
        = ( minus_1356011639430497352at_nat @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1009_insert__Diff1,axiom,
    ! [X3: nat,B: set_nat,A2: set_nat] :
      ( ( member_nat @ X3 @ B )
     => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B )
        = ( minus_minus_set_nat @ A2 @ B ) ) ) ).

% insert_Diff1
thf(fact_1010_Diff__insert0,axiom,
    ! [X3: b,A2: set_b,B: set_b] :
      ( ~ ( member_b @ X3 @ A2 )
     => ( ( minus_minus_set_b @ A2 @ ( insert_b @ X3 @ B ) )
        = ( minus_minus_set_b @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1011_Diff__insert0,axiom,
    ! [X3: a,A2: set_a,B: set_a] :
      ( ~ ( member_a @ X3 @ A2 )
     => ( ( minus_minus_set_a @ A2 @ ( insert_a @ X3 @ B ) )
        = ( minus_minus_set_a @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1012_Diff__insert0,axiom,
    ! [X3: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ~ ( member5466445112152945266term_a @ X3 @ A2 )
     => ( ( minus_3019981187013541264term_a @ A2 @ ( insert8574850016668666393term_a @ X3 @ B ) )
        = ( minus_3019981187013541264term_a @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1013_Diff__insert0,axiom,
    ! [X3: list_a,A2: set_list_a,B: set_list_a] :
      ( ~ ( member_list_a @ X3 @ A2 )
     => ( ( minus_646659088055828811list_a @ A2 @ ( insert_list_a @ X3 @ B ) )
        = ( minus_646659088055828811list_a @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1014_Diff__insert0,axiom,
    ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
     => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X3 @ B ) )
        = ( minus_1356011639430497352at_nat @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1015_Diff__insert0,axiom,
    ! [X3: nat,A2: set_nat,B: set_nat] :
      ( ~ ( member_nat @ X3 @ A2 )
     => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ B ) )
        = ( minus_minus_set_nat @ A2 @ B ) ) ) ).

% Diff_insert0
thf(fact_1016_Un__Diff__cancel,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( sup_sup_set_a @ A2 @ ( minus_minus_set_a @ B @ A2 ) )
      = ( sup_sup_set_a @ A2 @ B ) ) ).

% Un_Diff_cancel
thf(fact_1017_Un__Diff__cancel,axiom,
    ! [A2: set_b,B: set_b] :
      ( ( sup_sup_set_b @ A2 @ ( minus_minus_set_b @ B @ A2 ) )
      = ( sup_sup_set_b @ A2 @ B ) ) ).

% Un_Diff_cancel
thf(fact_1018_Un__Diff__cancel,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B @ A2 ) )
      = ( sup_sup_set_nat @ A2 @ B ) ) ).

% Un_Diff_cancel
thf(fact_1019_Un__Diff__cancel2,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( sup_sup_set_a @ ( minus_minus_set_a @ B @ A2 ) @ A2 )
      = ( sup_sup_set_a @ B @ A2 ) ) ).

% Un_Diff_cancel2
thf(fact_1020_Un__Diff__cancel2,axiom,
    ! [B: set_b,A2: set_b] :
      ( ( sup_sup_set_b @ ( minus_minus_set_b @ B @ A2 ) @ A2 )
      = ( sup_sup_set_b @ B @ A2 ) ) ).

% Un_Diff_cancel2
thf(fact_1021_Un__Diff__cancel2,axiom,
    ! [B: set_nat,A2: set_nat] :
      ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B @ A2 ) @ A2 )
      = ( sup_sup_set_nat @ B @ A2 ) ) ).

% Un_Diff_cancel2
thf(fact_1022_Id__on__empty,axiom,
    ( ( id_on_nat @ bot_bot_set_nat )
    = bot_bo2099793752762293965at_nat ) ).

% Id_on_empty
thf(fact_1023_singleton__conv2,axiom,
    ! [A: list_nat] :
      ( ( collect_list_nat
        @ ( ^ [Y5: list_nat,Z4: list_nat] : ( Y5 = Z4 )
          @ A ) )
      = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).

% singleton_conv2
thf(fact_1024_singleton__conv2,axiom,
    ! [A: nat] :
      ( ( collect_nat
        @ ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
          @ A ) )
      = ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singleton_conv2
thf(fact_1025_singleton__conv,axiom,
    ! [A: list_nat] :
      ( ( collect_list_nat
        @ ^ [X: list_nat] : ( X = A ) )
      = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).

% singleton_conv
thf(fact_1026_singleton__conv,axiom,
    ! [A: nat] :
      ( ( collect_nat
        @ ^ [X: nat] : ( X = A ) )
      = ( insert_nat @ A @ bot_bot_set_nat ) ) ).

% singleton_conv
thf(fact_1027_insert__Diff__single,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
      = ( insert_nat @ A @ A2 ) ) ).

% insert_Diff_single
thf(fact_1028_fv__exists,axiom,
    ! [X3: nat,Q: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relati3989891337220013914ts_a_b @ X3 @ Q ) )
      = ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).

% fv_exists
thf(fact_1029_fv__term__set_Osimps_I1_J,axiom,
    ! [N2: nat] :
      ( ( relati6004689760767320788_set_a @ ( relational_Var_a @ N2 ) )
      = ( insert_nat @ N2 @ bot_bot_set_nat ) ) ).

% fv_term_set.simps(1)
thf(fact_1030_boolean__algebra_Odisj__zero__right,axiom,
    ! [X3: set_a] :
      ( ( sup_sup_set_a @ X3 @ bot_bot_set_a )
      = X3 ) ).

% boolean_algebra.disj_zero_right
thf(fact_1031_boolean__algebra_Odisj__zero__right,axiom,
    ! [X3: set_b] :
      ( ( sup_sup_set_b @ X3 @ bot_bot_set_b )
      = X3 ) ).

% boolean_algebra.disj_zero_right
thf(fact_1032_boolean__algebra_Odisj__zero__right,axiom,
    ! [X3: set_nat] :
      ( ( sup_sup_set_nat @ X3 @ bot_bot_set_nat )
      = X3 ) ).

% boolean_algebra.disj_zero_right
thf(fact_1033_boolean__algebra_Odisj__zero__right,axiom,
    ! [X3: nat > $o] :
      ( ( sup_sup_nat_o @ X3 @ bot_bot_nat_o )
      = X3 ) ).

% boolean_algebra.disj_zero_right
thf(fact_1034_insert__is__Un,axiom,
    ( insert_a
    = ( ^ [A4: a] : ( sup_sup_set_a @ ( insert_a @ A4 @ bot_bot_set_a ) ) ) ) ).

% insert_is_Un
thf(fact_1035_insert__is__Un,axiom,
    ( insert_b
    = ( ^ [A4: b] : ( sup_sup_set_b @ ( insert_b @ A4 @ bot_bot_set_b ) ) ) ) ).

% insert_is_Un
thf(fact_1036_insert__is__Un,axiom,
    ( insert_nat
    = ( ^ [A4: nat] : ( sup_sup_set_nat @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ).

% insert_is_Un
thf(fact_1037_Un__singleton__iff,axiom,
    ! [A2: set_a,B: set_a,X3: a] :
      ( ( ( sup_sup_set_a @ A2 @ B )
        = ( insert_a @ X3 @ bot_bot_set_a ) )
      = ( ( ( A2 = bot_bot_set_a )
          & ( B
            = ( insert_a @ X3 @ bot_bot_set_a ) ) )
        | ( ( A2
            = ( insert_a @ X3 @ bot_bot_set_a ) )
          & ( B = bot_bot_set_a ) )
        | ( ( A2
            = ( insert_a @ X3 @ bot_bot_set_a ) )
          & ( B
            = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1038_Un__singleton__iff,axiom,
    ! [A2: set_b,B: set_b,X3: b] :
      ( ( ( sup_sup_set_b @ A2 @ B )
        = ( insert_b @ X3 @ bot_bot_set_b ) )
      = ( ( ( A2 = bot_bot_set_b )
          & ( B
            = ( insert_b @ X3 @ bot_bot_set_b ) ) )
        | ( ( A2
            = ( insert_b @ X3 @ bot_bot_set_b ) )
          & ( B = bot_bot_set_b ) )
        | ( ( A2
            = ( insert_b @ X3 @ bot_bot_set_b ) )
          & ( B
            = ( insert_b @ X3 @ bot_bot_set_b ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1039_Un__singleton__iff,axiom,
    ! [A2: set_nat,B: set_nat,X3: nat] :
      ( ( ( sup_sup_set_nat @ A2 @ B )
        = ( insert_nat @ X3 @ bot_bot_set_nat ) )
      = ( ( ( A2 = bot_bot_set_nat )
          & ( B
            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
        | ( ( A2
            = ( insert_nat @ X3 @ bot_bot_set_nat ) )
          & ( B = bot_bot_set_nat ) )
        | ( ( A2
            = ( insert_nat @ X3 @ bot_bot_set_nat ) )
          & ( B
            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1040_singleton__Un__iff,axiom,
    ! [X3: a,A2: set_a,B: set_a] :
      ( ( ( insert_a @ X3 @ bot_bot_set_a )
        = ( sup_sup_set_a @ A2 @ B ) )
      = ( ( ( A2 = bot_bot_set_a )
          & ( B
            = ( insert_a @ X3 @ bot_bot_set_a ) ) )
        | ( ( A2
            = ( insert_a @ X3 @ bot_bot_set_a ) )
          & ( B = bot_bot_set_a ) )
        | ( ( A2
            = ( insert_a @ X3 @ bot_bot_set_a ) )
          & ( B
            = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1041_singleton__Un__iff,axiom,
    ! [X3: b,A2: set_b,B: set_b] :
      ( ( ( insert_b @ X3 @ bot_bot_set_b )
        = ( sup_sup_set_b @ A2 @ B ) )
      = ( ( ( A2 = bot_bot_set_b )
          & ( B
            = ( insert_b @ X3 @ bot_bot_set_b ) ) )
        | ( ( A2
            = ( insert_b @ X3 @ bot_bot_set_b ) )
          & ( B = bot_bot_set_b ) )
        | ( ( A2
            = ( insert_b @ X3 @ bot_bot_set_b ) )
          & ( B
            = ( insert_b @ X3 @ bot_bot_set_b ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1042_singleton__Un__iff,axiom,
    ! [X3: nat,A2: set_nat,B: set_nat] :
      ( ( ( insert_nat @ X3 @ bot_bot_set_nat )
        = ( sup_sup_set_nat @ A2 @ B ) )
      = ( ( ( A2 = bot_bot_set_nat )
          & ( B
            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
        | ( ( A2
            = ( insert_nat @ X3 @ bot_bot_set_nat ) )
          & ( B = bot_bot_set_nat ) )
        | ( ( A2
            = ( insert_nat @ X3 @ bot_bot_set_nat ) )
          & ( B
            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1043_Un__Diff,axiom,
    ! [A2: set_a,B: set_a,C2: set_a] :
      ( ( minus_minus_set_a @ ( sup_sup_set_a @ A2 @ B ) @ C2 )
      = ( sup_sup_set_a @ ( minus_minus_set_a @ A2 @ C2 ) @ ( minus_minus_set_a @ B @ C2 ) ) ) ).

