TPTP Problem File: ITP198^1.p

%------------------------------------------------------------------------------
% File     : ITP198^1 : TPTP v8.2.0. Released v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer USubst problem prob_1023__6346468_1
% Version  : Especial.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : USubst/prob_1023__6346468_1 [Des21]

% Status   : Theorem
% Rating   : 0.30 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% Syntax   : Number of formulae    :  581 ( 242 unt; 223 typ;   0 def)
%            Number of atoms       :  744 ( 408 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 2581 (  78   ~;   4   |;  51   &;2225   @)
%                                         (   0 <=>; 223  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :   38 (  37 usr)
%            Number of type conns  : 2463 (2463   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  189 ( 186 usr;   8 con; 0-4 aty)
%            Number of variables   : 1218 ( 165   ^;1031   !;  22   ?;1218   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Sledgehammer 2021-02-23 15:36:34.994
%------------------------------------------------------------------------------
% Could-be-implicit typings (37)
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thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_J,type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J_J,type,
    set_Pr1730352763l_real: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1120170903e_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    produc729247771l_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1020032539e_real: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J_J,type,
    set_Pr366573913real_o: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J_J,type,
    set_Pr1919093775l_real: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    set_ch845833233e_real: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    produc96687023l_real: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
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thf(ty_n_t__Set__Oset_I_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
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thf(ty_n_t__Denotational____Semantics__Ointerp,type,
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thf(ty_n_t__Syntax__Ovariable,type,
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thf(ty_n_t__String__Ochar,type,
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thf(ty_n_t__Real__Oreal,type,
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% Explicit typings (186)
thf(sy_c_BNF__Def_OGr_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    bNF_Gr1652860930e_real: set_char_real_o > ( ( char > real > $o ) > char > set_variable_real > set_variable_real ) > set_Pr268868489e_real ).

thf(sy_c_BNF__Def_OGr_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
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thf(sy_c_Denotational__Semantics_OConsts,type,
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thf(sy_c_Denotational__Semantics_OFuncs,type,
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thf(sy_c_Denotational__Semantics_OGames,type,
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thf(sy_c_Denotational__Semantics_OPreds,type,
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thf(sy_c_Denotational__Semantics_Omkinterp,type,
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thf(sy_c_Denotational__Semantics_Oworlds,type,
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thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
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thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    the_Pr429269900e_real: ( produc104944723e_real > $o ) > produc104944723e_real ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    the_Pr1196831286l_real: ( produc96687023l_real > $o ) > produc96687023l_real ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    the_Pr1679925410e_real: ( produc1020032539e_real > $o ) > produc1020032539e_real ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    the_Pr1930357084real_o: ( produc1606031907real_o > $o ) > produc1606031907real_o ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    the_Pr198758430e_real: ( produc1120170903e_real > $o ) > produc1120170903e_real ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
    the_Pr1076580896r_real: ( produc928489369r_real > $o ) > produc928489369r_real ).

thf(sy_c_HOL_OThe_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    the_Pr543709229e_real: ( produc1993135732e_real > $o ) > produc1993135732e_real ).

thf(sy_c_If_001t__Real__Oreal,type,
    if_real: $o > real > real > real ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    bot_bo721182586e_real: set_variable_real ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    ord_le2056633321e_real: set_Pr268868489e_real > set_Pr268868489e_real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    ord_le780198939e_real: set_Pr307567739e_real > set_Pr307567739e_real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_J,type,
    ord_le1631106314e_real: set_Pr397354154e_real > set_Pr397354154e_real > $o ).

thf(sy_c_Orderings_Oorder__class_Omono_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    order_1507925822e_real: ( set_variable_real > set_variable_real ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    top_to239690646e_real: set_variable_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1566957527real_o: ( char > real > $o ) > ( char > real > $o ) > produc2070499431real_o ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc2007437005e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc686464615l_real: ( char > real > real ) > ( char > real > real ) > produc96687023l_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc141013715e_real: ( char > real > real ) > produc104944723e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1285468373real_o: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc1606031907real_o ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc525232719e_real: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > produc1120170903e_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc700235985r_real: ( char > real ) > ( char > real ) > produc928489369r_real ).

thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc2125489830e_real: ( char > real ) > produc1020032539e_real > produc1993135732e_real ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc1053845203l_real: produc104944723e_real > ( char > real > real ) > produc729247771l_real ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1957227327e_real: produc104944723e_real > produc104944723e_real > produc1416364679e_real ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc1317530464r_real: produc1020032539e_real > ( char > real ) > produc2139219430r_real ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc680410711e_real: produc1020032539e_real > produc1020032539e_real > produc199503591e_real ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    produc638505729e_real: produc1993135732e_real > produc1993135732e_real > produc1014656201e_real ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc214490950real_o: ( char > real > $o ) > ( char > real > $o ) > ( char > real > $o ) > ( char > real > $o ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc210225566e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc1051282262l_real: ( char > real > real ) > ( char > real > real ) > ( char > real > real ) > ( char > real > real ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc619891650e_real: ( char > real > real ) > produc104944723e_real > ( char > real > real ) > produc104944723e_real > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1635740582real_o: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1689380158e_real: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc885334464r_real: ( char > real ) > ( char > real ) > ( char > real ) > ( char > real ) > $o ).

thf(sy_c_Product__Type_OPair__Rep_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc345845751e_real: ( char > real ) > produc1020032539e_real > ( char > real ) > produc1020032539e_real > $o ).

thf(sy_c_Product__Type_OSigma_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1853244124e_real: set_char_real_o > ( ( char > real > $o ) > set_ch845833233e_real ) > set_Pr268868489e_real ).

thf(sy_c_Product__Type_OSigma_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc522711812e_real: set_char_real_real > ( ( char > real > real ) > set_Pr268868489e_real ) > set_Pr307567739e_real ).

thf(sy_c_Product__Type_OSigma_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1131275492real_o: set_ch845833233e_real > ( ( char > set_variable_real > set_variable_real ) > set_char_real_o ) > set_Pr366573913real_o ).

thf(sy_c_Product__Type_OSigma_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc34356277e_real: set_char_real > ( ( char > real ) > set_Pr307567739e_real ) > set_Pr397354154e_real ).

thf(sy_c_Product__Type_OSigma_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
    produc979346218e_real: set_variable_real > ( ( variable > real ) > set_variable_real ) > set_Pr1530225953e_real ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc1435543300l_real: set_Pr268868489e_real > ( produc104944723e_real > set_char_real_real ) > set_Pr1730352763l_real ).

thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc1373880559r_real: set_Pr307567739e_real > ( produc1020032539e_real > set_char_real ) > set_Pr821009180r_real ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_Eo,type,
    produc169502925al_o_o: ( produc2070499431real_o > $o ) > ( char > real > $o ) > ( char > real > $o ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_Eo,type,
    produc809977789real_o: ( produc104944723e_real > $o ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_Eo,type,
    produc311008957real_o: ( produc96687023l_real > $o ) > ( char > real > real ) > ( char > real > real ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_Eo,type,
    produc753879889real_o: ( produc1020032539e_real > $o ) > ( char > real > real ) > produc104944723e_real > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_Eo,type,
    produc647541685al_o_o: ( produc1606031907real_o > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_Eo,type,
    produc1935758037real_o: ( produc1120170903e_real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_Eo,type,
    produc1735668179real_o: ( produc928489369r_real > $o ) > ( char > real ) > ( char > real ) > $o ).

thf(sy_c_Product__Type_Ocurry_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_Eo,type,
    produc998184740real_o: ( produc1993135732e_real > $o ) > ( char > real ) > produc1020032539e_real > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_Eo,type,
    produc1070892532real_o: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc584529143e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_Eo,type,
    produc677394266real_o: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1138486237e_real: ( ( char > real > real ) > produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1941565183e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real ) > produc1606031907real_o > produc104944723e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc355430254e_real: ( ( char > real > $o ) > char > real > $o ) > ( ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real ) > produc104944723e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc753666538e_real: ( ( char > real > $o ) > char > real > real ) > ( ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1251731407e_real: ( ( char > real > $o ) > char > real ) > ( ( char > set_variable_real > set_variable_real ) > produc1020032539e_real ) > produc104944723e_real > produc1993135732e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc683016410e_real: ( ( char > real > real ) > char > real > $o ) > ( produc104944723e_real > char > set_variable_real > set_variable_real ) > produc1020032539e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc2131385966e_real: ( ( char > real > real ) > char > real > real ) > ( produc104944723e_real > produc104944723e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc348783435e_real: ( ( char > real > real ) > char > real ) > ( produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1993135732e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1797673857e_real: ( ( char > real ) > char > real > $o ) > ( produc1020032539e_real > char > set_variable_real > set_variable_real ) > produc1993135732e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc202772275e_real: ( ( char > real ) > char > real > real ) > ( produc1020032539e_real > produc104944723e_real ) > produc1993135732e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Omap__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc552964208e_real: ( ( char > real ) > char > real ) > ( produc1020032539e_real > produc1020032539e_real ) > produc1993135732e_real > produc1993135732e_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc2033648741real_o: ( ( char > real > $o ) > ( char > real > $o ) > $o ) > produc2070499431real_o ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc540070591e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc606131701l_real: ( ( char > real > real ) > ( char > real > real ) > $o ) > produc96687023l_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc877953633e_real: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1965585607real_o: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ) > produc1606031907real_o ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1545903581e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc1120170903e_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc1022533727r_real: ( ( char > real ) > ( char > real ) > $o ) > produc928489369r_real ).

thf(sy_c_Product__Type_Oprod_OAbs__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1448824728e_real: ( ( char > real ) > produc1020032539e_real > $o ) > produc1993135732e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_Eo,type,
    produc131289260al_o_o: ( ( char > real > $o ) > ( char > real > $o ) > $o ) > produc2070499431real_o > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_Eo,type,
    produc1629511198real_o: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1906464077e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_Eo,type,
    produc1095814172real_o: ( ( char > real > real ) > ( char > real > real ) > $o ) > produc96687023l_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_Eo,type,
    produc679978160real_o: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1202665267e_real: ( ( char > real > real ) > produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_Eo,type,
    produc1467075094al_o_o: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ) > produc1606031907real_o > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1116016469e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real ) > produc1606031907real_o > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_Eo,type,
    produc143994420real_o: ( ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc1120170903e_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_Eo,type,
    produc1655853874real_o: ( ( char > real ) > ( char > real ) > $o ) > produc928489369r_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_Eo,type,
    produc569598981real_o: ( ( char > real ) > produc1020032539e_real > $o ) > produc1993135732e_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    produc315720647e_real: ( ( char > real ) > produc1020032539e_real > produc1993135732e_real ) > produc1993135732e_real > produc1993135732e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_001_Eo,type,
    produc1299805450real_o: ( ( variable > real ) > ( variable > real ) > $o ) > produc1863992257e_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_Eo,type,
    produc421130416real_o: ( produc104944723e_real > ( char > real > real ) > $o ) > produc729247771l_real > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc991789875e_real: ( produc104944723e_real > ( char > real > real ) > produc1020032539e_real ) > produc729247771l_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    produc864726913e_real: ( produc1020032539e_real > ( char > real ) > produc1993135732e_real ) > produc2139219430r_real > produc1993135732e_real ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1486464481e_real: produc104944723e_real > char > real > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc634910399e_real: produc1020032539e_real > char > real > real ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc764495849real_o: produc1606031907real_o > char > set_variable_real > set_variable_real ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1146879930e_real: produc1993135732e_real > char > real ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc1547741887l_real: produc729247771l_real > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc338920564r_real: produc2139219430r_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc504912415e_real: produc104944723e_real > char > set_variable_real > set_variable_real ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc1179001601e_real: produc1020032539e_real > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc1930427431real_o: produc1606031907real_o > char > real > $o ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1176159992e_real: produc1993135732e_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc2091833089l_real: produc729247771l_real > char > real > real ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc368200626r_real: produc2139219430r_real > char > real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc443915639real_o: produc2070499431real_o > produc2070499431real_o ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc914893101e_real: produc104944723e_real > produc1606031907real_o ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc995978247l_real: produc96687023l_real > produc96687023l_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    produc865271923e_real: produc1020032539e_real > produc729247771l_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    produc192924469real_o: produc1606031907real_o > produc104944723e_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    produc1656125423e_real: produc1120170903e_real > produc1120170903e_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc1564675697r_real: produc928489369r_real > produc928489369r_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    produc1726279942e_real: produc1993135732e_real > produc2139219430r_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    produc1778103411l_real: produc729247771l_real > produc1020032539e_real ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    produc918320576r_real: produc2139219430r_real > produc1993135732e_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    inv_im1954866834real_o: set_Pr1053253703real_o > ( ( char > real > $o ) > char > real > $o ) > set_Pr1053253703real_o ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    inv_im576609886l_real: set_Pr1053253703real_o > ( ( char > real > real ) > char > real > $o ) > set_Pr1919093775l_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    inv_im255337747r_real: set_Pr1053253703real_o > ( ( char > real ) > char > real > $o ) > set_Pr42335993r_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    inv_im1748900174real_o: set_Pr1919093775l_real > ( ( char > real > $o ) > char > real > real ) > set_Pr1053253703real_o ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    inv_im2119069858l_real: set_Pr1919093775l_real > ( ( char > real > real ) > char > real > real ) > set_Pr1919093775l_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    inv_im854642519r_real: set_Pr1919093775l_real > ( ( char > real ) > char > real > real ) > set_Pr42335993r_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    inv_im710342731r_real: set_Pr1588228599e_real > ( ( char > real ) > char > set_variable_real > set_variable_real ) > set_Pr42335993r_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    inv_im331529689real_o: set_Pr42335993r_real > ( ( char > real > $o ) > char > real ) > set_Pr1053253703real_o ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    inv_im96827991l_real: set_Pr42335993r_real > ( ( char > real > real ) > char > real ) > set_Pr1919093775l_real ).

thf(sy_c_Relation_Oinv__image_001_062_It__String__Ochar_Mt__Real__Oreal_J_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    inv_im817616652r_real: set_Pr42335993r_real > ( ( char > real ) > char > real ) > set_Pr42335993r_real ).

thf(sy_c_Set_OCollect_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    collect_char_real_o: ( ( char > real > $o ) > $o ) > set_char_real_o ).

thf(sy_c_Set_OCollect_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    collec1429138108l_real: ( ( char > real > real ) > $o ) > set_char_real_real ).

thf(sy_c_Set_OCollect_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    collec425771440e_real: ( ( char > set_variable_real > set_variable_real ) > $o ) > set_ch845833233e_real ).

thf(sy_c_Set_OCollect_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    collect_char_real: ( ( char > real ) > $o ) > set_char_real ).

thf(sy_c_Set_OCollect_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
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thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    collec1042577836e_real: ( produc1863992257e_real > $o ) > set_Pr1530225953e_real ).

thf(sy_c_Set_Oimage_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
    image_1599134823e_real: ( ( variable > real ) > variable > real ) > set_variable_real > set_variable_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    image_448624581real_o: ( produc2070499431real_o > produc2070499431real_o ) > set_Pr1053253703real_o > set_Pr1053253703real_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    image_670686893e_real: ( produc104944723e_real > produc104944723e_real ) > set_Pr268868489e_real > set_Pr268868489e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    image_1739334977e_real: ( produc104944723e_real > produc1020032539e_real ) > set_Pr268868489e_real > set_Pr307567739e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    image_24290429real_o: ( produc104944723e_real > produc1606031907real_o ) > set_Pr268868489e_real > set_Pr366573913real_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    image_300296654e_real: ( produc104944723e_real > produc1993135732e_real ) > set_Pr268868489e_real > set_Pr397354154e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
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thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    image_450993193e_real: ( produc1020032539e_real > produc104944723e_real ) > set_Pr307567739e_real > set_Pr268868489e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    image_1823533253e_real: ( produc1020032539e_real > produc1020032539e_real ) > set_Pr307567739e_real > set_Pr307567739e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    image_1698073930e_real: ( produc1020032539e_real > produc1993135732e_real ) > set_Pr307567739e_real > set_Pr397354154e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    image_1532748485l_real: ( produc1020032539e_real > produc729247771l_real ) > set_Pr307567739e_real > set_Pr1730352763l_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    image_2028344445e_real: ( produc1606031907real_o > produc104944723e_real ) > set_Pr366573913real_o > set_Pr268868489e_real ).