% Un_Diff
thf(fact_1044_Un__Diff,axiom,
    ! [A2: set_b,B: set_b,C2: set_b] :
      ( ( minus_minus_set_b @ ( sup_sup_set_b @ A2 @ B ) @ C2 )
      = ( sup_sup_set_b @ ( minus_minus_set_b @ A2 @ C2 ) @ ( minus_minus_set_b @ B @ C2 ) ) ) ).

% Un_Diff
thf(fact_1045_Un__Diff,axiom,
    ! [A2: set_nat,B: set_nat,C2: set_nat] :
      ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ C2 )
      = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ C2 ) @ ( minus_minus_set_nat @ B @ C2 ) ) ) ).

% Un_Diff
thf(fact_1046_empty__def,axiom,
    ( bot_bot_set_list_nat
    = ( collect_list_nat
      @ ^ [X: list_nat] : $false ) ) ).

% empty_def
thf(fact_1047_empty__def,axiom,
    ( bot_bot_set_nat
    = ( collect_nat
      @ ^ [X: nat] : $false ) ) ).

% empty_def
thf(fact_1048_mk__disjoint__insert,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ? [B6: set_b] :
          ( ( A2
            = ( insert_b @ A @ B6 ) )
          & ~ ( member_b @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1049_mk__disjoint__insert,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ? [B6: set_a] :
          ( ( A2
            = ( insert_a @ A @ B6 ) )
          & ~ ( member_a @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1050_mk__disjoint__insert,axiom,
    ! [A: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ A2 )
     => ? [B6: set_Re5178783185447174953term_a] :
          ( ( A2
            = ( insert8574850016668666393term_a @ A @ B6 ) )
          & ~ ( member5466445112152945266term_a @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1051_mk__disjoint__insert,axiom,
    ! [A: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ A2 )
     => ? [B6: set_list_a] :
          ( ( A2
            = ( insert_list_a @ A @ B6 ) )
          & ~ ( member_list_a @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1052_mk__disjoint__insert,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ A2 )
     => ? [B6: set_Pr1261947904930325089at_nat] :
          ( ( A2
            = ( insert8211810215607154385at_nat @ A @ B6 ) )
          & ~ ( member8440522571783428010at_nat @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1053_mk__disjoint__insert,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ? [B6: set_nat] :
          ( ( A2
            = ( insert_nat @ A @ B6 ) )
          & ~ ( member_nat @ A @ B6 ) ) ) ).

% mk_disjoint_insert
thf(fact_1054_Diff__insert__absorb,axiom,
    ! [X3: b,A2: set_b] :
      ( ~ ( member_b @ X3 @ A2 )
     => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A2 ) @ ( insert_b @ X3 @ bot_bot_set_b ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1055_Diff__insert__absorb,axiom,
    ! [X3: a,A2: set_a] :
      ( ~ ( member_a @ X3 @ A2 )
     => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A2 ) @ ( insert_a @ X3 @ bot_bot_set_a ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1056_Diff__insert__absorb,axiom,
    ! [X3: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ~ ( member5466445112152945266term_a @ X3 @ A2 )
     => ( ( minus_3019981187013541264term_a @ ( insert8574850016668666393term_a @ X3 @ A2 ) @ ( insert8574850016668666393term_a @ X3 @ bot_bo8783692591515826581term_a ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1057_Diff__insert__absorb,axiom,
    ! [X3: list_a,A2: set_list_a] :
      ( ~ ( member_list_a @ X3 @ A2 )
     => ( ( minus_646659088055828811list_a @ ( insert_list_a @ X3 @ A2 ) @ ( insert_list_a @ X3 @ bot_bot_set_list_a ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1058_Diff__insert__absorb,axiom,
    ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
     => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X3 @ A2 ) @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1059_Diff__insert__absorb,axiom,
    ! [X3: nat,A2: set_nat] :
      ( ~ ( member_nat @ X3 @ A2 )
     => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
        = A2 ) ) ).

% Diff_insert_absorb
thf(fact_1060_fun__diff__def,axiom,
    ( minus_minus_nat_o
    = ( ^ [A3: nat > $o,B3: nat > $o,X: nat] : ( minus_minus_o @ ( A3 @ X ) @ ( B3 @ X ) ) ) ) ).

% fun_diff_def
thf(fact_1061_singleton__inject,axiom,
    ! [A: nat,B2: nat] :
      ( ( ( insert_nat @ A @ bot_bot_set_nat )
        = ( insert_nat @ B2 @ bot_bot_set_nat ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_1062_insert__not__empty,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( insert_nat @ A @ A2 )
     != bot_bot_set_nat ) ).

% insert_not_empty
thf(fact_1063_doubleton__eq__iff,axiom,
    ! [A: nat,B2: nat,C: nat,D: nat] :
      ( ( ( insert_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) )
        = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
      = ( ( ( A = C )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C ) ) ) ) ).

% doubleton_eq_iff
thf(fact_1064_Collect__conv__if2,axiom,
    ! [P: list_nat > $o,A: list_nat] :
      ( ( ( P @ A )
       => ( ( collect_list_nat
            @ ^ [X: list_nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_list_nat
            @ ^ [X: list_nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = bot_bot_set_list_nat ) ) ) ).

% Collect_conv_if2
thf(fact_1065_Collect__conv__if2,axiom,
    ! [P: nat > $o,A: nat] :
      ( ( ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = ( insert_nat @ A @ bot_bot_set_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( A = X )
                & ( P @ X ) ) )
          = bot_bot_set_nat ) ) ) ).

% Collect_conv_if2
thf(fact_1066_Collect__conv__if,axiom,
    ! [P: list_nat > $o,A: list_nat] :
      ( ( ( P @ A )
       => ( ( collect_list_nat
            @ ^ [X: list_nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_list_nat
            @ ^ [X: list_nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = bot_bot_set_list_nat ) ) ) ).

% Collect_conv_if
thf(fact_1067_Collect__conv__if,axiom,
    ! [P: nat > $o,A: nat] :
      ( ( ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = ( insert_nat @ A @ bot_bot_set_nat ) ) )
      & ( ~ ( P @ A )
       => ( ( collect_nat
            @ ^ [X: nat] :
                ( ( X = A )
                & ( P @ X ) ) )
          = bot_bot_set_nat ) ) ) ).

% Collect_conv_if
thf(fact_1068_insert__commute,axiom,
    ! [X3: nat,Y: nat,A2: set_nat] :
      ( ( insert_nat @ X3 @ ( insert_nat @ Y @ A2 ) )
      = ( insert_nat @ Y @ ( insert_nat @ X3 @ A2 ) ) ) ).

% insert_commute
thf(fact_1069_insert__Diff__if,axiom,
    ! [X3: b,B: set_b,A2: set_b] :
      ( ( ( member_b @ X3 @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A2 ) @ B )
          = ( minus_minus_set_b @ A2 @ B ) ) )
      & ( ~ ( member_b @ X3 @ B )
       => ( ( minus_minus_set_b @ ( insert_b @ X3 @ A2 ) @ B )
          = ( insert_b @ X3 @ ( minus_minus_set_b @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1070_insert__Diff__if,axiom,
    ! [X3: a,B: set_a,A2: set_a] :
      ( ( ( member_a @ X3 @ B )
       => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A2 ) @ B )
          = ( minus_minus_set_a @ A2 @ B ) ) )
      & ( ~ ( member_a @ X3 @ B )
       => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A2 ) @ B )
          = ( insert_a @ X3 @ ( minus_minus_set_a @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1071_insert__Diff__if,axiom,
    ! [X3: relational_term_a,B: set_Re5178783185447174953term_a,A2: set_Re5178783185447174953term_a] :
      ( ( ( member5466445112152945266term_a @ X3 @ B )
       => ( ( minus_3019981187013541264term_a @ ( insert8574850016668666393term_a @ X3 @ A2 ) @ B )
          = ( minus_3019981187013541264term_a @ A2 @ B ) ) )
      & ( ~ ( member5466445112152945266term_a @ X3 @ B )
       => ( ( minus_3019981187013541264term_a @ ( insert8574850016668666393term_a @ X3 @ A2 ) @ B )
          = ( insert8574850016668666393term_a @ X3 @ ( minus_3019981187013541264term_a @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1072_insert__Diff__if,axiom,
    ! [X3: list_a,B: set_list_a,A2: set_list_a] :
      ( ( ( member_list_a @ X3 @ B )
       => ( ( minus_646659088055828811list_a @ ( insert_list_a @ X3 @ A2 ) @ B )
          = ( minus_646659088055828811list_a @ A2 @ B ) ) )
      & ( ~ ( member_list_a @ X3 @ B )
       => ( ( minus_646659088055828811list_a @ ( insert_list_a @ X3 @ A2 ) @ B )
          = ( insert_list_a @ X3 @ ( minus_646659088055828811list_a @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1073_insert__Diff__if,axiom,
    ! [X3: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( ( member8440522571783428010at_nat @ X3 @ B )
       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X3 @ A2 ) @ B )
          = ( minus_1356011639430497352at_nat @ A2 @ B ) ) )
      & ( ~ ( member8440522571783428010at_nat @ X3 @ B )
       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X3 @ A2 ) @ B )
          = ( insert8211810215607154385at_nat @ X3 @ ( minus_1356011639430497352at_nat @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1074_insert__Diff__if,axiom,
    ! [X3: nat,B: set_nat,A2: set_nat] :
      ( ( ( member_nat @ X3 @ B )
       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B )
          = ( minus_minus_set_nat @ A2 @ B ) ) )
      & ( ~ ( member_nat @ X3 @ B )
       => ( ( minus_minus_set_nat @ ( insert_nat @ X3 @ A2 ) @ B )
          = ( insert_nat @ X3 @ ( minus_minus_set_nat @ A2 @ B ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1075_insert__Collect,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( insert_nat @ A @ ( collect_nat @ P ) )
      = ( collect_nat
        @ ^ [U: nat] :
            ( ( U != A )
           => ( P @ U ) ) ) ) ).

% insert_Collect
thf(fact_1076_insert__Collect,axiom,
    ! [A: list_nat,P: list_nat > $o] :
      ( ( insert_list_nat @ A @ ( collect_list_nat @ P ) )
      = ( collect_list_nat
        @ ^ [U: list_nat] :
            ( ( U != A )
           => ( P @ U ) ) ) ) ).

% insert_Collect
thf(fact_1077_singleton__iff,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1078_singleton__iff,axiom,
    ! [B2: a,A: a] :
      ( ( member_a @ B2 @ ( insert_a @ A @ bot_bot_set_a ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1079_singleton__iff,axiom,
    ! [B2: relational_term_a,A: relational_term_a] :
      ( ( member5466445112152945266term_a @ B2 @ ( insert8574850016668666393term_a @ A @ bot_bo8783692591515826581term_a ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1080_singleton__iff,axiom,
    ! [B2: list_a,A: list_a] :
      ( ( member_list_a @ B2 @ ( insert_list_a @ A @ bot_bot_set_list_a ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1081_singleton__iff,axiom,
    ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
      ( ( member8440522571783428010at_nat @ B2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1082_singleton__iff,axiom,
    ! [B2: nat,A: nat] :
      ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_1083_insert__eq__iff,axiom,
    ! [A: b,A2: set_b,B2: b,B: set_b] :
      ( ~ ( member_b @ A @ A2 )
     => ( ~ ( member_b @ B2 @ B )
       => ( ( ( insert_b @ A @ A2 )
            = ( insert_b @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_b] :
                  ( ( A2
                    = ( insert_b @ B2 @ C3 ) )
                  & ~ ( member_b @ B2 @ C3 )
                  & ( B
                    = ( insert_b @ A @ C3 ) )
                  & ~ ( member_b @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1084_insert__eq__iff,axiom,
    ! [A: a,A2: set_a,B2: a,B: set_a] :
      ( ~ ( member_a @ A @ A2 )
     => ( ~ ( member_a @ B2 @ B )
       => ( ( ( insert_a @ A @ A2 )
            = ( insert_a @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_a] :
                  ( ( A2
                    = ( insert_a @ B2 @ C3 ) )
                  & ~ ( member_a @ B2 @ C3 )
                  & ( B
                    = ( insert_a @ A @ C3 ) )
                  & ~ ( member_a @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1085_insert__eq__iff,axiom,
    ! [A: relational_term_a,A2: set_Re5178783185447174953term_a,B2: relational_term_a,B: set_Re5178783185447174953term_a] :
      ( ~ ( member5466445112152945266term_a @ A @ A2 )
     => ( ~ ( member5466445112152945266term_a @ B2 @ B )
       => ( ( ( insert8574850016668666393term_a @ A @ A2 )
            = ( insert8574850016668666393term_a @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_Re5178783185447174953term_a] :
                  ( ( A2
                    = ( insert8574850016668666393term_a @ B2 @ C3 ) )
                  & ~ ( member5466445112152945266term_a @ B2 @ C3 )
                  & ( B
                    = ( insert8574850016668666393term_a @ A @ C3 ) )
                  & ~ ( member5466445112152945266term_a @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1086_insert__eq__iff,axiom,
    ! [A: list_a,A2: set_list_a,B2: list_a,B: set_list_a] :
      ( ~ ( member_list_a @ A @ A2 )
     => ( ~ ( member_list_a @ B2 @ B )
       => ( ( ( insert_list_a @ A @ A2 )
            = ( insert_list_a @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_list_a] :
                  ( ( A2
                    = ( insert_list_a @ B2 @ C3 ) )
                  & ~ ( member_list_a @ B2 @ C3 )
                  & ( B
                    = ( insert_list_a @ A @ C3 ) )
                  & ~ ( member_list_a @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1087_insert__eq__iff,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] :
      ( ~ ( member8440522571783428010at_nat @ A @ A2 )
     => ( ~ ( member8440522571783428010at_nat @ B2 @ B )
       => ( ( ( insert8211810215607154385at_nat @ A @ A2 )
            = ( insert8211810215607154385at_nat @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_Pr1261947904930325089at_nat] :
                  ( ( A2
                    = ( insert8211810215607154385at_nat @ B2 @ C3 ) )
                  & ~ ( member8440522571783428010at_nat @ B2 @ C3 )
                  & ( B
                    = ( insert8211810215607154385at_nat @ A @ C3 ) )
                  & ~ ( member8440522571783428010at_nat @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1088_insert__eq__iff,axiom,
    ! [A: nat,A2: set_nat,B2: nat,B: set_nat] :
      ( ~ ( member_nat @ A @ A2 )
     => ( ~ ( member_nat @ B2 @ B )
       => ( ( ( insert_nat @ A @ A2 )
            = ( insert_nat @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C3: set_nat] :
                  ( ( A2
                    = ( insert_nat @ B2 @ C3 ) )
                  & ~ ( member_nat @ B2 @ C3 )
                  & ( B
                    = ( insert_nat @ A @ C3 ) )
                  & ~ ( member_nat @ A @ C3 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1089_insert__absorb,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ( ( insert_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1090_insert__absorb,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ( ( insert_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1091_insert__absorb,axiom,
    ! [A: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ A2 )
     => ( ( insert8574850016668666393term_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1092_insert__absorb,axiom,
    ! [A: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ A2 )
     => ( ( insert_list_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1093_insert__absorb,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ A2 )
     => ( ( insert8211810215607154385at_nat @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1094_insert__absorb,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( ( insert_nat @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_1095_insert__ident,axiom,
    ! [X3: b,A2: set_b,B: set_b] :
      ( ~ ( member_b @ X3 @ A2 )
     => ( ~ ( member_b @ X3 @ B )
       => ( ( ( insert_b @ X3 @ A2 )
            = ( insert_b @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1096_insert__ident,axiom,
    ! [X3: a,A2: set_a,B: set_a] :
      ( ~ ( member_a @ X3 @ A2 )
     => ( ~ ( member_a @ X3 @ B )
       => ( ( ( insert_a @ X3 @ A2 )
            = ( insert_a @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1097_insert__ident,axiom,
    ! [X3: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ~ ( member5466445112152945266term_a @ X3 @ A2 )
     => ( ~ ( member5466445112152945266term_a @ X3 @ B )
       => ( ( ( insert8574850016668666393term_a @ X3 @ A2 )
            = ( insert8574850016668666393term_a @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1098_insert__ident,axiom,
    ! [X3: list_a,A2: set_list_a,B: set_list_a] :
      ( ~ ( member_list_a @ X3 @ A2 )
     => ( ~ ( member_list_a @ X3 @ B )
       => ( ( ( insert_list_a @ X3 @ A2 )
            = ( insert_list_a @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1099_insert__ident,axiom,
    ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ~ ( member8440522571783428010at_nat @ X3 @ A2 )
     => ( ~ ( member8440522571783428010at_nat @ X3 @ B )
       => ( ( ( insert8211810215607154385at_nat @ X3 @ A2 )
            = ( insert8211810215607154385at_nat @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1100_insert__ident,axiom,
    ! [X3: nat,A2: set_nat,B: set_nat] :
      ( ~ ( member_nat @ X3 @ A2 )
     => ( ~ ( member_nat @ X3 @ B )
       => ( ( ( insert_nat @ X3 @ A2 )
            = ( insert_nat @ X3 @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_1101_insert__compr,axiom,
    ( insert_b
    = ( ^ [A4: b,B3: set_b] :
          ( collect_b
          @ ^ [X: b] :
              ( ( X = A4 )
              | ( member_b @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1102_insert__compr,axiom,
    ( insert_a
    = ( ^ [A4: a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( X = A4 )
              | ( member_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1103_insert__compr,axiom,
    ( insert8574850016668666393term_a
    = ( ^ [A4: relational_term_a,B3: set_Re5178783185447174953term_a] :
          ( collec7376311432011962548term_a
          @ ^ [X: relational_term_a] :
              ( ( X = A4 )
              | ( member5466445112152945266term_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1104_insert__compr,axiom,
    ( insert_list_a
    = ( ^ [A4: list_a,B3: set_list_a] :
          ( collect_list_a
          @ ^ [X: list_a] :
              ( ( X = A4 )
              | ( member_list_a @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1105_insert__compr,axiom,
    ( insert8211810215607154385at_nat
    = ( ^ [A4: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
          ( collec3392354462482085612at_nat
          @ ^ [X: product_prod_nat_nat] :
              ( ( X = A4 )
              | ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1106_insert__compr,axiom,
    ( insert_list_nat
    = ( ^ [A4: list_nat,B3: set_list_nat] :
          ( collect_list_nat
          @ ^ [X: list_nat] :
              ( ( X = A4 )
              | ( member_list_nat @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1107_insert__compr,axiom,
    ( insert_nat
    = ( ^ [A4: nat,B3: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ( ( X = A4 )
              | ( member_nat @ X @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_1108_Diff__insert2,axiom,
    ! [A2: set_nat,A: nat,B: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B ) )
      = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B ) ) ).