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    image_1495813573e_real: ( produc1120170903e_real > produc1120170903e_real ) > set_Pr1588228599e_real > set_Pr1588228599e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
    image_1523756869r_real: ( produc928489369r_real > produc928489369r_real ) > set_Pr42335993r_real > set_Pr42335993r_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    image_426244814e_real: ( produc1993135732e_real > produc104944723e_real ) > set_Pr397354154e_real > set_Pr268868489e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    image_479987936e_real: ( produc1993135732e_real > produc1020032539e_real ) > set_Pr397354154e_real > set_Pr307567739e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    image_866442351e_real: ( produc1993135732e_real > produc1993135732e_real ) > set_Pr397354154e_real > set_Pr397354154e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
    image_1012526049r_real: ( produc1993135732e_real > produc2139219430r_real ) > set_Pr397354154e_real > set_Pr821009180r_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    image_711552709e_real: ( produc729247771l_real > produc1020032539e_real ) > set_Pr1730352763l_real > set_Pr307567739e_real ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
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thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Orepc,type,
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thf(sy_c_Wellfounded_Olex__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
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thf(sy_c_Wellfounded_Olex__prod_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    lex_pr592421611e_real: set_Pr1919093775l_real > set_Pr521705191e_real > set_Pr1517071815e_real ).

thf(sy_c_Wellfounded_Olex__prod_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    lex_pr1793499278e_real: set_Pr42335993r_real > set_Pr1517071815e_real > set_Pr605909289e_real ).

thf(sy_c_Wfrec_Osame__fst_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    same_f1185518776e_real: ( ( char > real > $o ) > $o ) > ( ( char > real > $o ) > set_Pr1588228599e_real ) > set_Pr521705191e_real ).

thf(sy_c_Wfrec_Osame__fst_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    same_f1243548200e_real: ( ( char > real > real ) > $o ) > ( ( char > real > real ) > set_Pr521705191e_real ) > set_Pr1517071815e_real ).

thf(sy_c_Wfrec_Osame__fst_001_062_It__String__Ochar_Mt__Real__Oreal_J_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    same_f764716049e_real: ( ( char > real ) > $o ) > ( ( char > real ) > set_Pr1517071815e_real ) > set_Pr605909289e_real ).

thf(sy_c_member_001_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J,type,
    member_char_real_o: ( char > real > $o ) > set_char_real_o > $o ).

thf(sy_c_member_001_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
    member312374654l_real: ( char > real > real ) > set_char_real_real > $o ).

thf(sy_c_member_001_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J,type,
    member2042895986e_real: ( char > set_variable_real > set_variable_real ) > set_ch845833233e_real > $o ).

thf(sy_c_member_001_062_It__String__Ochar_Mt__Real__Oreal_J,type,
    member_char_real: ( char > real ) > set_char_real > $o ).

thf(sy_c_member_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
    member_variable_real: ( variable > real ) > set_variable_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    member1795186320real_o: produc2070499431real_o > set_Pr1053253703real_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    member1871517162e_real: produc104944723e_real > set_Pr268868489e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    member1801875544l_real: produc96687023l_real > set_Pr1919093775l_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    member544802500e_real: produc1020032539e_real > set_Pr307567739e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_J,type,
    member1225120698real_o: produc1606031907real_o > set_Pr366573913real_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J,type,
    member625963584e_real: produc1120170903e_real > set_Pr1588228599e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
    member1086859330r_real: produc928489369r_real > set_Pr42335993r_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    member1491807627e_real: produc1993135732e_real > set_Pr397354154e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
    member561592938e_real: produc1863992257e_real > set_Pr1530225953e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_M_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
    member254017732l_real: produc729247771l_real > set_Pr1730352763l_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J,type,
    member2016544560e_real: produc1416364679e_real > set_Pr521705191e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_M_062_It__String__Ochar_Mt__Real__Oreal_J_J,type,
    member1637891325r_real: produc2139219430r_real > set_Pr821009180r_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J,type,
    member1778419728e_real: produc199503591e_real > set_Pr1517071815e_real > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Real__Oreal_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_Mt__Real__Oreal_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_M_062_It__Real__Oreal_M_Eo_J_J_M_062_It__String__Ochar_M_062_It__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_Mt__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J_J_J_J_J_J,type,
    member1966130802e_real: produc1014656201e_real > set_Pr605909289e_real > $o ).

thf(sy_v_I,type,
    i: denotational_interp ).

thf(sy_v_d,type,
    d: real ).

thf(sy_v_f,type,
    f: char ).

% Relevant facts (354)
thf(fact_0_Preds__mkinterp,axiom,
    ! [C: char > real,F: char > real > real,P: char > real > $o,G: char > set_variable_real > set_variable_real] :
      ( ( denotational_Preds @ ( denota1150374853interp @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ F @ ( produc2007437005e_real @ P @ G ) ) ) ) )
      = P ) ).

% Preds_mkinterp
thf(fact_1_Funcs__mkinterp,axiom,
    ! [C: char > real,F: char > real > real,P: char > real > $o,G: char > set_variable_real > set_variable_real] :
      ( ( denotational_Funcs @ ( denota1150374853interp @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ F @ ( produc2007437005e_real @ P @ G ) ) ) ) )
      = F ) ).

% Funcs_mkinterp
thf(fact_2_Consts__mkinterp,axiom,
    ! [C: char > real,F: char > real > real,P: char > real > $o,G: char > set_variable_real > set_variable_real] :
      ( ( denotational_Consts @ ( denota1150374853interp @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ F @ ( produc2007437005e_real @ P @ G ) ) ) ) )
      = C ) ).

% Consts_mkinterp
thf(fact_3_mkinterp__eq,axiom,
    ! [I: denotational_interp,J: denotational_interp] :
      ( ( ( ( denotational_Consts @ I )
          = ( denotational_Consts @ J ) )
        & ( ( denotational_Funcs @ I )
          = ( denotational_Funcs @ J ) )
        & ( ( denotational_Preds @ I )
          = ( denotational_Preds @ J ) )
        & ( ( denotational_Games @ I )
          = ( denotational_Games @ J ) ) )
      = ( I = J ) ) ).

% mkinterp_eq
thf(fact_4_repc__def,axiom,
    ( uSubst1505767257e_repc
    = ( ^ [I2: denotational_interp,F2: char,D: real] :
          ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [C2: char] : ( if_real @ ( C2 = F2 ) @ D @ ( denotational_Consts @ I2 @ C2 ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ I2 ) @ ( produc2007437005e_real @ ( denotational_Preds @ I2 ) @ ( denotational_Games @ I2 ) ) ) ) ) ) ) ).

% repc_def
thf(fact_5_prod__cases4,axiom,
    ! [Y: produc1993135732e_real] :
      ~ ! [A: char > real,B: char > real > real,C3: char > real > $o,D2: char > set_variable_real > set_variable_real] :
          ( Y
         != ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C3 @ D2 ) ) ) ) ).

% prod_cases4
thf(fact_6_prod__induct4,axiom,
    ! [P: produc1993135732e_real > $o,X: produc1993135732e_real] :
      ( ! [A: char > real,B: char > real > real,C3: char > real > $o,D2: char > set_variable_real > set_variable_real] : ( P @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C3 @ D2 ) ) ) )
     => ( P @ X ) ) ).

% prod_induct4
thf(fact_7_old_Oprod_Oinject,axiom,
    ! [A2: char > real,B2: char > real,A3: char > real,B3: char > real] :
      ( ( ( produc700235985r_real @ A2 @ B2 )
        = ( produc700235985r_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_8_old_Oprod_Oinject,axiom,
    ! [A2: char > real > real,B2: char > real > real,A3: char > real > real,B3: char > real > real] :
      ( ( ( produc686464615l_real @ A2 @ B2 )
        = ( produc686464615l_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_9_old_Oprod_Oinject,axiom,
    ! [A2: char > real > $o,B2: char > real > $o,A3: char > real > $o,B3: char > real > $o] :
      ( ( ( produc1566957527real_o @ A2 @ B2 )
        = ( produc1566957527real_o @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_10_old_Oprod_Oinject,axiom,
    ! [A2: char > set_variable_real > set_variable_real,B2: char > real > $o,A3: char > set_variable_real > set_variable_real,B3: char > real > $o] :
      ( ( ( produc1285468373real_o @ A2 @ B2 )
        = ( produc1285468373real_o @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_11_old_Oprod_Oinject,axiom,
    ! [A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real,A3: char > set_variable_real > set_variable_real,B3: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A2 @ B2 )
        = ( produc525232719e_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_12_old_Oprod_Oinject,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A3: char > real,B3: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A2 @ B2 )
        = ( produc2125489830e_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_13_old_Oprod_Oinject,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A3: char > real > real,B3: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A2 @ B2 )
        = ( produc141013715e_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_14_old_Oprod_Oinject,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A3: char > real > $o,B3: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A2 @ B2 )
        = ( produc2007437005e_real @ A3 @ B3 ) )
      = ( ( A2 = A3 )
        & ( B2 = B3 ) ) ) ).

% old.prod.inject
thf(fact_15_prod_Oinject,axiom,
    ! [X1: char > real,X2: char > real,Y1: char > real,Y2: char > real] :
      ( ( ( produc700235985r_real @ X1 @ X2 )
        = ( produc700235985r_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_16_prod_Oinject,axiom,
    ! [X1: char > real > real,X2: char > real > real,Y1: char > real > real,Y2: char > real > real] :
      ( ( ( produc686464615l_real @ X1 @ X2 )
        = ( produc686464615l_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_17_prod_Oinject,axiom,
    ! [X1: char > real > $o,X2: char > real > $o,Y1: char > real > $o,Y2: char > real > $o] :
      ( ( ( produc1566957527real_o @ X1 @ X2 )
        = ( produc1566957527real_o @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_18_prod_Oinject,axiom,
    ! [X1: char > set_variable_real > set_variable_real,X2: char > real > $o,Y1: char > set_variable_real > set_variable_real,Y2: char > real > $o] :
      ( ( ( produc1285468373real_o @ X1 @ X2 )
        = ( produc1285468373real_o @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_19_prod_Oinject,axiom,
    ! [X1: char > set_variable_real > set_variable_real,X2: char > set_variable_real > set_variable_real,Y1: char > set_variable_real > set_variable_real,Y2: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ X1 @ X2 )
        = ( produc525232719e_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_20_prod_Oinject,axiom,
    ! [X1: char > real,X2: produc1020032539e_real,Y1: char > real,Y2: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ X1 @ X2 )
        = ( produc2125489830e_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_21_prod_Oinject,axiom,
    ! [X1: char > real > real,X2: produc104944723e_real,Y1: char > real > real,Y2: produc104944723e_real] :
      ( ( ( produc141013715e_real @ X1 @ X2 )
        = ( produc141013715e_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_22_prod_Oinject,axiom,
    ! [X1: char > real > $o,X2: char > set_variable_real > set_variable_real,Y1: char > real > $o,Y2: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ X1 @ X2 )
        = ( produc2007437005e_real @ Y1 @ Y2 ) )
      = ( ( X1 = Y1 )
        & ( X2 = Y2 ) ) ) ).

% prod.inject
thf(fact_23_repc__consts,axiom,
    ! [C4: char,F3: char,I: denotational_interp,D3: real] :
      ( ( ( C4 = F3 )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ I @ F3 @ D3 ) @ C4 )
          = D3 ) )
      & ( ( C4 != F3 )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ I @ F3 @ D3 ) @ C4 )
          = ( denotational_Consts @ I @ C4 ) ) ) ) ).

% repc_consts
thf(fact_24_repc__funcs,axiom,
    ! [I: denotational_interp,F3: char,D3: real] :
      ( ( denotational_Funcs @ ( uSubst1505767257e_repc @ I @ F3 @ D3 ) )
      = ( denotational_Funcs @ I ) ) ).

% repc_funcs
thf(fact_25_old_Oprod_Oinducts,axiom,
    ! [P: produc928489369r_real > $o,Prod: produc928489369r_real] :
      ( ! [A: char > real,B: char > real] : ( P @ ( produc700235985r_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_26_old_Oprod_Oinducts,axiom,
    ! [P: produc96687023l_real > $o,Prod: produc96687023l_real] :
      ( ! [A: char > real > real,B: char > real > real] : ( P @ ( produc686464615l_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_27_old_Oprod_Oinducts,axiom,
    ! [P: produc2070499431real_o > $o,Prod: produc2070499431real_o] :
      ( ! [A: char > real > $o,B: char > real > $o] : ( P @ ( produc1566957527real_o @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_28_old_Oprod_Oinducts,axiom,
    ! [P: produc1606031907real_o > $o,Prod: produc1606031907real_o] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] : ( P @ ( produc1285468373real_o @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_29_old_Oprod_Oinducts,axiom,
    ! [P: produc1120170903e_real > $o,Prod: produc1120170903e_real] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] : ( P @ ( produc525232719e_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_30_old_Oprod_Oinducts,axiom,
    ! [P: produc1993135732e_real > $o,Prod: produc1993135732e_real] :
      ( ! [A: char > real,B: produc1020032539e_real] : ( P @ ( produc2125489830e_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_31_old_Oprod_Oinducts,axiom,
    ! [P: produc1020032539e_real > $o,Prod: produc1020032539e_real] :
      ( ! [A: char > real > real,B: produc104944723e_real] : ( P @ ( produc141013715e_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_32_old_Oprod_Oinducts,axiom,
    ! [P: produc104944723e_real > $o,Prod: produc104944723e_real] :
      ( ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] : ( P @ ( produc2007437005e_real @ A @ B ) )
     => ( P @ Prod ) ) ).