% Diff_insert2
thf(fact_1109_set__diff__eq,axiom,
    ( minus_minus_set_b
    = ( ^ [A3: set_b,B3: set_b] :
          ( collect_b
          @ ^ [X: b] :
              ( ( member_b @ X @ A3 )
              & ~ ( member_b @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1110_set__diff__eq,axiom,
    ( minus_minus_set_a
    = ( ^ [A3: set_a,B3: set_a] :
          ( collect_a
          @ ^ [X: a] :
              ( ( member_a @ X @ A3 )
              & ~ ( member_a @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1111_set__diff__eq,axiom,
    ( minus_3019981187013541264term_a
    = ( ^ [A3: set_Re5178783185447174953term_a,B3: set_Re5178783185447174953term_a] :
          ( collec7376311432011962548term_a
          @ ^ [X: relational_term_a] :
              ( ( member5466445112152945266term_a @ X @ A3 )
              & ~ ( member5466445112152945266term_a @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1112_set__diff__eq,axiom,
    ( minus_646659088055828811list_a
    = ( ^ [A3: set_list_a,B3: set_list_a] :
          ( collect_list_a
          @ ^ [X: list_a] :
              ( ( member_list_a @ X @ A3 )
              & ~ ( member_list_a @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1113_set__diff__eq,axiom,
    ( minus_1356011639430497352at_nat
    = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
          ( collec3392354462482085612at_nat
          @ ^ [X: product_prod_nat_nat] :
              ( ( member8440522571783428010at_nat @ X @ A3 )
              & ~ ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1114_set__diff__eq,axiom,
    ( minus_7954133019191499631st_nat
    = ( ^ [A3: set_list_nat,B3: set_list_nat] :
          ( collect_list_nat
          @ ^ [X: list_nat] :
              ( ( member_list_nat @ X @ A3 )
              & ~ ( member_list_nat @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1115_set__diff__eq,axiom,
    ( minus_minus_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ( ( member_nat @ X @ A3 )
              & ~ ( member_nat @ X @ B3 ) ) ) ) ) ).

% set_diff_eq
thf(fact_1116_insert__Diff,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ( ( insert_b @ A @ ( minus_minus_set_b @ A2 @ ( insert_b @ A @ bot_bot_set_b ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1117_insert__Diff,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ( ( insert_a @ A @ ( minus_minus_set_a @ A2 @ ( insert_a @ A @ bot_bot_set_a ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1118_insert__Diff,axiom,
    ! [A: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ A2 )
     => ( ( insert8574850016668666393term_a @ A @ ( minus_3019981187013541264term_a @ A2 @ ( insert8574850016668666393term_a @ A @ bot_bo8783692591515826581term_a ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1119_insert__Diff,axiom,
    ! [A: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ A2 )
     => ( ( insert_list_a @ A @ ( minus_646659088055828811list_a @ A2 @ ( insert_list_a @ A @ bot_bot_set_list_a ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1120_insert__Diff,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ A2 )
     => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1121_insert__Diff,axiom,
    ! [A: nat,A2: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
        = A2 ) ) ).

% insert_Diff
thf(fact_1122_Diff__insert,axiom,
    ! [A2: set_nat,A: nat,B: set_nat] :
      ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B ) )
      = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).

% Diff_insert
thf(fact_1123_singletonD,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1124_singletonD,axiom,
    ! [B2: a,A: a] :
      ( ( member_a @ B2 @ ( insert_a @ A @ bot_bot_set_a ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1125_singletonD,axiom,
    ! [B2: relational_term_a,A: relational_term_a] :
      ( ( member5466445112152945266term_a @ B2 @ ( insert8574850016668666393term_a @ A @ bot_bo8783692591515826581term_a ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1126_singletonD,axiom,
    ! [B2: list_a,A: list_a] :
      ( ( member_list_a @ B2 @ ( insert_list_a @ A @ bot_bot_set_list_a ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1127_singletonD,axiom,
    ! [B2: product_prod_nat_nat,A: product_prod_nat_nat] :
      ( ( member8440522571783428010at_nat @ B2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1128_singletonD,axiom,
    ! [B2: nat,A: nat] :
      ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_1129_Set_Oset__insert,axiom,
    ! [X3: b,A2: set_b] :
      ( ( member_b @ X3 @ A2 )
     => ~ ! [B6: set_b] :
            ( ( A2
              = ( insert_b @ X3 @ B6 ) )
           => ( member_b @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1130_Set_Oset__insert,axiom,
    ! [X3: a,A2: set_a] :
      ( ( member_a @ X3 @ A2 )
     => ~ ! [B6: set_a] :
            ( ( A2
              = ( insert_a @ X3 @ B6 ) )
           => ( member_a @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1131_Set_Oset__insert,axiom,
    ! [X3: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ X3 @ A2 )
     => ~ ! [B6: set_Re5178783185447174953term_a] :
            ( ( A2
              = ( insert8574850016668666393term_a @ X3 @ B6 ) )
           => ( member5466445112152945266term_a @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1132_Set_Oset__insert,axiom,
    ! [X3: list_a,A2: set_list_a] :
      ( ( member_list_a @ X3 @ A2 )
     => ~ ! [B6: set_list_a] :
            ( ( A2
              = ( insert_list_a @ X3 @ B6 ) )
           => ( member_list_a @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1133_Set_Oset__insert,axiom,
    ! [X3: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ X3 @ A2 )
     => ~ ! [B6: set_Pr1261947904930325089at_nat] :
            ( ( A2
              = ( insert8211810215607154385at_nat @ X3 @ B6 ) )
           => ( member8440522571783428010at_nat @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1134_Set_Oset__insert,axiom,
    ! [X3: nat,A2: set_nat] :
      ( ( member_nat @ X3 @ A2 )
     => ~ ! [B6: set_nat] :
            ( ( A2
              = ( insert_nat @ X3 @ B6 ) )
           => ( member_nat @ X3 @ B6 ) ) ) ).

% Set.set_insert
thf(fact_1135_ex__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ? [X: b] : ( member_b @ X @ A2 ) )
      = ( A2 != bot_bot_set_b ) ) ).

% ex_in_conv
thf(fact_1136_ex__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ? [X: a] : ( member_a @ X @ A2 ) )
      = ( A2 != bot_bot_set_a ) ) ).

% ex_in_conv
thf(fact_1137_ex__in__conv,axiom,
    ! [A2: set_Re5178783185447174953term_a] :
      ( ( ? [X: relational_term_a] : ( member5466445112152945266term_a @ X @ A2 ) )
      = ( A2 != bot_bo8783692591515826581term_a ) ) ).

% ex_in_conv
thf(fact_1138_ex__in__conv,axiom,
    ! [A2: set_list_a] :
      ( ( ? [X: list_a] : ( member_list_a @ X @ A2 ) )
      = ( A2 != bot_bot_set_list_a ) ) ).

% ex_in_conv
thf(fact_1139_ex__in__conv,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] :
      ( ( ? [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
      = ( A2 != bot_bo2099793752762293965at_nat ) ) ).

% ex_in_conv
thf(fact_1140_ex__in__conv,axiom,
    ! [A2: set_nat] :
      ( ( ? [X: nat] : ( member_nat @ X @ A2 ) )
      = ( A2 != bot_bot_set_nat ) ) ).

% ex_in_conv
thf(fact_1141_insertI2,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( member_b @ A @ B )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1142_insertI2,axiom,
    ! [A: a,B: set_a,B2: a] :
      ( ( member_a @ A @ B )
     => ( member_a @ A @ ( insert_a @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1143_insertI2,axiom,
    ! [A: relational_term_a,B: set_Re5178783185447174953term_a,B2: relational_term_a] :
      ( ( member5466445112152945266term_a @ A @ B )
     => ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1144_insertI2,axiom,
    ! [A: list_a,B: set_list_a,B2: list_a] :
      ( ( member_list_a @ A @ B )
     => ( member_list_a @ A @ ( insert_list_a @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1145_insertI2,axiom,
    ! [A: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat,B2: product_prod_nat_nat] :
      ( ( member8440522571783428010at_nat @ A @ B )
     => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1146_insertI2,axiom,
    ! [A: nat,B: set_nat,B2: nat] :
      ( ( member_nat @ A @ B )
     => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).

% insertI2
thf(fact_1147_insertI1,axiom,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ) ).

% insertI1
thf(fact_1148_insertI1,axiom,
    ! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ) ).

% insertI1
thf(fact_1149_insertI1,axiom,
    ! [A: relational_term_a,B: set_Re5178783185447174953term_a] : ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ A @ B ) ) ).

% insertI1
thf(fact_1150_insertI1,axiom,
    ! [A: list_a,B: set_list_a] : ( member_list_a @ A @ ( insert_list_a @ A @ B ) ) ).

% insertI1
thf(fact_1151_insertI1,axiom,
    ! [A: product_prod_nat_nat,B: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ B ) ) ).

% insertI1
thf(fact_1152_insertI1,axiom,
    ! [A: nat,B: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B ) ) ).

% insertI1
thf(fact_1153_equals0I,axiom,
    ! [A2: set_b] :
      ( ! [Y3: b] :
          ~ ( member_b @ Y3 @ A2 )
     => ( A2 = bot_bot_set_b ) ) ).

% equals0I
thf(fact_1154_equals0I,axiom,
    ! [A2: set_a] :
      ( ! [Y3: a] :
          ~ ( member_a @ Y3 @ A2 )
     => ( A2 = bot_bot_set_a ) ) ).

% equals0I
thf(fact_1155_equals0I,axiom,
    ! [A2: set_Re5178783185447174953term_a] :
      ( ! [Y3: relational_term_a] :
          ~ ( member5466445112152945266term_a @ Y3 @ A2 )
     => ( A2 = bot_bo8783692591515826581term_a ) ) ).

% equals0I
thf(fact_1156_equals0I,axiom,
    ! [A2: set_list_a] :
      ( ! [Y3: list_a] :
          ~ ( member_list_a @ Y3 @ A2 )
     => ( A2 = bot_bot_set_list_a ) ) ).

% equals0I
thf(fact_1157_equals0I,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] :
      ( ! [Y3: product_prod_nat_nat] :
          ~ ( member8440522571783428010at_nat @ Y3 @ A2 )
     => ( A2 = bot_bo2099793752762293965at_nat ) ) ).

% equals0I
thf(fact_1158_equals0I,axiom,
    ! [A2: set_nat] :
      ( ! [Y3: nat] :
          ~ ( member_nat @ Y3 @ A2 )
     => ( A2 = bot_bot_set_nat ) ) ).

% equals0I
thf(fact_1159_equals0D,axiom,
    ! [A2: set_b,A: b] :
      ( ( A2 = bot_bot_set_b )
     => ~ ( member_b @ A @ A2 ) ) ).

% equals0D
thf(fact_1160_equals0D,axiom,
    ! [A2: set_a,A: a] :
      ( ( A2 = bot_bot_set_a )
     => ~ ( member_a @ A @ A2 ) ) ).

% equals0D
thf(fact_1161_equals0D,axiom,
    ! [A2: set_Re5178783185447174953term_a,A: relational_term_a] :
      ( ( A2 = bot_bo8783692591515826581term_a )
     => ~ ( member5466445112152945266term_a @ A @ A2 ) ) ).

% equals0D
thf(fact_1162_equals0D,axiom,
    ! [A2: set_list_a,A: list_a] :
      ( ( A2 = bot_bot_set_list_a )
     => ~ ( member_list_a @ A @ A2 ) ) ).

% equals0D
thf(fact_1163_equals0D,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
      ( ( A2 = bot_bo2099793752762293965at_nat )
     => ~ ( member8440522571783428010at_nat @ A @ A2 ) ) ).

% equals0D
thf(fact_1164_equals0D,axiom,
    ! [A2: set_nat,A: nat] :
      ( ( A2 = bot_bot_set_nat )
     => ~ ( member_nat @ A @ A2 ) ) ).

% equals0D
thf(fact_1165_insertE,axiom,
    ! [A: b,B2: b,A2: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_1166_insertE,axiom,
    ! [A: a,B2: a,A2: set_a] :
      ( ( member_a @ A @ ( insert_a @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_1167_insertE,axiom,
    ! [A: relational_term_a,B2: relational_term_a,A2: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ A @ ( insert8574850016668666393term_a @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member5466445112152945266term_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_1168_insertE,axiom,
    ! [A: list_a,B2: list_a,A2: set_list_a] :
      ( ( member_list_a @ A @ ( insert_list_a @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_list_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_1169_insertE,axiom,
    ! [A: product_prod_nat_nat,B2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member8440522571783428010at_nat @ A @ A2 ) ) ) ).

% insertE
thf(fact_1170_insertE,axiom,
    ! [A: nat,B2: nat,A2: set_nat] :
      ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_nat @ A @ A2 ) ) ) ).

% insertE
thf(fact_1171_emptyE,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ) ).

% emptyE
thf(fact_1172_emptyE,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ) ).

% emptyE
thf(fact_1173_emptyE,axiom,
    ! [A: relational_term_a] :
      ~ ( member5466445112152945266term_a @ A @ bot_bo8783692591515826581term_a ) ).

% emptyE
thf(fact_1174_emptyE,axiom,
    ! [A: list_a] :
      ~ ( member_list_a @ A @ bot_bot_set_list_a ) ).

% emptyE
thf(fact_1175_emptyE,axiom,
    ! [A: product_prod_nat_nat] :
      ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).

% emptyE
thf(fact_1176_emptyE,axiom,
    ! [A: nat] :
      ~ ( member_nat @ A @ bot_bot_set_nat ) ).

% emptyE
thf(fact_1177_DiffD2,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B ) )
     => ~ ( member_b @ C @ B ) ) ).

% DiffD2
thf(fact_1178_DiffD2,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B ) )
     => ~ ( member_a @ C @ B ) ) ).

% DiffD2
thf(fact_1179_DiffD2,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( minus_3019981187013541264term_a @ A2 @ B ) )
     => ~ ( member5466445112152945266term_a @ C @ B ) ) ).

% DiffD2
thf(fact_1180_DiffD2,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( minus_646659088055828811list_a @ A2 @ B ) )
     => ~ ( member_list_a @ C @ B ) ) ).

% DiffD2
thf(fact_1181_DiffD2,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B ) )
     => ~ ( member8440522571783428010at_nat @ C @ B ) ) ).

% DiffD2
thf(fact_1182_DiffD2,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
     => ~ ( member_nat @ C @ B ) ) ).

% DiffD2
thf(fact_1183_DiffD1,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B ) )
     => ( member_b @ C @ A2 ) ) ).

% DiffD1
thf(fact_1184_DiffD1,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B ) )
     => ( member_a @ C @ A2 ) ) ).

% DiffD1
thf(fact_1185_DiffD1,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( minus_3019981187013541264term_a @ A2 @ B ) )
     => ( member5466445112152945266term_a @ C @ A2 ) ) ).

% DiffD1
thf(fact_1186_DiffD1,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( minus_646659088055828811list_a @ A2 @ B ) )
     => ( member_list_a @ C @ A2 ) ) ).

% DiffD1
thf(fact_1187_DiffD1,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B ) )
     => ( member8440522571783428010at_nat @ C @ A2 ) ) ).

% DiffD1
thf(fact_1188_DiffD1,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
     => ( member_nat @ C @ A2 ) ) ).

% DiffD1
thf(fact_1189_DiffE,axiom,
    ! [C: b,A2: set_b,B: set_b] :
      ( ( member_b @ C @ ( minus_minus_set_b @ A2 @ B ) )
     => ~ ( ( member_b @ C @ A2 )
         => ( member_b @ C @ B ) ) ) ).

% DiffE
thf(fact_1190_DiffE,axiom,
    ! [C: a,A2: set_a,B: set_a] :
      ( ( member_a @ C @ ( minus_minus_set_a @ A2 @ B ) )
     => ~ ( ( member_a @ C @ A2 )
         => ( member_a @ C @ B ) ) ) ).

% DiffE
thf(fact_1191_DiffE,axiom,
    ! [C: relational_term_a,A2: set_Re5178783185447174953term_a,B: set_Re5178783185447174953term_a] :
      ( ( member5466445112152945266term_a @ C @ ( minus_3019981187013541264term_a @ A2 @ B ) )
     => ~ ( ( member5466445112152945266term_a @ C @ A2 )
         => ( member5466445112152945266term_a @ C @ B ) ) ) ).

% DiffE
thf(fact_1192_DiffE,axiom,
    ! [C: list_a,A2: set_list_a,B: set_list_a] :
      ( ( member_list_a @ C @ ( minus_646659088055828811list_a @ A2 @ B ) )
     => ~ ( ( member_list_a @ C @ A2 )
         => ( member_list_a @ C @ B ) ) ) ).

% DiffE
thf(fact_1193_DiffE,axiom,
    ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B ) )
     => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
         => ( member8440522571783428010at_nat @ C @ B ) ) ) ).

% DiffE
thf(fact_1194_DiffE,axiom,
    ! [C: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B ) )
     => ~ ( ( member_nat @ C @ A2 )
         => ( member_nat @ C @ B ) ) ) ).

% DiffE
thf(fact_1195_fv_Osimps_I7_J,axiom,
    ! [Z: nat,Phi: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relati591517084277583526ts_a_b @ Z @ Phi ) )
      = ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi ) @ ( insert_nat @ Z @ bot_bot_set_nat ) ) ) ).

% fv.simps(7)
thf(fact_1196_fmla_Osimps_I127_J,axiom,
    ! [X112: b,X122: list_R6823256787227418703term_a] :
      ( ( relati8924981150291758614la_a_b @ ( relational_Pred_b_a @ X112 @ X122 ) )
      = ( insert_b @ X112 @ bot_bot_set_b ) ) ).

% fmla.simps(127)
thf(fact_1197_fmla_Osimps_I127_J,axiom,
    ! [X112: nat,X122: list_R114826772386431851rm_nat] :
      ( ( relati2567137625159299127at_nat @ ( relati5908763325135257836at_nat @ X112 @ X122 ) )
      = ( insert_nat @ X112 @ bot_bot_set_nat ) ) ).