% old.prod.inducts
thf(fact_33_old_Oprod_Oexhaust,axiom,
    ! [Y: produc928489369r_real] :
      ~ ! [A: char > real,B: char > real] :
          ( Y
         != ( produc700235985r_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_34_old_Oprod_Oexhaust,axiom,
    ! [Y: produc96687023l_real] :
      ~ ! [A: char > real > real,B: char > real > real] :
          ( Y
         != ( produc686464615l_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_35_old_Oprod_Oexhaust,axiom,
    ! [Y: produc2070499431real_o] :
      ~ ! [A: char > real > $o,B: char > real > $o] :
          ( Y
         != ( produc1566957527real_o @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_36_old_Oprod_Oexhaust,axiom,
    ! [Y: produc1606031907real_o] :
      ~ ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
          ( Y
         != ( produc1285468373real_o @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_37_old_Oprod_Oexhaust,axiom,
    ! [Y: produc1120170903e_real] :
      ~ ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
          ( Y
         != ( produc525232719e_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_38_old_Oprod_Oexhaust,axiom,
    ! [Y: produc1993135732e_real] :
      ~ ! [A: char > real,B: produc1020032539e_real] :
          ( Y
         != ( produc2125489830e_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_39_old_Oprod_Oexhaust,axiom,
    ! [Y: produc1020032539e_real] :
      ~ ! [A: char > real > real,B: produc104944723e_real] :
          ( Y
         != ( produc141013715e_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_40_old_Oprod_Oexhaust,axiom,
    ! [Y: produc104944723e_real] :
      ~ ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
          ( Y
         != ( produc2007437005e_real @ A @ B ) ) ).

% old.prod.exhaust
thf(fact_41_Pair__inject,axiom,
    ! [A2: char > real,B2: char > real,A3: char > real,B3: char > real] :
      ( ( ( produc700235985r_real @ A2 @ B2 )
        = ( produc700235985r_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_42_Pair__inject,axiom,
    ! [A2: char > real > real,B2: char > real > real,A3: char > real > real,B3: char > real > real] :
      ( ( ( produc686464615l_real @ A2 @ B2 )
        = ( produc686464615l_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_43_Pair__inject,axiom,
    ! [A2: char > real > $o,B2: char > real > $o,A3: char > real > $o,B3: char > real > $o] :
      ( ( ( produc1566957527real_o @ A2 @ B2 )
        = ( produc1566957527real_o @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_44_Pair__inject,axiom,
    ! [A2: char > set_variable_real > set_variable_real,B2: char > real > $o,A3: char > set_variable_real > set_variable_real,B3: char > real > $o] :
      ( ( ( produc1285468373real_o @ A2 @ B2 )
        = ( produc1285468373real_o @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_45_Pair__inject,axiom,
    ! [A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real,A3: char > set_variable_real > set_variable_real,B3: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A2 @ B2 )
        = ( produc525232719e_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_46_Pair__inject,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A3: char > real,B3: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A2 @ B2 )
        = ( produc2125489830e_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_47_Pair__inject,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A3: char > real > real,B3: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A2 @ B2 )
        = ( produc141013715e_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_48_Pair__inject,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A3: char > real > $o,B3: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A2 @ B2 )
        = ( produc2007437005e_real @ A3 @ B3 ) )
     => ~ ( ( A2 = A3 )
         => ( B2 != B3 ) ) ) ).

% Pair_inject
thf(fact_49_prod__cases,axiom,
    ! [P: produc928489369r_real > $o,P2: produc928489369r_real] :
      ( ! [A: char > real,B: char > real] : ( P @ ( produc700235985r_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_50_prod__cases,axiom,
    ! [P: produc96687023l_real > $o,P2: produc96687023l_real] :
      ( ! [A: char > real > real,B: char > real > real] : ( P @ ( produc686464615l_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_51_prod__cases,axiom,
    ! [P: produc2070499431real_o > $o,P2: produc2070499431real_o] :
      ( ! [A: char > real > $o,B: char > real > $o] : ( P @ ( produc1566957527real_o @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_52_prod__cases,axiom,
    ! [P: produc1606031907real_o > $o,P2: produc1606031907real_o] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] : ( P @ ( produc1285468373real_o @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_53_prod__cases,axiom,
    ! [P: produc1120170903e_real > $o,P2: produc1120170903e_real] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] : ( P @ ( produc525232719e_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_54_prod__cases,axiom,
    ! [P: produc1993135732e_real > $o,P2: produc1993135732e_real] :
      ( ! [A: char > real,B: produc1020032539e_real] : ( P @ ( produc2125489830e_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_55_prod__cases,axiom,
    ! [P: produc1020032539e_real > $o,P2: produc1020032539e_real] :
      ( ! [A: char > real > real,B: produc104944723e_real] : ( P @ ( produc141013715e_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_56_prod__cases,axiom,
    ! [P: produc104944723e_real > $o,P2: produc104944723e_real] :
      ( ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] : ( P @ ( produc2007437005e_real @ A @ B ) )
     => ( P @ P2 ) ) ).

% prod_cases
thf(fact_57_surj__pair,axiom,
    ! [P2: produc928489369r_real] :
    ? [X3: char > real,Y3: char > real] :
      ( P2
      = ( produc700235985r_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_58_surj__pair,axiom,
    ! [P2: produc96687023l_real] :
    ? [X3: char > real > real,Y3: char > real > real] :
      ( P2
      = ( produc686464615l_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_59_surj__pair,axiom,
    ! [P2: produc2070499431real_o] :
    ? [X3: char > real > $o,Y3: char > real > $o] :
      ( P2
      = ( produc1566957527real_o @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_60_surj__pair,axiom,
    ! [P2: produc1606031907real_o] :
    ? [X3: char > set_variable_real > set_variable_real,Y3: char > real > $o] :
      ( P2
      = ( produc1285468373real_o @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_61_surj__pair,axiom,
    ! [P2: produc1120170903e_real] :
    ? [X3: char > set_variable_real > set_variable_real,Y3: char > set_variable_real > set_variable_real] :
      ( P2
      = ( produc525232719e_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_62_surj__pair,axiom,
    ! [P2: produc1993135732e_real] :
    ? [X3: char > real,Y3: produc1020032539e_real] :
      ( P2
      = ( produc2125489830e_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_63_surj__pair,axiom,
    ! [P2: produc1020032539e_real] :
    ? [X3: char > real > real,Y3: produc104944723e_real] :
      ( P2
      = ( produc141013715e_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_64_surj__pair,axiom,
    ! [P2: produc104944723e_real] :
    ? [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
      ( P2
      = ( produc2007437005e_real @ X3 @ Y3 ) ) ).

% surj_pair
thf(fact_65_prod__induct3,axiom,
    ! [P: produc1993135732e_real > $o,X: produc1993135732e_real] :
      ( ! [A: char > real,B: char > real > real,C3: produc104944723e_real] : ( P @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ C3 ) ) )
     => ( P @ X ) ) ).

% prod_induct3
thf(fact_66_prod__induct3,axiom,
    ! [P: produc1020032539e_real > $o,X: produc1020032539e_real] :
      ( ! [A: char > real > real,B: char > real > $o,C3: char > set_variable_real > set_variable_real] : ( P @ ( produc141013715e_real @ A @ ( produc2007437005e_real @ B @ C3 ) ) )
     => ( P @ X ) ) ).

% prod_induct3
thf(fact_67_prod__cases3,axiom,
    ! [Y: produc1993135732e_real] :
      ~ ! [A: char > real,B: char > real > real,C3: produc104944723e_real] :
          ( Y
         != ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ C3 ) ) ) ).

% prod_cases3
thf(fact_68_prod__cases3,axiom,
    ! [Y: produc1020032539e_real] :
      ~ ! [A: char > real > real,B: char > real > $o,C3: char > set_variable_real > set_variable_real] :
          ( Y
         != ( produc141013715e_real @ A @ ( produc2007437005e_real @ B @ C3 ) ) ) ).

% prod_cases3
thf(fact_69_Games__mkinterp,axiom,
    ! [G: char > set_variable_real > set_variable_real,C: char > real,F: char > real > real,P: char > real > $o] :
      ( ! [A: char] : ( order_1507925822e_real @ ( G @ A ) )
     => ( ( denotational_Games @ ( denota1150374853interp @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ F @ ( produc2007437005e_real @ P @ G ) ) ) ) )
        = G ) ) ).

% Games_mkinterp
thf(fact_70_pred__equals__eq2,axiom,
    ! [R: set_Pr42335993r_real,S: set_Pr42335993r_real] :
      ( ( ( ^ [X4: char > real,Y4: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real,Y4: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_71_pred__equals__eq2,axiom,
    ! [R: set_Pr1919093775l_real,S: set_Pr1919093775l_real] :
      ( ( ( ^ [X4: char > real > real,Y4: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real > real,Y4: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_72_pred__equals__eq2,axiom,
    ! [R: set_Pr1053253703real_o,S: set_Pr1053253703real_o] :
      ( ( ( ^ [X4: char > real > $o,Y4: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real > $o,Y4: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_73_pred__equals__eq2,axiom,
    ! [R: set_Pr366573913real_o,S: set_Pr366573913real_o] :
      ( ( ( ^ [X4: char > set_variable_real > set_variable_real,Y4: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > set_variable_real > set_variable_real,Y4: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_74_pred__equals__eq2,axiom,
    ! [R: set_Pr1588228599e_real,S: set_Pr1588228599e_real] :
      ( ( ( ^ [X4: char > set_variable_real > set_variable_real,Y4: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > set_variable_real > set_variable_real,Y4: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_75_pred__equals__eq2,axiom,
    ! [R: set_Pr397354154e_real,S: set_Pr397354154e_real] :
      ( ( ( ^ [X4: char > real,Y4: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real,Y4: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_76_pred__equals__eq2,axiom,
    ! [R: set_Pr307567739e_real,S: set_Pr307567739e_real] :
      ( ( ( ^ [X4: char > real > real,Y4: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real > real,Y4: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_77_pred__equals__eq2,axiom,
    ! [R: set_Pr268868489e_real,S: set_Pr268868489e_real] :
      ( ( ( ^ [X4: char > real > $o,Y4: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ X4 @ Y4 ) @ R ) )
        = ( ^ [X4: char > real > $o,Y4: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ X4 @ Y4 ) @ S ) ) )
      = ( R = S ) ) ).

% pred_equals_eq2
thf(fact_78_ssubst__Pair__rhs,axiom,
    ! [R2: char > real,S2: char > real,R: set_Pr42335993r_real,S3: char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1086859330r_real @ ( produc700235985r_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_79_ssubst__Pair__rhs,axiom,
    ! [R2: char > real > real,S2: char > real > real,R: set_Pr1919093775l_real,S3: char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1801875544l_real @ ( produc686464615l_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_80_ssubst__Pair__rhs,axiom,
    ! [R2: char > real > $o,S2: char > real > $o,R: set_Pr1053253703real_o,S3: char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1795186320real_o @ ( produc1566957527real_o @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_81_ssubst__Pair__rhs,axiom,
    ! [R2: char > set_variable_real > set_variable_real,S2: char > real > $o,R: set_Pr366573913real_o,S3: char > real > $o] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1225120698real_o @ ( produc1285468373real_o @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_82_ssubst__Pair__rhs,axiom,
    ! [R2: char > set_variable_real > set_variable_real,S2: char > set_variable_real > set_variable_real,R: set_Pr1588228599e_real,S3: char > set_variable_real > set_variable_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member625963584e_real @ ( produc525232719e_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_83_ssubst__Pair__rhs,axiom,
    ! [R2: char > real,S2: produc1020032539e_real,R: set_Pr397354154e_real,S3: produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1491807627e_real @ ( produc2125489830e_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_84_ssubst__Pair__rhs,axiom,
    ! [R2: char > real > real,S2: produc104944723e_real,R: set_Pr307567739e_real,S3: produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member544802500e_real @ ( produc141013715e_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_85_ssubst__Pair__rhs,axiom,
    ! [R2: char > real > $o,S2: char > set_variable_real > set_variable_real,R: set_Pr268868489e_real,S3: char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member1871517162e_real @ ( produc2007437005e_real @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_86_curry__conv,axiom,
    ( produc809977789real_o
    = ( ^ [F2: produc104944723e_real > $o,A4: char > real > $o,B4: char > set_variable_real > set_variable_real] : ( F2 @ ( produc2007437005e_real @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_87_curry__conv,axiom,
    ( produc753879889real_o
    = ( ^ [F2: produc1020032539e_real > $o,A4: char > real > real,B4: produc104944723e_real] : ( F2 @ ( produc141013715e_real @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_88_curry__conv,axiom,
    ( produc998184740real_o
    = ( ^ [F2: produc1993135732e_real > $o,A4: char > real,B4: produc1020032539e_real] : ( F2 @ ( produc2125489830e_real @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_89_curry__def,axiom,
    ( produc809977789real_o
    = ( ^ [C2: produc104944723e_real > $o,X4: char > real > $o,Y4: char > set_variable_real > set_variable_real] : ( C2 @ ( produc2007437005e_real @ X4 @ Y4 ) ) ) ) ).

% curry_def
thf(fact_90_curry__def,axiom,
    ( produc753879889real_o
    = ( ^ [C2: produc1020032539e_real > $o,X4: char > real > real,Y4: produc104944723e_real] : ( C2 @ ( produc141013715e_real @ X4 @ Y4 ) ) ) ) ).

% curry_def
thf(fact_91_curry__def,axiom,
    ( produc998184740real_o
    = ( ^ [C2: produc1993135732e_real > $o,X4: char > real,Y4: produc1020032539e_real] : ( C2 @ ( produc2125489830e_real @ X4 @ Y4 ) ) ) ) ).

% curry_def
thf(fact_92_curryI,axiom,
    ! [F3: produc928489369r_real > $o,A2: char > real,B2: char > real] :
      ( ( F3 @ ( produc700235985r_real @ A2 @ B2 ) )
     => ( produc1735668179real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_93_curryI,axiom,
    ! [F3: produc96687023l_real > $o,A2: char > real > real,B2: char > real > real] :
      ( ( F3 @ ( produc686464615l_real @ A2 @ B2 ) )
     => ( produc311008957real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_94_curryI,axiom,
    ! [F3: produc2070499431real_o > $o,A2: char > real > $o,B2: char > real > $o] :
      ( ( F3 @ ( produc1566957527real_o @ A2 @ B2 ) )
     => ( produc169502925al_o_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_95_curryI,axiom,
    ! [F3: produc1606031907real_o > $o,A2: char > set_variable_real > set_variable_real,B2: char > real > $o] :
      ( ( F3 @ ( produc1285468373real_o @ A2 @ B2 ) )
     => ( produc647541685al_o_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_96_curryI,axiom,
    ! [F3: produc1120170903e_real > $o,A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real] :
      ( ( F3 @ ( produc525232719e_real @ A2 @ B2 ) )
     => ( produc1935758037real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_97_curryI,axiom,
    ! [F3: produc1993135732e_real > $o,A2: char > real,B2: produc1020032539e_real] :
      ( ( F3 @ ( produc2125489830e_real @ A2 @ B2 ) )
     => ( produc998184740real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_98_curryI,axiom,
    ! [F3: produc1020032539e_real > $o,A2: char > real > real,B2: produc104944723e_real] :
      ( ( F3 @ ( produc141013715e_real @ A2 @ B2 ) )
     => ( produc753879889real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_99_curryI,axiom,
    ! [F3: produc104944723e_real > $o,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( F3 @ ( produc2007437005e_real @ A2 @ B2 ) )
     => ( produc809977789real_o @ F3 @ A2 @ B2 ) ) ).