% fmla.simps(127)
thf(fact_1198_Un__empty__right,axiom,
    ! [A2: set_a] :
      ( ( sup_sup_set_a @ A2 @ bot_bot_set_a )
      = A2 ) ).

% Un_empty_right
thf(fact_1199_Un__empty__right,axiom,
    ! [A2: set_b] :
      ( ( sup_sup_set_b @ A2 @ bot_bot_set_b )
      = A2 ) ).

% Un_empty_right
thf(fact_1200_Un__empty__right,axiom,
    ! [A2: set_nat] :
      ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
      = A2 ) ).

% Un_empty_right
thf(fact_1201_Un__empty__left,axiom,
    ! [B: set_a] :
      ( ( sup_sup_set_a @ bot_bot_set_a @ B )
      = B ) ).

% Un_empty_left
thf(fact_1202_Un__empty__left,axiom,
    ! [B: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ B )
      = B ) ).

% Un_empty_left
thf(fact_1203_Un__empty__left,axiom,
    ! [B: set_nat] :
      ( ( sup_sup_set_nat @ bot_bot_set_nat @ B )
      = B ) ).

% Un_empty_left
thf(fact_1204_fv_Osimps_I3_J,axiom,
    ! [X3: nat,T3: relational_term_a] :
      ( ( relational_fv_a_b @ ( relational_Eq_a_b @ X3 @ T3 ) )
      = ( sup_sup_set_nat @ ( insert_nat @ X3 @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T3 ) ) ) ).

% fv.simps(3)
thf(fact_1205_insert__def,axiom,
    ( insert_a
    = ( ^ [A4: a] :
          ( sup_sup_set_a
          @ ( collect_a
            @ ^ [X: a] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_1206_insert__def,axiom,
    ( insert_b
    = ( ^ [A4: b] :
          ( sup_sup_set_b
          @ ( collect_b
            @ ^ [X: b] : ( X = A4 ) ) ) ) ) ).

% insert_def
thf(fact_1207_fv_Osimps_I2_J,axiom,
    ! [B2: $o] :
      ( ( relational_fv_a_b @ ( relational_Bool_a_b @ B2 ) )
      = bot_bot_set_nat ) ).

% fv.simps(2)
thf(fact_1208_fv_Opelims,axiom,
    ! [X3: relational_fmla_a_b,Y: set_nat] :
      ( ( ( relational_fv_a_b @ X3 )
        = Y )
     => ( ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ X3 )
       => ( ! [Uu3: b,Ts: list_R6823256787227418703term_a] :
              ( ( X3
                = ( relational_Pred_b_a @ Uu3 @ Ts ) )
             => ( ( Y
                  = ( relati4569515538964159125_set_a @ Ts ) )
               => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Pred_b_a @ Uu3 @ Ts ) ) ) )
         => ( ! [B5: $o] :
                ( ( X3
                  = ( relational_Bool_a_b @ B5 ) )
               => ( ( Y = bot_bot_set_nat )
                 => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Bool_a_b @ B5 ) ) ) )
           => ( ! [X2: nat,T2: relational_term_a] :
                  ( ( X3
                    = ( relational_Eq_a_b @ X2 @ T2 ) )
                 => ( ( Y
                      = ( sup_sup_set_nat @ ( insert_nat @ X2 @ bot_bot_set_nat ) @ ( relati6004689760767320788_set_a @ T2 ) ) )
                   => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Eq_a_b @ X2 @ T2 ) ) ) )
             => ( ! [Phi2: relational_fmla_a_b] :
                    ( ( X3
                      = ( relational_Neg_a_b @ Phi2 ) )
                   => ( ( Y
                        = ( relational_fv_a_b @ Phi2 ) )
                     => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Neg_a_b @ Phi2 ) ) ) )
               => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                      ( ( X3
                        = ( relational_Conj_a_b @ Phi2 @ Psi2 ) )
                     => ( ( Y
                          = ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) )
                       => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Conj_a_b @ Phi2 @ Psi2 ) ) ) )
                 => ( ! [Phi2: relational_fmla_a_b,Psi2: relational_fmla_a_b] :
                        ( ( X3
                          = ( relational_Disj_a_b @ Phi2 @ Psi2 ) )
                       => ( ( Y
                            = ( sup_sup_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( relational_fv_a_b @ Psi2 ) ) )
                         => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relational_Disj_a_b @ Phi2 @ Psi2 ) ) ) )
                   => ~ ! [Z3: nat,Phi2: relational_fmla_a_b] :
                          ( ( X3
                            = ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) )
                         => ( ( Y
                              = ( minus_minus_set_nat @ ( relational_fv_a_b @ Phi2 ) @ ( insert_nat @ Z3 @ bot_bot_set_nat ) ) )
                           => ~ ( accp_R989495437599811158la_a_b @ relati5703530512245835757el_a_b @ ( relati591517084277583526ts_a_b @ Z3 @ Phi2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% fv.pelims
thf(fact_1209_fv__EXISTS,axiom,
    ! [Xs: list_nat,Q: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relati7004044288120072026TS_a_b @ Xs @ Q ) )
      = ( minus_minus_set_nat @ ( relational_fv_a_b @ Q ) @ ( set_nat2 @ Xs ) ) ) ).

% fv_EXISTS
thf(fact_1210_bot__empty__eq,axiom,
    ( bot_bot_nat_o
    = ( ^ [X: nat] : ( member_nat @ X @ bot_bot_set_nat ) ) ) ).

% bot_empty_eq
thf(fact_1211_minus__set__def,axiom,
    ( minus_minus_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( collect_nat
          @ ( minus_minus_nat_o
            @ ^ [X: nat] : ( member_nat @ X @ A3 )
            @ ^ [X: nat] : ( member_nat @ X @ B3 ) ) ) ) ) ).

% minus_set_def
thf(fact_1212_fv__close,axiom,
    ! [Q: relational_fmla_a_b] :
      ( ( relational_fv_a_b @ ( relati7004044288120072026TS_a_b @ ( linord2614967742042102400et_nat @ ( relational_fv_a_b @ Q ) ) @ Q ) )
      = bot_bot_set_nat ) ).

% fv_close
thf(fact_1213_member__remove,axiom,
    ! [X3: nat,Y: nat,A2: set_nat] :
      ( ( member_nat @ X3 @ ( remove_nat @ Y @ A2 ) )
      = ( ( member_nat @ X3 @ A2 )
        & ( X3 != Y ) ) ) ).

% member_remove
thf(fact_1214_is__singletonI_H,axiom,
    ! [A2: set_nat] :
      ( ( A2 != bot_bot_set_nat )
     => ( ! [X2: nat,Y3: nat] :
            ( ( member_nat @ X2 @ A2 )
           => ( ( member_nat @ Y3 @ A2 )
             => ( X2 = Y3 ) ) )
       => ( is_singleton_nat @ A2 ) ) ) ).

% is_singletonI'
thf(fact_1215_term_Oset__cases,axiom,
    ! [E: nat,A: relational_term_nat] :
      ( ( member_nat @ E @ ( relati7416457470477713926rm_nat @ A ) )
     => ( A
        = ( relational_Const_nat @ E ) ) ) ).

% term.set_cases
thf(fact_1216_term_Oset__intros,axiom,
    ! [X14: nat] : ( member_nat @ X14 @ ( relati7416457470477713926rm_nat @ ( relational_Const_nat @ X14 ) ) ) ).

% term.set_intros
thf(fact_1217_FieldI2,axiom,
    ! [I4: nat,J: nat,R: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I4 @ J ) @ R )
     => ( member_nat @ J @ ( field_nat @ R ) ) ) ).

% FieldI2
thf(fact_1218_FieldI1,axiom,
    ! [I4: nat,J: nat,R: set_Pr1261947904930325089at_nat] :
      ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I4 @ J ) @ R )
     => ( member_nat @ I4 @ ( field_nat @ R ) ) ) ).

% FieldI1
thf(fact_1219_Under__def,axiom,
    ( order_Under_nat
    = ( ^ [R5: set_Pr1261947904930325089at_nat,A3: set_nat] :
          ( collect_nat
          @ ^ [B4: nat] :
              ( ( member_nat @ B4 @ ( field_nat @ R5 ) )
              & ! [X: nat] :
                  ( ( member_nat @ X @ A3 )
                 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ X ) @ R5 ) ) ) ) ) ) ).

% Under_def
thf(fact_1220_UnderS__def,axiom,
    ( order_UnderS_nat
    = ( ^ [R5: set_Pr1261947904930325089at_nat,A3: set_nat] :
          ( collect_nat
          @ ^ [B4: nat] :
              ( ( member_nat @ B4 @ ( field_nat @ R5 ) )
              & ! [X: nat] :
                  ( ( member_nat @ X @ A3 )
                 => ( ( B4 != X )
                    & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ X ) @ R5 ) ) ) ) ) ) ) ).

% UnderS_def
thf(fact_1221_Above__def,axiom,
    ( order_Above_nat
    = ( ^ [R5: set_Pr1261947904930325089at_nat,A3: set_nat] :
          ( collect_nat
          @ ^ [B4: nat] :
              ( ( member_nat @ B4 @ ( field_nat @ R5 ) )
              & ! [X: nat] :
                  ( ( member_nat @ X @ A3 )
                 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ B4 ) @ R5 ) ) ) ) ) ) ).

% Above_def
thf(fact_1222_AboveS__def,axiom,
    ( order_AboveS_nat
    = ( ^ [R5: set_Pr1261947904930325089at_nat,A3: set_nat] :
          ( collect_nat
          @ ^ [B4: nat] :
              ( ( member_nat @ B4 @ ( field_nat @ R5 ) )
              & ! [X: nat] :
                  ( ( member_nat @ X @ A3 )
                 => ( ( B4 != X )
                    & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ B4 ) @ R5 ) ) ) ) ) ) ) ).