% curryI
thf(fact_100_worlds__def,axiom,
    ( denotational_worlds
    = ( collec633296133e_real
      @ ^ [Nu: variable > real] : $true ) ) ).

% worlds_def
thf(fact_101_swap__simp,axiom,
    ! [X: char > real,Y: char > real] :
      ( ( produc1564675697r_real @ ( produc700235985r_real @ X @ Y ) )
      = ( produc700235985r_real @ Y @ X ) ) ).

% swap_simp
thf(fact_102_swap__simp,axiom,
    ! [X: char > real > real,Y: char > real > real] :
      ( ( produc995978247l_real @ ( produc686464615l_real @ X @ Y ) )
      = ( produc686464615l_real @ Y @ X ) ) ).

% swap_simp
thf(fact_103_swap__simp,axiom,
    ! [X: char > real > $o,Y: char > real > $o] :
      ( ( produc443915639real_o @ ( produc1566957527real_o @ X @ Y ) )
      = ( produc1566957527real_o @ Y @ X ) ) ).

% swap_simp
thf(fact_104_swap__simp,axiom,
    ! [X: char > set_variable_real > set_variable_real,Y: char > set_variable_real > set_variable_real] :
      ( ( produc1656125423e_real @ ( produc525232719e_real @ X @ Y ) )
      = ( produc525232719e_real @ Y @ X ) ) ).

% swap_simp
thf(fact_105_swap__simp,axiom,
    ! [X: produc1020032539e_real,Y: char > real] :
      ( ( produc918320576r_real @ ( produc1317530464r_real @ X @ Y ) )
      = ( produc2125489830e_real @ Y @ X ) ) ).

% swap_simp
thf(fact_106_swap__simp,axiom,
    ! [X: produc104944723e_real,Y: char > real > real] :
      ( ( produc1778103411l_real @ ( produc1053845203l_real @ X @ Y ) )
      = ( produc141013715e_real @ Y @ X ) ) ).

% swap_simp
thf(fact_107_swap__simp,axiom,
    ! [X: char > set_variable_real > set_variable_real,Y: char > real > $o] :
      ( ( produc192924469real_o @ ( produc1285468373real_o @ X @ Y ) )
      = ( produc2007437005e_real @ Y @ X ) ) ).

% swap_simp
thf(fact_108_swap__simp,axiom,
    ! [X: char > real,Y: produc1020032539e_real] :
      ( ( produc1726279942e_real @ ( produc2125489830e_real @ X @ Y ) )
      = ( produc1317530464r_real @ Y @ X ) ) ).

% swap_simp
thf(fact_109_swap__simp,axiom,
    ! [X: char > real > real,Y: produc104944723e_real] :
      ( ( produc865271923e_real @ ( produc141013715e_real @ X @ Y ) )
      = ( produc1053845203l_real @ Y @ X ) ) ).

% swap_simp
thf(fact_110_swap__simp,axiom,
    ! [X: char > real > $o,Y: char > set_variable_real > set_variable_real] :
      ( ( produc914893101e_real @ ( produc2007437005e_real @ X @ Y ) )
      = ( produc1285468373real_o @ Y @ X ) ) ).

% swap_simp
thf(fact_111_Pair__Rep__def,axiom,
    ( produc210225566e_real
    = ( ^ [A4: char > real > $o,B4: char > set_variable_real > set_variable_real,X4: char > real > $o,Y4: char > set_variable_real > set_variable_real] :
          ( ( X4 = A4 )
          & ( Y4 = B4 ) ) ) ) ).

% Pair_Rep_def
thf(fact_112_Pair__Rep__def,axiom,
    ( produc619891650e_real
    = ( ^ [A4: char > real > real,B4: produc104944723e_real,X4: char > real > real,Y4: produc104944723e_real] :
          ( ( X4 = A4 )
          & ( Y4 = B4 ) ) ) ) ).

% Pair_Rep_def
thf(fact_113_Pair__Rep__def,axiom,
    ( produc345845751e_real
    = ( ^ [A4: char > real,B4: produc1020032539e_real,X4: char > real,Y4: produc1020032539e_real] :
          ( ( X4 = A4 )
          & ( Y4 = B4 ) ) ) ) ).

% Pair_Rep_def
thf(fact_114_swap__swap,axiom,
    ! [P2: produc1993135732e_real] :
      ( ( produc918320576r_real @ ( produc1726279942e_real @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_115_swap__swap,axiom,
    ! [P2: produc1020032539e_real] :
      ( ( produc1778103411l_real @ ( produc865271923e_real @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_116_swap__swap,axiom,
    ! [P2: produc2139219430r_real] :
      ( ( produc1726279942e_real @ ( produc918320576r_real @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_117_swap__swap,axiom,
    ! [P2: produc729247771l_real] :
      ( ( produc865271923e_real @ ( produc1778103411l_real @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_118_swap__swap,axiom,
    ! [P2: produc1606031907real_o] :
      ( ( produc914893101e_real @ ( produc192924469real_o @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_119_swap__swap,axiom,
    ! [P2: produc104944723e_real] :
      ( ( produc192924469real_o @ ( produc914893101e_real @ P2 ) )
      = P2 ) ).

% swap_swap
thf(fact_120_curry__K,axiom,
    ! [C4: $o] :
      ( ( produc809977789real_o
        @ ^ [X4: produc104944723e_real] : C4 )
      = ( ^ [X4: char > real > $o,Y4: char > set_variable_real > set_variable_real] : C4 ) ) ).

% curry_K
thf(fact_121_curry__K,axiom,
    ! [C4: $o] :
      ( ( produc753879889real_o
        @ ^ [X4: produc1020032539e_real] : C4 )
      = ( ^ [X4: char > real > real,Y4: produc104944723e_real] : C4 ) ) ).

% curry_K
thf(fact_122_curry__K,axiom,
    ! [C4: $o] :
      ( ( produc998184740real_o
        @ ^ [X4: produc1993135732e_real] : C4 )
      = ( ^ [X4: char > real,Y4: produc1020032539e_real] : C4 ) ) ).

% curry_K
thf(fact_123_curryD,axiom,
    ! [F3: produc928489369r_real > $o,A2: char > real,B2: char > real] :
      ( ( produc1735668179real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc700235985r_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_124_curryD,axiom,
    ! [F3: produc96687023l_real > $o,A2: char > real > real,B2: char > real > real] :
      ( ( produc311008957real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc686464615l_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_125_curryD,axiom,
    ! [F3: produc2070499431real_o > $o,A2: char > real > $o,B2: char > real > $o] :
      ( ( produc169502925al_o_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc1566957527real_o @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_126_curryD,axiom,
    ! [F3: produc1606031907real_o > $o,A2: char > set_variable_real > set_variable_real,B2: char > real > $o] :
      ( ( produc647541685al_o_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc1285468373real_o @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_127_curryD,axiom,
    ! [F3: produc1120170903e_real > $o,A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc525232719e_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_128_curryD,axiom,
    ! [F3: produc1993135732e_real > $o,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc998184740real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc2125489830e_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_129_curryD,axiom,
    ! [F3: produc1020032539e_real > $o,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc753879889real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc141013715e_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_130_curryD,axiom,
    ! [F3: produc104944723e_real > $o,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc2007437005e_real @ A2 @ B2 ) ) ) ).

% curryD
thf(fact_131_curryE,axiom,
    ! [F3: produc928489369r_real > $o,A2: char > real,B2: char > real] :
      ( ( produc1735668179real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc700235985r_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_132_curryE,axiom,
    ! [F3: produc96687023l_real > $o,A2: char > real > real,B2: char > real > real] :
      ( ( produc311008957real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc686464615l_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_133_curryE,axiom,
    ! [F3: produc2070499431real_o > $o,A2: char > real > $o,B2: char > real > $o] :
      ( ( produc169502925al_o_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc1566957527real_o @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_134_curryE,axiom,
    ! [F3: produc1606031907real_o > $o,A2: char > set_variable_real > set_variable_real,B2: char > real > $o] :
      ( ( produc647541685al_o_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc1285468373real_o @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_135_curryE,axiom,
    ! [F3: produc1120170903e_real > $o,A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc525232719e_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_136_curryE,axiom,
    ! [F3: produc1993135732e_real > $o,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc998184740real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc2125489830e_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_137_curryE,axiom,
    ! [F3: produc1020032539e_real > $o,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc753879889real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc141013715e_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_138_curryE,axiom,
    ! [F3: produc104944723e_real > $o,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ F3 @ A2 @ B2 )
     => ( F3 @ ( produc2007437005e_real @ A2 @ B2 ) ) ) ).

% curryE
thf(fact_139_Pair__def,axiom,
    ( produc700235985r_real
    = ( ^ [A4: char > real,B4: char > real] : ( produc1022533727r_real @ ( produc885334464r_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_140_Pair__def,axiom,
    ( produc686464615l_real
    = ( ^ [A4: char > real > real,B4: char > real > real] : ( produc606131701l_real @ ( produc1051282262l_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_141_Pair__def,axiom,
    ( produc1566957527real_o
    = ( ^ [A4: char > real > $o,B4: char > real > $o] : ( produc2033648741real_o @ ( produc214490950real_o @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_142_Pair__def,axiom,
    ( produc1285468373real_o
    = ( ^ [A4: char > set_variable_real > set_variable_real,B4: char > real > $o] : ( produc1965585607real_o @ ( produc1635740582real_o @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_143_Pair__def,axiom,
    ( produc525232719e_real
    = ( ^ [A4: char > set_variable_real > set_variable_real,B4: char > set_variable_real > set_variable_real] : ( produc1545903581e_real @ ( produc1689380158e_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_144_Pair__def,axiom,
    ( produc2125489830e_real
    = ( ^ [A4: char > real,B4: produc1020032539e_real] : ( produc1448824728e_real @ ( produc345845751e_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_145_Pair__def,axiom,
    ( produc141013715e_real
    = ( ^ [A4: char > real > real,B4: produc104944723e_real] : ( produc877953633e_real @ ( produc619891650e_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_146_Pair__def,axiom,
    ( produc2007437005e_real
    = ( ^ [A4: char > real > $o,B4: char > set_variable_real > set_variable_real] : ( produc540070591e_real @ ( produc210225566e_real @ A4 @ B4 ) ) ) ) ).

% Pair_def
thf(fact_147_pair__in__swap__image,axiom,
    ! [Y: char > real,X: char > real,A5: set_Pr42335993r_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ Y @ X ) @ ( image_1523756869r_real @ produc1564675697r_real @ A5 ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_148_pair__in__swap__image,axiom,
    ! [Y: char > real > real,X: char > real > real,A5: set_Pr1919093775l_real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ Y @ X ) @ ( image_1347499973l_real @ produc995978247l_real @ A5 ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_149_pair__in__swap__image,axiom,
    ! [Y: char > real > $o,X: char > real > $o,A5: set_Pr1053253703real_o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ Y @ X ) @ ( image_448624581real_o @ produc443915639real_o @ A5 ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_150_pair__in__swap__image,axiom,
    ! [Y: char > set_variable_real > set_variable_real,X: char > set_variable_real > set_variable_real,A5: set_Pr1588228599e_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ Y @ X ) @ ( image_1495813573e_real @ produc1656125423e_real @ A5 ) )
      = ( member625963584e_real @ ( produc525232719e_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_151_pair__in__swap__image,axiom,
    ! [Y: produc1020032539e_real,X: char > real,A5: set_Pr397354154e_real] :
      ( ( member1637891325r_real @ ( produc1317530464r_real @ Y @ X ) @ ( image_1012526049r_real @ produc1726279942e_real @ A5 ) )
      = ( member1491807627e_real @ ( produc2125489830e_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_152_pair__in__swap__image,axiom,
    ! [Y: produc104944723e_real,X: char > real > real,A5: set_Pr307567739e_real] :
      ( ( member254017732l_real @ ( produc1053845203l_real @ Y @ X ) @ ( image_1532748485l_real @ produc865271923e_real @ A5 ) )
      = ( member544802500e_real @ ( produc141013715e_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_153_pair__in__swap__image,axiom,
    ! [Y: char > set_variable_real > set_variable_real,X: char > real > $o,A5: set_Pr268868489e_real] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ Y @ X ) @ ( image_24290429real_o @ produc914893101e_real @ A5 ) )
      = ( member1871517162e_real @ ( produc2007437005e_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_154_pair__in__swap__image,axiom,
    ! [Y: char > real,X: produc1020032539e_real,A5: set_Pr821009180r_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ Y @ X ) @ ( image_152725217e_real @ produc918320576r_real @ A5 ) )
      = ( member1637891325r_real @ ( produc1317530464r_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_155_pair__in__swap__image,axiom,
    ! [Y: char > real > real,X: produc104944723e_real,A5: set_Pr1730352763l_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ Y @ X ) @ ( image_711552709e_real @ produc1778103411l_real @ A5 ) )
      = ( member254017732l_real @ ( produc1053845203l_real @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_156_pair__in__swap__image,axiom,
    ! [Y: char > real > $o,X: char > set_variable_real > set_variable_real,A5: set_Pr366573913real_o] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ Y @ X ) @ ( image_2028344445e_real @ produc192924469real_o @ A5 ) )
      = ( member1225120698real_o @ ( produc1285468373real_o @ X @ Y ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_157_in__inv__image,axiom,
    ! [X: char > real,Y: char > real,R2: set_Pr42335993r_real,F3: ( char > real ) > char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ X @ Y ) @ ( inv_im817616652r_real @ R2 @ F3 ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_158_in__inv__image,axiom,
    ! [X: char > real,Y: char > real,R2: set_Pr1919093775l_real,F3: ( char > real ) > char > real > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ X @ Y ) @ ( inv_im854642519r_real @ R2 @ F3 ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_159_in__inv__image,axiom,
    ! [X: char > real,Y: char > real,R2: set_Pr1053253703real_o,F3: ( char > real ) > char > real > $o] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ X @ Y ) @ ( inv_im255337747r_real @ R2 @ F3 ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_160_in__inv__image,axiom,
    ! [X: char > real > real,Y: char > real > real,R2: set_Pr42335993r_real,F3: ( char > real > real ) > char > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ X @ Y ) @ ( inv_im96827991l_real @ R2 @ F3 ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_161_in__inv__image,axiom,
    ! [X: char > real > $o,Y: char > real > $o,R2: set_Pr42335993r_real,F3: ( char > real > $o ) > char > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ X @ Y ) @ ( inv_im331529689real_o @ R2 @ F3 ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_162_in__inv__image,axiom,
    ! [X: char > real > real,Y: char > real > real,R2: set_Pr1919093775l_real,F3: ( char > real > real ) > char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ X @ Y ) @ ( inv_im2119069858l_real @ R2 @ F3 ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_163_in__inv__image,axiom,
    ! [X: char > real > real,Y: char > real > real,R2: set_Pr1053253703real_o,F3: ( char > real > real ) > char > real > $o] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ X @ Y ) @ ( inv_im576609886l_real @ R2 @ F3 ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_164_in__inv__image,axiom,
    ! [X: char > real > $o,Y: char > real > $o,R2: set_Pr1919093775l_real,F3: ( char > real > $o ) > char > real > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ X @ Y ) @ ( inv_im1748900174real_o @ R2 @ F3 ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_165_in__inv__image,axiom,
    ! [X: char > real > $o,Y: char > real > $o,R2: set_Pr1053253703real_o,F3: ( char > real > $o ) > char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ X @ Y ) @ ( inv_im1954866834real_o @ R2 @ F3 ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_166_in__inv__image,axiom,
    ! [X: char > real,Y: char > real,R2: set_Pr1588228599e_real,F3: ( char > real ) > char > set_variable_real > set_variable_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ X @ Y ) @ ( inv_im710342731r_real @ R2 @ F3 ) )
      = ( member625963584e_real @ ( produc525232719e_real @ ( F3 @ X ) @ ( F3 @ Y ) ) @ R2 ) ) ).

% in_inv_image
thf(fact_167_mem__Collect__eq,axiom,
    ! [A2: char > real,P: ( char > real ) > $o] :
      ( ( member_char_real @ A2 @ ( collect_char_real @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_168_mem__Collect__eq,axiom,
    ! [A2: char > real > real,P: ( char > real > real ) > $o] :
      ( ( member312374654l_real @ A2 @ ( collec1429138108l_real @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_169_mem__Collect__eq,axiom,
    ! [A2: char > real > $o,P: ( char > real > $o ) > $o] :
      ( ( member_char_real_o @ A2 @ ( collect_char_real_o @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_170_mem__Collect__eq,axiom,
    ! [A2: char > set_variable_real > set_variable_real,P: ( char > set_variable_real > set_variable_real ) > $o] :
      ( ( member2042895986e_real @ A2 @ ( collec425771440e_real @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_171_mem__Collect__eq,axiom,
    ! [A2: produc1863992257e_real,P: produc1863992257e_real > $o] :
      ( ( member561592938e_real @ A2 @ ( collec1042577836e_real @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_172_mem__Collect__eq,axiom,
    ! [A2: variable > real,P: ( variable > real ) > $o] :
      ( ( member_variable_real @ A2 @ ( collec633296133e_real @ P ) )
      = ( P @ A2 ) ) ).

% mem_Collect_eq
thf(fact_173_Collect__mem__eq,axiom,
    ! [A5: set_char_real] :
      ( ( collect_char_real
        @ ^ [X4: char > real] : ( member_char_real @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_174_Collect__mem__eq,axiom,
    ! [A5: set_char_real_real] :
      ( ( collec1429138108l_real
        @ ^ [X4: char > real > real] : ( member312374654l_real @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_175_Collect__mem__eq,axiom,
    ! [A5: set_char_real_o] :
      ( ( collect_char_real_o
        @ ^ [X4: char > real > $o] : ( member_char_real_o @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_176_Collect__mem__eq,axiom,
    ! [A5: set_ch845833233e_real] :
      ( ( collec425771440e_real
        @ ^ [X4: char > set_variable_real > set_variable_real] : ( member2042895986e_real @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_177_Collect__mem__eq,axiom,
    ! [A5: set_Pr1530225953e_real] :
      ( ( collec1042577836e_real
        @ ^ [X4: produc1863992257e_real] : ( member561592938e_real @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_178_Collect__mem__eq,axiom,
    ! [A5: set_variable_real] :
      ( ( collec633296133e_real
        @ ^ [X4: variable > real] : ( member_variable_real @ X4 @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_179_Collect__cong,axiom,
    ! [P: produc1863992257e_real > $o,Q: produc1863992257e_real > $o] :
      ( ! [X3: produc1863992257e_real] :
          ( ( P @ X3 )
          = ( Q @ X3 ) )
     => ( ( collec1042577836e_real @ P )
        = ( collec1042577836e_real @ Q ) ) ) ).

% Collect_cong
thf(fact_180_Collect__cong,axiom,
    ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
      ( ! [X3: variable > real] :
          ( ( P @ X3 )
          = ( Q @ X3 ) )
     => ( ( collec633296133e_real @ P )
        = ( collec633296133e_real @ Q ) ) ) ).

% Collect_cong
thf(fact_181_internal__case__prod__def,axiom,
    produc1138486237e_real = produc1202665267e_real ).

% internal_case_prod_def
thf(fact_182_internal__case__prod__def,axiom,
    produc677394266real_o = produc679978160real_o ).

% internal_case_prod_def
thf(fact_183_internal__case__prod__def,axiom,
    produc584529143e_real = produc1906464077e_real ).

% internal_case_prod_def
thf(fact_184_internal__case__prod__def,axiom,
    produc1070892532real_o = produc1629511198real_o ).

% internal_case_prod_def
thf(fact_185_internal__case__prod__def,axiom,
    produc1941565183e_real = produc1116016469e_real ).

% internal_case_prod_def
thf(fact_186_case__swap,axiom,
    ! [F3: ( char > real > real ) > produc104944723e_real > produc1020032539e_real,P2: produc1020032539e_real] :
      ( ( produc991789875e_real
        @ ^ [Y4: produc104944723e_real,X4: char > real > real] : ( F3 @ X4 @ Y4 )
        @ ( produc865271923e_real @ P2 ) )
      = ( produc1202665267e_real @ F3 @ P2 ) ) ).

% case_swap
thf(fact_187_case__swap,axiom,
    ! [F3: ( char > real > real ) > produc104944723e_real > $o,P2: produc1020032539e_real] :
      ( ( produc421130416real_o
        @ ^ [Y4: produc104944723e_real,X4: char > real > real] : ( F3 @ X4 @ Y4 )
        @ ( produc865271923e_real @ P2 ) )
      = ( produc679978160real_o @ F3 @ P2 ) ) ).

% case_swap
thf(fact_188_case__swap,axiom,
    ! [F3: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,P2: produc104944723e_real] :
      ( ( produc1467075094al_o_o
        @ ^ [Y4: char > set_variable_real > set_variable_real,X4: char > real > $o] : ( F3 @ X4 @ Y4 )
        @ ( produc914893101e_real @ P2 ) )
      = ( produc1629511198real_o @ F3 @ P2 ) ) ).

% case_swap
thf(fact_189_case__swap,axiom,
    ! [F3: produc104944723e_real > ( char > real > real ) > produc1020032539e_real,P2: produc729247771l_real] :
      ( ( produc1202665267e_real
        @ ^ [Y4: char > real > real,X4: produc104944723e_real] : ( F3 @ X4 @ Y4 )
        @ ( produc1778103411l_real @ P2 ) )
      = ( produc991789875e_real @ F3 @ P2 ) ) ).

% case_swap
thf(fact_190_case__swap,axiom,
    ! [F3: produc104944723e_real > ( char > real > real ) > $o,P2: produc729247771l_real] :
      ( ( produc679978160real_o
        @ ^ [Y4: char > real > real,X4: produc104944723e_real] : ( F3 @ X4 @ Y4 )
        @ ( produc1778103411l_real @ P2 ) )
      = ( produc421130416real_o @ F3 @ P2 ) ) ).

% case_swap
thf(fact_191_case__swap,axiom,
    ! [F3: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real,P2: produc1606031907real_o] :
      ( ( produc1906464077e_real
        @ ^ [Y4: char > real > $o,X4: char > set_variable_real > set_variable_real] : ( F3 @ X4 @ Y4 )
        @ ( produc192924469real_o @ P2 ) )
      = ( produc1116016469e_real @ F3 @ P2 ) ) ).

% case_swap
thf(fact_192_case__swap,axiom,
    ! [F3: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,P2: produc1606031907real_o] :
      ( ( produc1629511198real_o
        @ ^ [Y4: char > real > $o,X4: char > set_variable_real > set_variable_real] : ( F3 @ X4 @ Y4 )
        @ ( produc192924469real_o @ P2 ) )
      = ( produc1467075094al_o_o @ F3 @ P2 ) ) ).

% case_swap
thf(fact_193_case__swap,axiom,
    ! [F3: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real,P2: produc104944723e_real] :
      ( ( produc1116016469e_real
        @ ^ [Y4: char > set_variable_real > set_variable_real,X4: char > real > $o] : ( F3 @ X4 @ Y4 )
        @ ( produc914893101e_real @ P2 ) )
      = ( produc1906464077e_real @ F3 @ P2 ) ) ).

% case_swap
thf(fact_194_The__split__eq,axiom,
    ! [X: char > real,Y: char > real] :
      ( ( the_Pr1076580896r_real
        @ ( produc1655853874real_o
          @ ^ [X5: char > real,Y5: char > real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc700235985r_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_195_The__split__eq,axiom,
    ! [X: char > real > real,Y: char > real > real] :
      ( ( the_Pr1196831286l_real
        @ ( produc1095814172real_o
          @ ^ [X5: char > real > real,Y5: char > real > real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc686464615l_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_196_The__split__eq,axiom,
    ! [X: char > real > $o,Y: char > real > $o] :
      ( ( the_Pr1811203438real_o
        @ ( produc131289260al_o_o
          @ ^ [X5: char > real > $o,Y5: char > real > $o] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc1566957527real_o @ X @ Y ) ) ).

% The_split_eq
thf(fact_197_The__split__eq,axiom,
    ! [X: char > set_variable_real > set_variable_real,Y: char > real > $o] :
      ( ( the_Pr1930357084real_o
        @ ( produc1467075094al_o_o
          @ ^ [X5: char > set_variable_real > set_variable_real,Y5: char > real > $o] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc1285468373real_o @ X @ Y ) ) ).

% The_split_eq
thf(fact_198_The__split__eq,axiom,
    ! [X: char > set_variable_real > set_variable_real,Y: char > set_variable_real > set_variable_real] :
      ( ( the_Pr198758430e_real
        @ ( produc143994420real_o
          @ ^ [X5: char > set_variable_real > set_variable_real,Y5: char > set_variable_real > set_variable_real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc525232719e_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_199_The__split__eq,axiom,
    ! [X: char > real,Y: produc1020032539e_real] :
      ( ( the_Pr543709229e_real
        @ ( produc569598981real_o
          @ ^ [X5: char > real,Y5: produc1020032539e_real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc2125489830e_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_200_The__split__eq,axiom,
    ! [X: char > real > real,Y: produc104944723e_real] :
      ( ( the_Pr1679925410e_real
        @ ( produc679978160real_o
          @ ^ [X5: char > real > real,Y5: produc104944723e_real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc141013715e_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_201_The__split__eq,axiom,
    ! [X: char > real > $o,Y: char > set_variable_real > set_variable_real] :
      ( ( the_Pr429269900e_real
        @ ( produc1629511198real_o
          @ ^ [X5: char > real > $o,Y5: char > set_variable_real > set_variable_real] :
              ( ( X = X5 )
              & ( Y = Y5 ) ) ) )
      = ( produc2007437005e_real @ X @ Y ) ) ).

% The_split_eq
thf(fact_202_case__prodI2,axiom,
    ! [P2: produc928489369r_real,C4: ( char > real ) > ( char > real ) > $o] :
      ( ! [A: char > real,B: char > real] :
          ( ( P2
            = ( produc700235985r_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc1655853874real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_203_case__prodI2,axiom,
    ! [P2: produc96687023l_real,C4: ( char > real > real ) > ( char > real > real ) > $o] :
      ( ! [A: char > real > real,B: char > real > real] :
          ( ( P2
            = ( produc686464615l_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc1095814172real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_204_case__prodI2,axiom,
    ! [P2: produc2070499431real_o,C4: ( char > real > $o ) > ( char > real > $o ) > $o] :
      ( ! [A: char > real > $o,B: char > real > $o] :
          ( ( P2
            = ( produc1566957527real_o @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc131289260al_o_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_205_case__prodI2,axiom,
    ! [P2: produc1606031907real_o,C4: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
          ( ( P2
            = ( produc1285468373real_o @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc1467075094al_o_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_206_case__prodI2,axiom,
    ! [P2: produc1120170903e_real,C4: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
          ( ( P2
            = ( produc525232719e_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc143994420real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_207_case__prodI2,axiom,
    ! [P2: produc1993135732e_real,C4: ( char > real ) > produc1020032539e_real > $o] :
      ( ! [A: char > real,B: produc1020032539e_real] :
          ( ( P2
            = ( produc2125489830e_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc569598981real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_208_case__prodI2,axiom,
    ! [P2: produc1020032539e_real,C4: ( char > real > real ) > produc104944723e_real > $o] :
      ( ! [A: char > real > real,B: produc104944723e_real] :
          ( ( P2
            = ( produc141013715e_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc679978160real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_209_case__prodI2,axiom,
    ! [P2: produc104944723e_real,C4: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
          ( ( P2
            = ( produc2007437005e_real @ A @ B ) )
         => ( C4 @ A @ B ) )
     => ( produc1629511198real_o @ C4 @ P2 ) ) ).

% case_prodI2
thf(fact_210_case__prodI,axiom,
    ! [F3: ( char > real ) > ( char > real ) > $o,A2: char > real,B2: char > real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc1655853874real_o @ F3 @ ( produc700235985r_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_211_case__prodI,axiom,
    ! [F3: ( char > real > real ) > ( char > real > real ) > $o,A2: char > real > real,B2: char > real > real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc1095814172real_o @ F3 @ ( produc686464615l_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_212_case__prodI,axiom,
    ! [F3: ( char > real > $o ) > ( char > real > $o ) > $o,A2: char > real > $o,B2: char > real > $o] :
      ( ( F3 @ A2 @ B2 )
     => ( produc131289260al_o_o @ F3 @ ( produc1566957527real_o @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_213_case__prodI,axiom,
    ! [F3: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,A2: char > set_variable_real > set_variable_real,B2: char > real > $o] :
      ( ( F3 @ A2 @ B2 )
     => ( produc1467075094al_o_o @ F3 @ ( produc1285468373real_o @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_214_case__prodI,axiom,
    ! [F3: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o,A2: char > set_variable_real > set_variable_real,B2: char > set_variable_real > set_variable_real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc143994420real_o @ F3 @ ( produc525232719e_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_215_case__prodI,axiom,
    ! [F3: ( char > real ) > produc1020032539e_real > $o,A2: char > real,B2: produc1020032539e_real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc569598981real_o @ F3 @ ( produc2125489830e_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_216_case__prodI,axiom,
    ! [F3: ( char > real > real ) > produc104944723e_real > $o,A2: char > real > real,B2: produc104944723e_real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc679978160real_o @ F3 @ ( produc141013715e_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_217_case__prodI,axiom,
    ! [F3: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( F3 @ A2 @ B2 )
     => ( produc1629511198real_o @ F3 @ ( produc2007437005e_real @ A2 @ B2 ) ) ) ).