% AboveS_def
thf(fact_1223_refl__onD2,axiom,
    ! [A2: set_nat,R4: set_Pr1261947904930325089at_nat,X3: nat,Y: nat] :
      ( ( refl_on_nat @ A2 @ R4 )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R4 )
       => ( member_nat @ Y @ A2 ) ) ) ).

% refl_onD2
thf(fact_1224_refl__onD1,axiom,
    ! [A2: set_nat,R4: set_Pr1261947904930325089at_nat,X3: nat,Y: nat] :
      ( ( refl_on_nat @ A2 @ R4 )
     => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R4 )
       => ( member_nat @ X3 @ A2 ) ) ) ).

% refl_onD1
thf(fact_1225_refl__onD,axiom,
    ! [A2: set_nat,R4: set_Pr1261947904930325089at_nat,A: nat] :
      ( ( refl_on_nat @ A2 @ R4 )
     => ( ( member_nat @ A @ A2 )
       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ R4 ) ) ) ).

% refl_onD
thf(fact_1226_insort__insert__triv,axiom,
    ! [X3: nat,Xs: list_nat] :
      ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
     => ( ( linord1921536354676448932at_nat
          @ ^ [X: nat] : X
          @ X3
          @ Xs )
        = Xs ) ) ).

% insort_insert_triv
thf(fact_1227_pairwiseI,axiom,
    ! [S: set_nat,R: nat > nat > $o] :
      ( ! [X2: nat,Y3: nat] :
          ( ( member_nat @ X2 @ S )
         => ( ( member_nat @ Y3 @ S )
           => ( ( X2 != Y3 )
             => ( R @ X2 @ Y3 ) ) ) )
     => ( pairwise_nat @ R @ S ) ) ).

% pairwiseI
thf(fact_1228_pairwiseD,axiom,
    ! [R: nat > nat > $o,S: set_nat,X3: nat,Y: nat] :
      ( ( pairwise_nat @ R @ S )
     => ( ( member_nat @ X3 @ S )
       => ( ( member_nat @ Y @ S )
         => ( ( X3 != Y )
           => ( R @ X3 @ Y ) ) ) ) ) ).

% pairwiseD
thf(fact_1229_pairwise__insert,axiom,
    ! [R4: nat > nat > $o,X3: nat,S2: set_nat] :
      ( ( pairwise_nat @ R4 @ ( insert_nat @ X3 @ S2 ) )
      = ( ! [Y2: nat] :
            ( ( ( member_nat @ Y2 @ S2 )
              & ( Y2 != X3 ) )
           => ( ( R4 @ X3 @ Y2 )
              & ( R4 @ Y2 @ X3 ) ) )
        & ( pairwise_nat @ R4 @ S2 ) ) ) ).

% pairwise_insert
thf(fact_1230_refl__onI,axiom,
    ! [R4: set_Pr1261947904930325089at_nat,A2: set_nat] :
      ( ( ord_le3146513528884898305at_nat @ R4
        @ ( produc457027306803732586at_nat @ A2
          @ ^ [Uu: nat] : A2 ) )
     => ( ! [X2: nat] :
            ( ( member_nat @ X2 @ A2 )
           => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ R4 ) )
       => ( refl_on_nat @ A2 @ R4 ) ) ) ).

% refl_onI
thf(fact_1231_subsetI,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ! [X2: nat] :
          ( ( member_nat @ X2 @ A2 )
         => ( member_nat @ X2 @ B ) )
     => ( ord_less_eq_set_nat @ A2 @ B ) ) ).

% subsetI
thf(fact_1232_insert__subset,axiom,
    ! [X3: nat,A2: set_nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ ( insert_nat @ X3 @ A2 ) @ B )
      = ( ( member_nat @ X3 @ B )
        & ( ord_less_eq_set_nat @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_1233_set__filter,axiom,
    ! [P: nat > $o,Xs: list_nat] :
      ( ( set_nat2 @ ( filter_nat @ P @ Xs ) )
      = ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
            & ( P @ X ) ) ) ) ).

% set_filter
thf(fact_1234_subset__insert,axiom,
    ! [X3: nat,A2: set_nat,B: set_nat] :
      ( ~ ( member_nat @ X3 @ A2 )
     => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B ) )
        = ( ord_less_eq_set_nat @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_1235_in__mono,axiom,
    ! [A2: set_nat,B: set_nat,X3: nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B )
     => ( ( member_nat @ X3 @ A2 )
       => ( member_nat @ X3 @ B ) ) ) ).

% in_mono
thf(fact_1236_subsetD,axiom,
    ! [A2: set_nat,B: set_nat,C: nat] :
      ( ( ord_less_eq_set_nat @ A2 @ B )
     => ( ( member_nat @ C @ A2 )
       => ( member_nat @ C @ B ) ) ) ).

% subsetD
thf(fact_1237_subset__eq,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
        ! [X: nat] :
          ( ( member_nat @ X @ A3 )
         => ( member_nat @ X @ B3 ) ) ) ) ).

% subset_eq
thf(fact_1238_subset__iff,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
        ! [T4: nat] :
          ( ( member_nat @ T4 @ A3 )
         => ( member_nat @ T4 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_1239_Collect__subset,axiom,
    ! [A2: set_nat,P: nat > $o] :
      ( ord_less_eq_set_nat
      @ ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ A2 )
            & ( P @ X ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_1240_subset__Diff__insert,axiom,
    ! [A2: set_nat,B: set_nat,X3: nat,C2: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B @ ( insert_nat @ X3 @ C2 ) ) )
      = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B @ C2 ) )
        & ~ ( member_nat @ X3 @ A2 ) ) ) ).

% subset_Diff_insert
thf(fact_1241_subset__insert__iff,axiom,
    ! [A2: set_nat,X3: nat,B: set_nat] :
      ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X3 @ B ) )
      = ( ( ( member_nat @ X3 @ A2 )
         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B ) )
        & ( ~ ( member_nat @ X3 @ A2 )
         => ( ord_less_eq_set_nat @ A2 @ B ) ) ) ) ).

% subset_insert_iff
thf(fact_1242_minus__coset__filter,axiom,
    ! [A2: set_nat,Xs: list_nat] :
      ( ( minus_minus_set_nat @ A2 @ ( coset_nat @ Xs ) )
      = ( set_nat2
        @ ( filter_nat
          @ ^ [X: nat] : ( member_nat @ X @ A2 )
          @ Xs ) ) ) ).

% minus_coset_filter
thf(fact_1243_less__eq__set__def,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( ord_less_eq_nat_o
          @ ^ [X: nat] : ( member_nat @ X @ A3 )
          @ ^ [X: nat] : ( member_nat @ X @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_1244_fmla_Opred__mono,axiom,
    ! [P1: a > $o,P1a: a > $o,P2: b > $o,P2a: b > $o] :
      ( ( ord_less_eq_a_o @ P1 @ P1a )
     => ( ( ord_less_eq_b_o @ P2 @ P2a )
       => ( ord_le7191224889845164944_a_b_o @ ( relati3660035184769383399la_a_b @ P1 @ P2 ) @ ( relati3660035184769383399la_a_b @ P1a @ P2a ) ) ) ) ).

% fmla.pred_mono
thf(fact_1245_pred__subset__eq,axiom,
    ! [R: set_nat,S: set_nat] :
      ( ( ord_less_eq_nat_o
        @ ^ [X: nat] : ( member_nat @ X @ R )
        @ ^ [X: nat] : ( member_nat @ X @ S ) )
      = ( ord_less_eq_set_nat @ R @ S ) ) ).

% pred_subset_eq
thf(fact_1246_union__coset__filter,axiom,
    ! [Xs: list_nat,A2: set_nat] :
      ( ( sup_sup_set_nat @ ( coset_nat @ Xs ) @ A2 )
      = ( coset_nat
        @ ( filter_nat
          @ ^ [X: nat] :
              ~ ( member_nat @ X @ A2 )
          @ Xs ) ) ) ).

% union_coset_filter
thf(fact_1247_flat__lub__def,axiom,
    ( partial_flat_lub_nat
    = ( ^ [B4: nat,A3: set_nat] :
          ( if_nat @ ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B4 @ bot_bot_set_nat ) ) @ B4
          @ ( the_nat
            @ ^ [X: nat] : ( member_nat @ X @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ B4 @ bot_bot_set_nat ) ) ) ) ) ) ) ).

% flat_lub_def
thf(fact_1248_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_nat] :
      ( ( ? [A4: nat] : ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) )
      = ( uniq_nat
        @ ^ [X: nat] : ( member_nat @ X @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_1249_subset__Collect__iff,axiom,
    ! [B: set_nat,A2: set_nat,P: nat > $o] :
      ( ( ord_less_eq_set_nat @ B @ A2 )
     => ( ( ord_less_eq_set_nat @ B
          @ ( collect_nat
            @ ^ [X: nat] :
                ( ( member_nat @ X @ A2 )
                & ( P @ X ) ) ) )
        = ( ! [X: nat] :
              ( ( member_nat @ X @ B )
             => ( P @ X ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_1250_subset__CollectI,axiom,
    ! [B: set_nat,A2: set_nat,Q: nat > $o,P: nat > $o] :
      ( ( ord_less_eq_set_nat @ B @ A2 )
     => ( ! [X2: nat] :
            ( ( member_nat @ X2 @ B )
           => ( ( Q @ X2 )
             => ( P @ X2 ) ) )
       => ( ord_less_eq_set_nat
          @ ( collect_nat
            @ ^ [X: nat] :
                ( ( member_nat @ X @ B )
                & ( Q @ X ) ) )
          @ ( collect_nat
            @ ^ [X: nat] :
                ( ( member_nat @ X @ A2 )
                & ( P @ X ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_1251_prop__restrict,axiom,
    ! [X3: nat,Z6: set_nat,X6: set_nat,P: nat > $o] :
      ( ( member_nat @ X3 @ Z6 )
     => ( ( ord_less_eq_set_nat @ Z6
          @ ( collect_nat
            @ ^ [X: nat] :
                ( ( member_nat @ X @ X6 )
                & ( P @ X ) ) ) )
       => ( P @ X3 ) ) ) ).