% case_prodI
thf(fact_218_case__prodE,axiom,
    ! [C4: ( char > real ) > produc1020032539e_real > $o,P2: produc1993135732e_real] :
      ( ( produc569598981real_o @ C4 @ P2 )
     => ~ ! [X3: char > real,Y3: produc1020032539e_real] :
            ( ( P2
              = ( produc2125489830e_real @ X3 @ Y3 ) )
           => ~ ( C4 @ X3 @ Y3 ) ) ) ).

% case_prodE
thf(fact_219_case__prodE,axiom,
    ! [C4: ( char > real > real ) > produc104944723e_real > $o,P2: produc1020032539e_real] :
      ( ( produc679978160real_o @ C4 @ P2 )
     => ~ ! [X3: char > real > real,Y3: produc104944723e_real] :
            ( ( P2
              = ( produc141013715e_real @ X3 @ Y3 ) )
           => ~ ( C4 @ X3 @ Y3 ) ) ) ).

% case_prodE
thf(fact_220_case__prodE,axiom,
    ! [C4: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,P2: produc104944723e_real] :
      ( ( produc1629511198real_o @ C4 @ P2 )
     => ~ ! [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
            ( ( P2
              = ( produc2007437005e_real @ X3 @ Y3 ) )
           => ~ ( C4 @ X3 @ Y3 ) ) ) ).

% case_prodE
thf(fact_221_case__prodD,axiom,
    ! [F3: ( char > real ) > produc1020032539e_real > $o,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc569598981real_o @ F3 @ ( produc2125489830e_real @ A2 @ B2 ) )
     => ( F3 @ A2 @ B2 ) ) ).

% case_prodD
thf(fact_222_case__prodD,axiom,
    ! [F3: ( char > real > real ) > produc104944723e_real > $o,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc679978160real_o @ F3 @ ( produc141013715e_real @ A2 @ B2 ) )
     => ( F3 @ A2 @ B2 ) ) ).

% case_prodD
thf(fact_223_case__prodD,axiom,
    ! [F3: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc1629511198real_o @ F3 @ ( produc2007437005e_real @ A2 @ B2 ) )
     => ( F3 @ A2 @ B2 ) ) ).

% case_prodD
thf(fact_224_Compr__image__eq,axiom,
    ! [F3: ( variable > real ) > variable > real,A5: set_variable_real,P: ( variable > real ) > $o] :
      ( ( collec633296133e_real
        @ ^ [X4: variable > real] :
            ( ( member_variable_real @ X4 @ ( image_1599134823e_real @ F3 @ A5 ) )
            & ( P @ X4 ) ) )
      = ( image_1599134823e_real @ F3
        @ ( collec633296133e_real
          @ ^ [X4: variable > real] :
              ( ( member_variable_real @ X4 @ A5 )
              & ( P @ ( F3 @ X4 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_225_case__prod__Pair__iden,axiom,
    ! [P2: produc1993135732e_real] :
      ( ( produc315720647e_real @ produc2125489830e_real @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_226_case__prod__Pair__iden,axiom,
    ! [P2: produc1020032539e_real] :
      ( ( produc1202665267e_real @ produc141013715e_real @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_227_case__prod__Pair__iden,axiom,
    ! [P2: produc104944723e_real] :
      ( ( produc1906464077e_real @ produc2007437005e_real @ P2 )
      = P2 ) ).

% case_prod_Pair_iden
thf(fact_228_SigmaI,axiom,
    ! [A2: char > real,A5: set_char_real,B2: produc1020032539e_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member_char_real @ A2 @ A5 )
     => ( ( member544802500e_real @ B2 @ ( B5 @ A2 ) )
       => ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc34356277e_real @ A5 @ B5 ) ) ) ) ).

% SigmaI
thf(fact_229_SigmaI,axiom,
    ! [A2: char > real > real,A5: set_char_real_real,B2: produc104944723e_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member312374654l_real @ A2 @ A5 )
     => ( ( member1871517162e_real @ B2 @ ( B5 @ A2 ) )
       => ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc522711812e_real @ A5 @ B5 ) ) ) ) ).

% SigmaI
thf(fact_230_SigmaI,axiom,
    ! [A2: char > real > $o,A5: set_char_real_o,B2: char > set_variable_real > set_variable_real,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member_char_real_o @ A2 @ A5 )
     => ( ( member2042895986e_real @ B2 @ ( B5 @ A2 ) )
       => ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc1853244124e_real @ A5 @ B5 ) ) ) ) ).

% SigmaI
thf(fact_231_mem__Sigma__iff,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A5: set_char_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc34356277e_real @ A5 @ B5 ) )
      = ( ( member_char_real @ A2 @ A5 )
        & ( member544802500e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% mem_Sigma_iff
thf(fact_232_mem__Sigma__iff,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A5: set_char_real_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc522711812e_real @ A5 @ B5 ) )
      = ( ( member312374654l_real @ A2 @ A5 )
        & ( member1871517162e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% mem_Sigma_iff
thf(fact_233_mem__Sigma__iff,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A5: set_char_real_o,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc1853244124e_real @ A5 @ B5 ) )
      = ( ( member_char_real_o @ A2 @ A5 )
        & ( member2042895986e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% mem_Sigma_iff
thf(fact_234_Collect__case__prod,axiom,
    ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
      ( ( collec1042577836e_real
        @ ( produc1299805450real_o
          @ ^ [A4: variable > real,B4: variable > real] :
              ( ( P @ A4 )
              & ( Q @ B4 ) ) ) )
      = ( produc979346218e_real @ ( collec633296133e_real @ P )
        @ ^ [Uu: variable > real] : ( collec633296133e_real @ Q ) ) ) ).

% Collect_case_prod
thf(fact_235_SigmaE2,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A5: set_char_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc34356277e_real @ A5 @ B5 ) )
     => ~ ( ( member_char_real @ A2 @ A5 )
         => ~ ( member544802500e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% SigmaE2
thf(fact_236_SigmaE2,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A5: set_char_real_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc522711812e_real @ A5 @ B5 ) )
     => ~ ( ( member312374654l_real @ A2 @ A5 )
         => ~ ( member1871517162e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% SigmaE2
thf(fact_237_SigmaE2,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A5: set_char_real_o,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc1853244124e_real @ A5 @ B5 ) )
     => ~ ( ( member_char_real_o @ A2 @ A5 )
         => ~ ( member2042895986e_real @ B2 @ ( B5 @ A2 ) ) ) ) ).

% SigmaE2
thf(fact_238_SigmaD2,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A5: set_char_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc34356277e_real @ A5 @ B5 ) )
     => ( member544802500e_real @ B2 @ ( B5 @ A2 ) ) ) ).

% SigmaD2
thf(fact_239_SigmaD2,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A5: set_char_real_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc522711812e_real @ A5 @ B5 ) )
     => ( member1871517162e_real @ B2 @ ( B5 @ A2 ) ) ) ).

% SigmaD2
thf(fact_240_SigmaD2,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A5: set_char_real_o,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc1853244124e_real @ A5 @ B5 ) )
     => ( member2042895986e_real @ B2 @ ( B5 @ A2 ) ) ) ).

% SigmaD2
thf(fact_241_SigmaD1,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A5: set_char_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc34356277e_real @ A5 @ B5 ) )
     => ( member_char_real @ A2 @ A5 ) ) ).

% SigmaD1
thf(fact_242_SigmaD1,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A5: set_char_real_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc522711812e_real @ A5 @ B5 ) )
     => ( member312374654l_real @ A2 @ A5 ) ) ).

% SigmaD1
thf(fact_243_SigmaD1,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A5: set_char_real_o,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc1853244124e_real @ A5 @ B5 ) )
     => ( member_char_real_o @ A2 @ A5 ) ) ).

% SigmaD1
thf(fact_244_SigmaE,axiom,
    ! [C4: produc1993135732e_real,A5: set_char_real,B5: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ C4 @ ( produc34356277e_real @ A5 @ B5 ) )
     => ~ ! [X3: char > real] :
            ( ( member_char_real @ X3 @ A5 )
           => ! [Y3: produc1020032539e_real] :
                ( ( member544802500e_real @ Y3 @ ( B5 @ X3 ) )
               => ( C4
                 != ( produc2125489830e_real @ X3 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_245_SigmaE,axiom,
    ! [C4: produc1020032539e_real,A5: set_char_real_real,B5: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ C4 @ ( produc522711812e_real @ A5 @ B5 ) )
     => ~ ! [X3: char > real > real] :
            ( ( member312374654l_real @ X3 @ A5 )
           => ! [Y3: produc104944723e_real] :
                ( ( member1871517162e_real @ Y3 @ ( B5 @ X3 ) )
               => ( C4
                 != ( produc141013715e_real @ X3 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_246_SigmaE,axiom,
    ! [C4: produc104944723e_real,A5: set_char_real_o,B5: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ C4 @ ( produc1853244124e_real @ A5 @ B5 ) )
     => ~ ! [X3: char > real > $o] :
            ( ( member_char_real_o @ X3 @ A5 )
           => ! [Y3: char > set_variable_real > set_variable_real] :
                ( ( member2042895986e_real @ Y3 @ ( B5 @ X3 ) )
               => ( C4
                 != ( produc2007437005e_real @ X3 @ Y3 ) ) ) ) ) ).

% SigmaE
thf(fact_247_UNIV__def,axiom,
    ( top_to239690646e_real
    = ( collec633296133e_real
      @ ^ [X4: variable > real] : $true ) ) ).

% UNIV_def
thf(fact_248_Collect__case__prod__Sigma,axiom,
    ! [P: ( variable > real ) > $o,Q: ( variable > real ) > ( variable > real ) > $o] :
      ( ( collec1042577836e_real
        @ ( produc1299805450real_o
          @ ^ [X4: variable > real,Y4: variable > real] :
              ( ( P @ X4 )
              & ( Q @ X4 @ Y4 ) ) ) )
      = ( produc979346218e_real @ ( collec633296133e_real @ P )
        @ ^ [X4: variable > real] : ( collec633296133e_real @ ( Q @ X4 ) ) ) ) ).

% Collect_case_prod_Sigma
thf(fact_249_swap__product,axiom,
    ! [A5: set_Pr307567739e_real,B5: set_char_real] :
      ( ( image_152725217e_real
        @ ( produc864726913e_real
          @ ^ [I3: produc1020032539e_real,J2: char > real] : ( produc2125489830e_real @ J2 @ I3 ) )
        @ ( produc1373880559r_real @ A5
          @ ^ [Uu: produc1020032539e_real] : B5 ) )
      = ( produc34356277e_real @ B5
        @ ^ [Uu: char > real] : A5 ) ) ).

% swap_product
thf(fact_250_swap__product,axiom,
    ! [A5: set_Pr268868489e_real,B5: set_char_real_real] :
      ( ( image_711552709e_real
        @ ( produc991789875e_real
          @ ^ [I3: produc104944723e_real,J2: char > real > real] : ( produc141013715e_real @ J2 @ I3 ) )
        @ ( produc1435543300l_real @ A5
          @ ^ [Uu: produc104944723e_real] : B5 ) )
      = ( produc522711812e_real @ B5
        @ ^ [Uu: char > real > real] : A5 ) ) ).

% swap_product
thf(fact_251_swap__product,axiom,
    ! [A5: set_ch845833233e_real,B5: set_char_real_o] :
      ( ( image_2028344445e_real
        @ ( produc1116016469e_real
          @ ^ [I3: char > set_variable_real > set_variable_real,J2: char > real > $o] : ( produc2007437005e_real @ J2 @ I3 ) )
        @ ( produc1131275492real_o @ A5
          @ ^ [Uu: char > set_variable_real > set_variable_real] : B5 ) )
      = ( produc1853244124e_real @ B5
        @ ^ [Uu: char > real > $o] : A5 ) ) ).

% swap_product
thf(fact_252_same__fstI,axiom,
    ! [P: ( char > real ) > $o,X: char > real,Y6: produc1020032539e_real,Y: produc1020032539e_real,R: ( char > real ) > set_Pr1517071815e_real] :
      ( ( P @ X )
     => ( ( member1778419728e_real @ ( produc680410711e_real @ Y6 @ Y ) @ ( R @ X ) )
       => ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ X @ Y6 ) @ ( produc2125489830e_real @ X @ Y ) ) @ ( same_f764716049e_real @ P @ R ) ) ) ) ).

% same_fstI
thf(fact_253_same__fstI,axiom,
    ! [P: ( char > real > real ) > $o,X: char > real > real,Y6: produc104944723e_real,Y: produc104944723e_real,R: ( char > real > real ) > set_Pr521705191e_real] :
      ( ( P @ X )
     => ( ( member2016544560e_real @ ( produc1957227327e_real @ Y6 @ Y ) @ ( R @ X ) )
       => ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ X @ Y6 ) @ ( produc141013715e_real @ X @ Y ) ) @ ( same_f1243548200e_real @ P @ R ) ) ) ) ).

% same_fstI
thf(fact_254_same__fstI,axiom,
    ! [P: ( char > real > $o ) > $o,X: char > real > $o,Y6: char > set_variable_real > set_variable_real,Y: char > set_variable_real > set_variable_real,R: ( char > real > $o ) > set_Pr1588228599e_real] :
      ( ( P @ X )
     => ( ( member625963584e_real @ ( produc525232719e_real @ Y6 @ Y ) @ ( R @ X ) )
       => ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ X @ Y6 ) @ ( produc2007437005e_real @ X @ Y ) ) @ ( same_f1185518776e_real @ P @ R ) ) ) ) ).