% prop_restrict
thf(fact_1252_Collect__restrict,axiom,
    ! [X6: set_nat,P: nat > $o] :
      ( ord_less_eq_set_nat
      @ ( collect_nat
        @ ^ [X: nat] :
            ( ( member_nat @ X @ X6 )
            & ( P @ X ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_1253_psubset__insert__iff,axiom,
    ! [A2: set_nat,X3: nat,B: set_nat] :
      ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X3 @ B ) )
      = ( ( ( member_nat @ X3 @ B )
         => ( ord_less_set_nat @ A2 @ B ) )
        & ( ~ ( member_nat @ X3 @ B )
         => ( ( ( member_nat @ X3 @ A2 )
             => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ B ) )
            & ( ~ ( member_nat @ X3 @ A2 )
             => ( ord_less_eq_set_nat @ A2 @ B ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1254_psubset__imp__ex__mem,axiom,
    ! [A2: set_nat,B: set_nat] :
      ( ( ord_less_set_nat @ A2 @ B )
     => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B @ A2 ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1255_psubsetD,axiom,
    ! [A2: set_nat,B: set_nat,C: nat] :
      ( ( ord_less_set_nat @ A2 @ B )
     => ( ( member_nat @ C @ A2 )
       => ( member_nat @ C @ B ) ) ) ).

% psubsetD
thf(fact_1256_less__set__def,axiom,
    ( ord_less_set_nat
    = ( ^ [A3: set_nat,B3: set_nat] :
          ( ord_less_nat_o
          @ ^ [X: nat] : ( member_nat @ X @ A3 )
          @ ^ [X: nat] : ( member_nat @ X @ B3 ) ) ) ) ).

% less_set_def
thf(fact_1257_subset__Compl__singleton,axiom,
    ! [A2: set_nat,B2: nat] :
      ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B2 @ bot_bot_set_nat ) ) )
      = ( ~ ( member_nat @ B2 @ A2 ) ) ) ).

% subset_Compl_singleton
thf(fact_1258_Compl__iff,axiom,
    ! [C: nat,A2: set_nat] :
      ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
      = ( ~ ( member_nat @ C @ A2 ) ) ) ).

% Compl_iff
thf(fact_1259_ComplI,axiom,
    ! [C: nat,A2: set_nat] :
      ( ~ ( member_nat @ C @ A2 )
     => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).

% ComplI
thf(fact_1260_Compl__eq,axiom,
    ( uminus5710092332889474511et_nat
    = ( ^ [A3: set_nat] :
          ( collect_nat
          @ ^ [X: nat] :
              ~ ( member_nat @ X @ A3 ) ) ) ) ).

% Compl_eq
thf(fact_1261_ComplD,axiom,
    ! [C: nat,A2: set_nat] :
      ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
     => ~ ( member_nat @ C @ A2 ) ) ).

% ComplD
thf(fact_1262_uminus__set__def,axiom,
    ( uminus5710092332889474511et_nat
    = ( ^ [A3: set_nat] :
          ( collect_nat
          @ ( uminus_uminus_nat_o
            @ ^ [X: nat] : ( member_nat @ X @ A3 ) ) ) ) ) ).

% uminus_set_def
thf(fact_1263_UNIV__I,axiom,
    ! [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).

% UNIV_I
thf(fact_1264_UNIV__witness,axiom,
    ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).

% UNIV_witness
thf(fact_1265_UNIV__eq__I,axiom,
    ! [A2: set_nat] :
      ( ! [X2: nat] : ( member_nat @ X2 @ A2 )
     => ( top_top_set_nat = A2 ) ) ).

% UNIV_eq_I
thf(fact_1266_fmla_Opred__inject_I2_J,axiom,
    ! [P1: a > $o,P2: b > $o,A: $o] :
      ( ( relati3660035184769383399la_a_b @ P1 @ P2 @ ( relational_Bool_a_b @ A ) )
      = ( top_top_o_o @ A ) ) ).

% fmla.pred_inject(2)
thf(fact_1267_top__empty__eq,axiom,
    ( top_top_nat_o
    = ( ^ [X: nat] : ( member_nat @ X @ top_top_set_nat ) ) ) ).

% top_empty_eq
thf(fact_1268_trans__onI,axiom,
    ! [A2: set_nat,R4: set_Pr1261947904930325089at_nat] :
      ( ! [X2: nat,Y3: nat,Z3: nat] :
          ( ( member_nat @ X2 @ A2 )
         => ( ( member_nat @ Y3 @ A2 )
           => ( ( member_nat @ Z3 @ A2 )
             => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R4 )
               => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ R4 )
                 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z3 ) @ R4 ) ) ) ) ) )
     => ( trans_on_nat @ A2 @ R4 ) ) ).

% trans_onI
thf(fact_1269_trans__onD,axiom,
    ! [A2: set_nat,R4: set_Pr1261947904930325089at_nat,X3: nat,Y: nat,Z: nat] :
      ( ( trans_on_nat @ A2 @ R4 )
     => ( ( member_nat @ X3 @ A2 )
       => ( ( member_nat @ Y @ A2 )
         => ( ( member_nat @ Z @ A2 )
           => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R4 )
             => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R4 )
               => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z ) @ R4 ) ) ) ) ) ) ) ).

% trans_onD
thf(fact_1270_Int__insert__right__if1,axiom,
    ! [A: nat,A2: set_nat,B: set_nat] :
      ( ( member_nat @ A @ A2 )
     => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B ) )
        = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1271_Int__insert__right__if0,axiom,
    ! [A: nat,A2: set_nat,B: set_nat] :
      ( ~ ( member_nat @ A @ A2 )
     => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B ) )
        = ( inf_inf_set_nat @ A2 @ B ) ) ) ).

% Int_insert_right_if0
thf(fact_1272_Int__insert__left__if1,axiom,
    ! [A: nat,C2: set_nat,B: set_nat] :
      ( ( member_nat @ A @ C2 )
     => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B ) @ C2 )
        = ( insert_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1273_Int__insert__left__if0,axiom,
    ! [A: nat,C2: set_nat,B: set_nat] :
      ( ~ ( member_nat @ A @ C2 )
     => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B ) @ C2 )
        = ( inf_inf_set_nat @ B @ C2 ) ) ) ).

% Int_insert_left_if0
thf(fact_1274_disjoint__insert_I2_J,axiom,
    ! [A2: set_nat,B2: nat,B: set_nat] :
      ( ( bot_bot_set_nat
        = ( inf_inf_set_nat @ A2 @ ( insert_nat @ B2 @ B ) ) )
      = ( ~ ( member_nat @ B2 @ A2 )
        & ( bot_bot_set_nat
          = ( inf_inf_set_nat @ A2 @ B ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1275_disjoint__insert_I1_J,axiom,
    ! [B: set_nat,A: nat,A2: set_nat] :
      ( ( ( inf_inf_set_nat @ B @ ( insert_nat @ A @ A2 ) )
        = bot_bot_set_nat )
      = ( ~ ( member_nat @ A @ B )
        & ( ( inf_inf_set_nat @ B @ A2 )
          = bot_bot_set_nat ) ) ) ).

% disjoint_insert(1)
thf(fact_1276_insert__disjoint_I2_J,axiom,
    ! [A: nat,A2: set_nat,B: set_nat] :
      ( ( bot_bot_set_nat
        = ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B ) )
      = ( ~ ( member_nat @ A @ B )
        & ( bot_bot_set_nat
          = ( inf_inf_set_nat @ A2 @ B ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1277_insert__disjoint_I1_J,axiom,
    ! [A: nat,A2: set_nat,B: set_nat] :
      ( ( ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B )
        = bot_bot_set_nat )
      = ( ~ ( member_nat @ A @ B )
        & ( ( inf_inf_set_nat @ A2 @ B )
          = bot_bot_set_nat ) ) ) ).

% insert_disjoint(1)
thf(fact_1278_inter__set__filter,axiom,
    ! [A2: set_nat,Xs: list_nat] :
      ( ( inf_inf_set_nat @ A2 @ ( set_nat2 @ Xs ) )
      = ( set_nat2
        @ ( filter_nat
          @ ^ [X: nat] : ( member_nat @ X @ A2 )
          @ Xs ) ) ) ).

% inter_set_filter

% Helper facts (5)
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X3: nat,Y: nat] :
      ( ( if_nat @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X3: nat,Y: nat] :
      ( ( if_nat @ $true @ X3 @ Y )
      = X3 ) ).

thf(help_If_3_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
    ! [X3: relational_fmla_a_b,Y: relational_fmla_a_b] :
      ( ( if_Rel1279876242545935705la_a_b @ $false @ X3 @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Relational____Calculus__Ofmla_Itf__a_Mtf__b_J_T,axiom,
    ! [X3: relational_fmla_a_b,Y: relational_fmla_a_b] :
      ( ( if_Rel1279876242545935705la_a_b @ $true @ X3 @ Y )
      = X3 ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( relational_sat_a_b @ ( relational_Conj_a_b @ phi @ psi ) @ i @ sigma2 )
    = ( relational_sat_a_b @ ( relational_Conj_a_b @ phi @ psi ) @ i @ sigma ) ) ).

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