% same_fstI
thf(fact_255_map__prod__simp,axiom,
    ! [F3: ( char > real ) > char > real,G2: produc1020032539e_real > produc1020032539e_real,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc552964208e_real @ F3 @ G2 @ ( produc2125489830e_real @ A2 @ B2 ) )
      = ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_256_map__prod__simp,axiom,
    ! [F3: ( char > real ) > char > real > real,G2: produc1020032539e_real > produc104944723e_real,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc202772275e_real @ F3 @ G2 @ ( produc2125489830e_real @ A2 @ B2 ) )
      = ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_257_map__prod__simp,axiom,
    ! [F3: ( char > real ) > char > real > $o,G2: produc1020032539e_real > char > set_variable_real > set_variable_real,A2: char > real,B2: produc1020032539e_real] :
      ( ( produc1797673857e_real @ F3 @ G2 @ ( produc2125489830e_real @ A2 @ B2 ) )
      = ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_258_map__prod__simp,axiom,
    ! [F3: ( char > real > real ) > char > real,G2: produc104944723e_real > produc1020032539e_real,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc348783435e_real @ F3 @ G2 @ ( produc141013715e_real @ A2 @ B2 ) )
      = ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_259_map__prod__simp,axiom,
    ! [F3: ( char > real > real ) > char > real > real,G2: produc104944723e_real > produc104944723e_real,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc2131385966e_real @ F3 @ G2 @ ( produc141013715e_real @ A2 @ B2 ) )
      = ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_260_map__prod__simp,axiom,
    ! [F3: ( char > real > real ) > char > real > $o,G2: produc104944723e_real > char > set_variable_real > set_variable_real,A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc683016410e_real @ F3 @ G2 @ ( produc141013715e_real @ A2 @ B2 ) )
      = ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_261_map__prod__simp,axiom,
    ! [F3: ( char > real > $o ) > char > real,G2: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc1251731407e_real @ F3 @ G2 @ ( produc2007437005e_real @ A2 @ B2 ) )
      = ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_262_map__prod__simp,axiom,
    ! [F3: ( char > real > $o ) > char > real > real,G2: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc753666538e_real @ F3 @ G2 @ ( produc2007437005e_real @ A2 @ B2 ) )
      = ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_263_map__prod__simp,axiom,
    ! [F3: ( char > real > $o ) > char > real > $o,G2: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc355430254e_real @ F3 @ G2 @ ( produc2007437005e_real @ A2 @ B2 ) )
      = ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) ) ).

% map_prod_simp
thf(fact_264_map__prod__imageI,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,R: set_Pr397354154e_real,F3: ( char > real ) > char > real,G2: produc1020032539e_real > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ R )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_866442351e_real @ ( produc552964208e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_265_map__prod__imageI,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,R: set_Pr397354154e_real,F3: ( char > real ) > char > real > real,G2: produc1020032539e_real > produc104944723e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ R )
     => ( member544802500e_real @ ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_479987936e_real @ ( produc202772275e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_266_map__prod__imageI,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,R: set_Pr397354154e_real,F3: ( char > real ) > char > real > $o,G2: produc1020032539e_real > char > set_variable_real > set_variable_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ R )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_426244814e_real @ ( produc1797673857e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_267_map__prod__imageI,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,R: set_Pr307567739e_real,F3: ( char > real > real ) > char > real,G2: produc104944723e_real > produc1020032539e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ R )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_1698073930e_real @ ( produc348783435e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_268_map__prod__imageI,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,R: set_Pr307567739e_real,F3: ( char > real > real ) > char > real > real,G2: produc104944723e_real > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ R )
     => ( member544802500e_real @ ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_1823533253e_real @ ( produc2131385966e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_269_map__prod__imageI,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,R: set_Pr307567739e_real,F3: ( char > real > real ) > char > real > $o,G2: produc104944723e_real > char > set_variable_real > set_variable_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A2 @ B2 ) @ R )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_450993193e_real @ ( produc683016410e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_270_map__prod__imageI,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,R: set_Pr268868489e_real,F3: ( char > real > $o ) > char > real,G2: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ R )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_300296654e_real @ ( produc1251731407e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_271_map__prod__imageI,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,R: set_Pr268868489e_real,F3: ( char > real > $o ) > char > real > real,G2: ( char > set_variable_real > set_variable_real ) > produc104944723e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ R )
     => ( member544802500e_real @ ( produc141013715e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_1739334977e_real @ ( produc753666538e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_272_map__prod__imageI,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,R: set_Pr268868489e_real,F3: ( char > real > $o ) > char > real > $o,G2: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ R )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( F3 @ A2 ) @ ( G2 @ B2 ) ) @ ( image_670686893e_real @ ( produc355430254e_real @ F3 @ G2 ) @ R ) ) ) ).

% map_prod_imageI
thf(fact_273_in__lex__prod,axiom,
    ! [A2: char > real,B2: produc1020032539e_real,A3: char > real,B3: produc1020032539e_real,R2: set_Pr42335993r_real,S2: set_Pr1517071815e_real] :
      ( ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ A2 @ B2 ) @ ( produc2125489830e_real @ A3 @ B3 ) ) @ ( lex_pr1793499278e_real @ R2 @ S2 ) )
      = ( ( member1086859330r_real @ ( produc700235985r_real @ A2 @ A3 ) @ R2 )
        | ( ( A2 = A3 )
          & ( member1778419728e_real @ ( produc680410711e_real @ B2 @ B3 ) @ S2 ) ) ) ) ).

% in_lex_prod
thf(fact_274_in__lex__prod,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real,A3: char > real > real,B3: produc104944723e_real,R2: set_Pr1919093775l_real,S2: set_Pr521705191e_real] :
      ( ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ A2 @ B2 ) @ ( produc141013715e_real @ A3 @ B3 ) ) @ ( lex_pr592421611e_real @ R2 @ S2 ) )
      = ( ( member1801875544l_real @ ( produc686464615l_real @ A2 @ A3 ) @ R2 )
        | ( ( A2 = A3 )
          & ( member2016544560e_real @ ( produc1957227327e_real @ B2 @ B3 ) @ S2 ) ) ) ) ).

% in_lex_prod
thf(fact_275_in__lex__prod,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real,A3: char > real > $o,B3: char > set_variable_real > set_variable_real,R2: set_Pr1053253703real_o,S2: set_Pr1588228599e_real] :
      ( ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ A2 @ B2 ) @ ( produc2007437005e_real @ A3 @ B3 ) ) @ ( lex_pr2056840373e_real @ R2 @ S2 ) )
      = ( ( member1795186320real_o @ ( produc1566957527real_o @ A2 @ A3 ) @ R2 )
        | ( ( A2 = A3 )
          & ( member625963584e_real @ ( produc525232719e_real @ B2 @ B3 ) @ S2 ) ) ) ) ).

% in_lex_prod
thf(fact_276_prod__fun__imageE,axiom,
    ! [C4: produc1993135732e_real,F3: ( char > real ) > char > real,G2: produc1020032539e_real > produc1020032539e_real,R: set_Pr397354154e_real] :
      ( ( member1491807627e_real @ C4 @ ( image_866442351e_real @ ( produc552964208e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real,Y3: produc1020032539e_real] :
            ( ( C4
              = ( produc2125489830e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_277_prod__fun__imageE,axiom,
    ! [C4: produc1993135732e_real,F3: ( char > real > real ) > char > real,G2: produc104944723e_real > produc1020032539e_real,R: set_Pr307567739e_real] :
      ( ( member1491807627e_real @ C4 @ ( image_1698073930e_real @ ( produc348783435e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > real,Y3: produc104944723e_real] :
            ( ( C4
              = ( produc2125489830e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_278_prod__fun__imageE,axiom,
    ! [C4: produc1993135732e_real,F3: ( char > real > $o ) > char > real,G2: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,R: set_Pr268868489e_real] :
      ( ( member1491807627e_real @ C4 @ ( image_300296654e_real @ ( produc1251731407e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
            ( ( C4
              = ( produc2125489830e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_279_prod__fun__imageE,axiom,
    ! [C4: produc1020032539e_real,F3: ( char > real ) > char > real > real,G2: produc1020032539e_real > produc104944723e_real,R: set_Pr397354154e_real] :
      ( ( member544802500e_real @ C4 @ ( image_479987936e_real @ ( produc202772275e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real,Y3: produc1020032539e_real] :
            ( ( C4
              = ( produc141013715e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_280_prod__fun__imageE,axiom,
    ! [C4: produc1020032539e_real,F3: ( char > real > real ) > char > real > real,G2: produc104944723e_real > produc104944723e_real,R: set_Pr307567739e_real] :
      ( ( member544802500e_real @ C4 @ ( image_1823533253e_real @ ( produc2131385966e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > real,Y3: produc104944723e_real] :
            ( ( C4
              = ( produc141013715e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_281_prod__fun__imageE,axiom,
    ! [C4: produc1020032539e_real,F3: ( char > real > $o ) > char > real > real,G2: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,R: set_Pr268868489e_real] :
      ( ( member544802500e_real @ C4 @ ( image_1739334977e_real @ ( produc753666538e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
            ( ( C4
              = ( produc141013715e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_282_prod__fun__imageE,axiom,
    ! [C4: produc104944723e_real,F3: ( char > real ) > char > real > $o,G2: produc1020032539e_real > char > set_variable_real > set_variable_real,R: set_Pr397354154e_real] :
      ( ( member1871517162e_real @ C4 @ ( image_426244814e_real @ ( produc1797673857e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real,Y3: produc1020032539e_real] :
            ( ( C4
              = ( produc2007437005e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_283_prod__fun__imageE,axiom,
    ! [C4: produc104944723e_real,F3: ( char > real > real ) > char > real > $o,G2: produc104944723e_real > char > set_variable_real > set_variable_real,R: set_Pr307567739e_real] :
      ( ( member1871517162e_real @ C4 @ ( image_450993193e_real @ ( produc683016410e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > real,Y3: produc104944723e_real] :
            ( ( C4
              = ( produc2007437005e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_284_prod__fun__imageE,axiom,
    ! [C4: produc104944723e_real,F3: ( char > real > $o ) > char > real > $o,G2: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,R: set_Pr268868489e_real] :
      ( ( member1871517162e_real @ C4 @ ( image_670686893e_real @ ( produc355430254e_real @ F3 @ G2 ) @ R ) )
     => ~ ! [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
            ( ( C4
              = ( produc2007437005e_real @ ( F3 @ X3 ) @ ( G2 @ Y3 ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ X3 @ Y3 ) @ R ) ) ) ).

% prod_fun_imageE
thf(fact_285_empty__Collect__eq,axiom,
    ! [P: ( variable > real ) > $o] :
      ( ( bot_bo721182586e_real
        = ( collec633296133e_real @ P ) )
      = ( ! [X4: variable > real] :
            ~ ( P @ X4 ) ) ) ).

% empty_Collect_eq
thf(fact_286_Collect__empty__eq,axiom,
    ! [P: ( variable > real ) > $o] :
      ( ( ( collec633296133e_real @ P )
        = bot_bo721182586e_real )
      = ( ! [X4: variable > real] :
            ~ ( P @ X4 ) ) ) ).

% Collect_empty_eq
thf(fact_287_Collect__const,axiom,
    ! [P: $o] :
      ( ( P
       => ( ( collec633296133e_real
            @ ^ [S4: variable > real] : P )
          = top_to239690646e_real ) )
      & ( ~ P
       => ( ( collec633296133e_real
            @ ^ [S4: variable > real] : P )
          = bot_bo721182586e_real ) ) ) ).

% Collect_const
thf(fact_288_prod_Ocollapse,axiom,
    ! [Prod: produc1993135732e_real] :
      ( ( produc2125489830e_real @ ( produc1146879930e_real @ Prod ) @ ( produc1176159992e_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_289_prod_Ocollapse,axiom,
    ! [Prod: produc1020032539e_real] :
      ( ( produc141013715e_real @ ( produc634910399e_real @ Prod ) @ ( produc1179001601e_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_290_prod_Ocollapse,axiom,
    ! [Prod: produc104944723e_real] :
      ( ( produc2007437005e_real @ ( produc1486464481e_real @ Prod ) @ ( produc504912415e_real @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_291_empty__def,axiom,
    ( bot_bo721182586e_real
    = ( collec633296133e_real
      @ ^ [X4: variable > real] : $false ) ) ).

% empty_def
thf(fact_292_surjective__pairing,axiom,
    ! [T: produc1993135732e_real] :
      ( T
      = ( produc2125489830e_real @ ( produc1146879930e_real @ T ) @ ( produc1176159992e_real @ T ) ) ) ).

% surjective_pairing
thf(fact_293_surjective__pairing,axiom,
    ! [T: produc1020032539e_real] :
      ( T
      = ( produc141013715e_real @ ( produc634910399e_real @ T ) @ ( produc1179001601e_real @ T ) ) ) ).

% surjective_pairing
thf(fact_294_surjective__pairing,axiom,
    ! [T: produc104944723e_real] :
      ( T
      = ( produc2007437005e_real @ ( produc1486464481e_real @ T ) @ ( produc504912415e_real @ T ) ) ) ).

% surjective_pairing
thf(fact_295_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1993135732e_real] :
      ( Prod
      = ( produc2125489830e_real @ ( produc1146879930e_real @ Prod ) @ ( produc1176159992e_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_296_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1020032539e_real] :
      ( Prod
      = ( produc141013715e_real @ ( produc634910399e_real @ Prod ) @ ( produc1179001601e_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_297_prod_Oexhaust__sel,axiom,
    ! [Prod: produc104944723e_real] :
      ( Prod
      = ( produc2007437005e_real @ ( produc1486464481e_real @ Prod ) @ ( produc504912415e_real @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_298_prod_Oswap__def,axiom,
    ( produc918320576r_real
    = ( ^ [P3: produc2139219430r_real] : ( produc2125489830e_real @ ( produc368200626r_real @ P3 ) @ ( produc338920564r_real @ P3 ) ) ) ) ).

% prod.swap_def
thf(fact_299_prod_Oswap__def,axiom,
    ( produc1778103411l_real
    = ( ^ [P3: produc729247771l_real] : ( produc141013715e_real @ ( produc2091833089l_real @ P3 ) @ ( produc1547741887l_real @ P3 ) ) ) ) ).

% prod.swap_def
thf(fact_300_prod_Oswap__def,axiom,
    ( produc192924469real_o
    = ( ^ [P3: produc1606031907real_o] : ( produc2007437005e_real @ ( produc1930427431real_o @ P3 ) @ ( produc764495849real_o @ P3 ) ) ) ) ).

% prod.swap_def
thf(fact_301_snd__conv,axiom,
    ! [X1: char > real,X2: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_302_snd__conv,axiom,
    ! [X1: char > real > real,X2: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_303_snd__conv,axiom,
    ! [X1: char > real > $o,X2: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ X1 @ X2 ) )
      = X2 ) ).

% snd_conv
thf(fact_304_snd__eqD,axiom,
    ! [X: char > real,Y: produc1020032539e_real,A2: produc1020032539e_real] :
      ( ( ( produc1176159992e_real @ ( produc2125489830e_real @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_305_snd__eqD,axiom,
    ! [X: char > real > real,Y: produc104944723e_real,A2: produc104944723e_real] :
      ( ( ( produc1179001601e_real @ ( produc141013715e_real @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_306_snd__eqD,axiom,
    ! [X: char > real > $o,Y: char > set_variable_real > set_variable_real,A2: char > set_variable_real > set_variable_real] :
      ( ( ( produc504912415e_real @ ( produc2007437005e_real @ X @ Y ) )
        = A2 )
     => ( Y = A2 ) ) ).

% snd_eqD
thf(fact_307_snd__pair,axiom,
    ! [A2: char > real,B2: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ A2 @ B2 ) )
      = B2 ) ).

% snd_pair
thf(fact_308_snd__pair,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ A2 @ B2 ) )
      = B2 ) ).

% snd_pair
thf(fact_309_snd__pair,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ A2 @ B2 ) )
      = B2 ) ).

% snd_pair
thf(fact_310_fst__conv,axiom,
    ! [X1: char > real,X2: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_311_fst__conv,axiom,
    ! [X1: char > real > real,X2: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_312_fst__conv,axiom,
    ! [X1: char > real > $o,X2: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ X1 @ X2 ) )
      = X1 ) ).

% fst_conv
thf(fact_313_fst__eqD,axiom,
    ! [X: char > real,Y: produc1020032539e_real,A2: char > real] :
      ( ( ( produc1146879930e_real @ ( produc2125489830e_real @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_314_fst__eqD,axiom,
    ! [X: char > real > real,Y: produc104944723e_real,A2: char > real > real] :
      ( ( ( produc634910399e_real @ ( produc141013715e_real @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_315_fst__eqD,axiom,
    ! [X: char > real > $o,Y: char > set_variable_real > set_variable_real,A2: char > real > $o] :
      ( ( ( produc1486464481e_real @ ( produc2007437005e_real @ X @ Y ) )
        = A2 )
     => ( X = A2 ) ) ).

% fst_eqD
thf(fact_316_fst__pair,axiom,
    ! [A2: char > real,B2: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ A2 @ B2 ) )
      = A2 ) ).

% fst_pair
thf(fact_317_fst__pair,axiom,
    ! [A2: char > real > real,B2: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ A2 @ B2 ) )
      = A2 ) ).

% fst_pair
thf(fact_318_fst__pair,axiom,
    ! [A2: char > real > $o,B2: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ A2 @ B2 ) )
      = A2 ) ).

% fst_pair
thf(fact_319_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( char > real ) > produc1020032539e_real > $o,X: char > real,Y: produc1020032539e_real,A2: produc1993135732e_real] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc2125489830e_real @ X @ Y ) )
       => ( P @ ( produc1146879930e_real @ A2 ) @ ( produc1176159992e_real @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_320_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( char > real > real ) > produc104944723e_real > $o,X: char > real > real,Y: produc104944723e_real,A2: produc1020032539e_real] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc141013715e_real @ X @ Y ) )
       => ( P @ ( produc634910399e_real @ A2 ) @ ( produc1179001601e_real @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_321_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,X: char > real > $o,Y: char > set_variable_real > set_variable_real,A2: produc104944723e_real] :
      ( ( P @ X @ Y )
     => ( ( A2
          = ( produc2007437005e_real @ X @ Y ) )
       => ( P @ ( produc1486464481e_real @ A2 ) @ ( produc504912415e_real @ A2 ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_322_conjI__realizer,axiom,
    ! [P: ( char > real ) > $o,P2: char > real,Q: produc1020032539e_real > $o,Q2: produc1020032539e_real] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc1146879930e_real @ ( produc2125489830e_real @ P2 @ Q2 ) ) )
          & ( Q @ ( produc1176159992e_real @ ( produc2125489830e_real @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_323_conjI__realizer,axiom,
    ! [P: ( char > real > real ) > $o,P2: char > real > real,Q: produc104944723e_real > $o,Q2: produc104944723e_real] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc634910399e_real @ ( produc141013715e_real @ P2 @ Q2 ) ) )
          & ( Q @ ( produc1179001601e_real @ ( produc141013715e_real @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_324_conjI__realizer,axiom,
    ! [P: ( char > real > $o ) > $o,P2: char > real > $o,Q: ( char > set_variable_real > set_variable_real ) > $o,Q2: char > set_variable_real > set_variable_real] :
      ( ( P @ P2 )
     => ( ( Q @ Q2 )
       => ( ( P @ ( produc1486464481e_real @ ( produc2007437005e_real @ P2 @ Q2 ) ) )
          & ( Q @ ( produc504912415e_real @ ( produc2007437005e_real @ P2 @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_325_exI__realizer,axiom,
    ! [P: produc1020032539e_real > ( char > real ) > $o,Y: produc1020032539e_real,X: char > real] :
      ( ( P @ Y @ X )
     => ( P @ ( produc1176159992e_real @ ( produc2125489830e_real @ X @ Y ) ) @ ( produc1146879930e_real @ ( produc2125489830e_real @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_326_exI__realizer,axiom,
    ! [P: produc104944723e_real > ( char > real > real ) > $o,Y: produc104944723e_real,X: char > real > real] :
      ( ( P @ Y @ X )
     => ( P @ ( produc1179001601e_real @ ( produc141013715e_real @ X @ Y ) ) @ ( produc634910399e_real @ ( produc141013715e_real @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_327_exI__realizer,axiom,
    ! [P: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,Y: char > set_variable_real > set_variable_real,X: char > real > $o] :
      ( ( P @ Y @ X )
     => ( P @ ( produc504912415e_real @ ( produc2007437005e_real @ X @ Y ) ) @ ( produc1486464481e_real @ ( produc2007437005e_real @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_328_eq__snd__iff,axiom,
    ! [B2: produc1020032539e_real,P2: produc1993135732e_real] :
      ( ( B2
        = ( produc1176159992e_real @ P2 ) )
      = ( ? [A4: char > real] :
            ( P2
            = ( produc2125489830e_real @ A4 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_329_eq__snd__iff,axiom,
    ! [B2: produc104944723e_real,P2: produc1020032539e_real] :
      ( ( B2
        = ( produc1179001601e_real @ P2 ) )
      = ( ? [A4: char > real > real] :
            ( P2
            = ( produc141013715e_real @ A4 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_330_eq__snd__iff,axiom,
    ! [B2: char > set_variable_real > set_variable_real,P2: produc104944723e_real] :
      ( ( B2
        = ( produc504912415e_real @ P2 ) )
      = ( ? [A4: char > real > $o] :
            ( P2
            = ( produc2007437005e_real @ A4 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_331_sndI,axiom,
    ! [X: produc1993135732e_real,Y: char > real,Z: produc1020032539e_real] :
      ( ( X
        = ( produc2125489830e_real @ Y @ Z ) )
     => ( ( produc1176159992e_real @ X )
        = Z ) ) ).

% sndI
thf(fact_332_sndI,axiom,
    ! [X: produc1020032539e_real,Y: char > real > real,Z: produc104944723e_real] :
      ( ( X
        = ( produc141013715e_real @ Y @ Z ) )
     => ( ( produc1179001601e_real @ X )
        = Z ) ) ).

% sndI
thf(fact_333_sndI,axiom,
    ! [X: produc104944723e_real,Y: char > real > $o,Z: char > set_variable_real > set_variable_real] :
      ( ( X
        = ( produc2007437005e_real @ Y @ Z ) )
     => ( ( produc504912415e_real @ X )
        = Z ) ) ).

% sndI
thf(fact_334_fstI,axiom,
    ! [X: produc1993135732e_real,Y: char > real,Z: produc1020032539e_real] :
      ( ( X
        = ( produc2125489830e_real @ Y @ Z ) )
     => ( ( produc1146879930e_real @ X )
        = Y ) ) ).

% fstI
thf(fact_335_fstI,axiom,
    ! [X: produc1020032539e_real,Y: char > real > real,Z: produc104944723e_real] :
      ( ( X
        = ( produc141013715e_real @ Y @ Z ) )
     => ( ( produc634910399e_real @ X )
        = Y ) ) ).

% fstI
thf(fact_336_fstI,axiom,
    ! [X: produc104944723e_real,Y: char > real > $o,Z: char > set_variable_real > set_variable_real] :
      ( ( X
        = ( produc2007437005e_real @ Y @ Z ) )
     => ( ( produc1486464481e_real @ X )
        = Y ) ) ).

% fstI
thf(fact_337_eq__fst__iff,axiom,
    ! [A2: char > real,P2: produc1993135732e_real] :
      ( ( A2
        = ( produc1146879930e_real @ P2 ) )
      = ( ? [B4: produc1020032539e_real] :
            ( P2
            = ( produc2125489830e_real @ A2 @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_338_eq__fst__iff,axiom,
    ! [A2: char > real > real,P2: produc1020032539e_real] :
      ( ( A2
        = ( produc634910399e_real @ P2 ) )
      = ( ? [B4: produc104944723e_real] :
            ( P2
            = ( produc141013715e_real @ A2 @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_339_eq__fst__iff,axiom,
    ! [A2: char > real > $o,P2: produc104944723e_real] :
      ( ( A2
        = ( produc1486464481e_real @ P2 ) )
      = ( ? [B4: char > set_variable_real > set_variable_real] :
            ( P2
            = ( produc2007437005e_real @ A2 @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_340_subrelI,axiom,
    ! [R2: set_Pr397354154e_real,S2: set_Pr397354154e_real] :
      ( ! [X3: char > real,Y3: produc1020032539e_real] :
          ( ( member1491807627e_real @ ( produc2125489830e_real @ X3 @ Y3 ) @ R2 )
         => ( member1491807627e_real @ ( produc2125489830e_real @ X3 @ Y3 ) @ S2 ) )
     => ( ord_le1631106314e_real @ R2 @ S2 ) ) ).

% subrelI
thf(fact_341_subrelI,axiom,
    ! [R2: set_Pr307567739e_real,S2: set_Pr307567739e_real] :
      ( ! [X3: char > real > real,Y3: produc104944723e_real] :
          ( ( member544802500e_real @ ( produc141013715e_real @ X3 @ Y3 ) @ R2 )
         => ( member544802500e_real @ ( produc141013715e_real @ X3 @ Y3 ) @ S2 ) )
     => ( ord_le780198939e_real @ R2 @ S2 ) ) ).

% subrelI
thf(fact_342_subrelI,axiom,
    ! [R2: set_Pr268868489e_real,S2: set_Pr268868489e_real] :
      ( ! [X3: char > real > $o,Y3: char > set_variable_real > set_variable_real] :
          ( ( member1871517162e_real @ ( produc2007437005e_real @ X3 @ Y3 ) @ R2 )
         => ( member1871517162e_real @ ( produc2007437005e_real @ X3 @ Y3 ) @ S2 ) )
     => ( ord_le2056633321e_real @ R2 @ S2 ) ) ).

% subrelI
thf(fact_343_mon__mono,axiom,
    ( order_1507925822e_real
    = ( ^ [R3: set_variable_real > set_variable_real] :
        ! [X6: set_variable_real,Y7: set_variable_real] :
          ( ( ord_le1113654598e_real @ X6 @ Y7 )
         => ( ord_le1113654598e_real @ ( R3 @ X6 ) @ ( R3 @ Y7 ) ) ) ) ) ).

% mon_mono
thf(fact_344_prop__restrict,axiom,
    ! [X: variable > real,Z2: set_variable_real,X7: set_variable_real,P: ( variable > real ) > $o] :
      ( ( member_variable_real @ X @ Z2 )
     => ( ( ord_le1113654598e_real @ Z2
          @ ( collec633296133e_real
            @ ^ [X4: variable > real] :
                ( ( member_variable_real @ X4 @ X7 )
                & ( P @ X4 ) ) ) )
       => ( P @ X ) ) ) ).

% prop_restrict
thf(fact_345_Collect__restrict,axiom,
    ! [X7: set_variable_real,P: ( variable > real ) > $o] :
      ( ord_le1113654598e_real
      @ ( collec633296133e_real
        @ ^ [X4: variable > real] :
            ( ( member_variable_real @ X4 @ X7 )
            & ( P @ X4 ) ) )
      @ X7 ) ).

% Collect_restrict
thf(fact_346_Collect__subset,axiom,
    ! [A5: set_variable_real,P: ( variable > real ) > $o] :
      ( ord_le1113654598e_real
      @ ( collec633296133e_real
        @ ^ [X4: variable > real] :
            ( ( member_variable_real @ X4 @ A5 )
            & ( P @ X4 ) ) )
      @ A5 ) ).

% Collect_subset
thf(fact_347_Collect__mono,axiom,
    ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
      ( ! [X3: variable > real] :
          ( ( P @ X3 )
         => ( Q @ X3 ) )
     => ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) ) ) ).

% Collect_mono
thf(fact_348_Collect__mono__iff,axiom,
    ! [P: ( variable > real ) > $o,Q: ( variable > real ) > $o] :
      ( ( ord_le1113654598e_real @ ( collec633296133e_real @ P ) @ ( collec633296133e_real @ Q ) )
      = ( ! [X4: variable > real] :
            ( ( P @ X4 )
           => ( Q @ X4 ) ) ) ) ).

% Collect_mono_iff
thf(fact_349_subset__Collect__iff,axiom,
    ! [B5: set_variable_real,A5: set_variable_real,P: ( variable > real ) > $o] :
      ( ( ord_le1113654598e_real @ B5 @ A5 )
     => ( ( ord_le1113654598e_real @ B5
          @ ( collec633296133e_real
            @ ^ [X4: variable > real] :
                ( ( member_variable_real @ X4 @ A5 )
                & ( P @ X4 ) ) ) )
        = ( ! [X4: variable > real] :
              ( ( member_variable_real @ X4 @ B5 )
             => ( P @ X4 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_350_subset__CollectI,axiom,
    ! [B5: set_variable_real,A5: set_variable_real,Q: ( variable > real ) > $o,P: ( variable > real ) > $o] :
      ( ( ord_le1113654598e_real @ B5 @ A5 )
     => ( ! [X3: variable > real] :
            ( ( member_variable_real @ X3 @ B5 )
           => ( ( Q @ X3 )
             => ( P @ X3 ) ) )
       => ( ord_le1113654598e_real
          @ ( collec633296133e_real
            @ ^ [X4: variable > real] :
                ( ( member_variable_real @ X4 @ B5 )
                & ( Q @ X4 ) ) )
          @ ( collec633296133e_real
            @ ^ [X4: variable > real] :
                ( ( member_variable_real @ X4 @ A5 )
                & ( P @ X4 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_351_GrD1,axiom,
    ! [X: char > real,Fx: produc1020032539e_real,A5: set_char_real,F3: ( char > real ) > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ X @ Fx ) @ ( bNF_Gr2096011355e_real @ A5 @ F3 ) )
     => ( member_char_real @ X @ A5 ) ) ).

% GrD1
thf(fact_352_GrD1,axiom,
    ! [X: char > real > real,Fx: produc104944723e_real,A5: set_char_real_real,F3: ( char > real > real ) > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ X @ Fx ) @ ( bNF_Gr574714974e_real @ A5 @ F3 ) )
     => ( member312374654l_real @ X @ A5 ) ) ).

% GrD1
thf(fact_353_GrD1,axiom,
    ! [X: char > real > $o,Fx: char > set_variable_real > set_variable_real,A5: set_char_real_o,F3: ( char > real > $o ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ X @ Fx ) @ ( bNF_Gr1652860930e_real @ A5 @ F3 ) )
     => ( member_char_real_o @ X @ A5 ) ) ).

% GrD1

% Helper facts (3)
thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( denotational_Preds
      @ ( denota1150374853interp
        @ ( produc2125489830e_real
          @ ^ [C2: char] : ( if_real @ ( C2 = f ) @ d @ ( denotational_Consts @ i @ C2 ) )
          @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
    = ( denotational_Preds @ i ) ) ).

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