ITP001 Axioms: ITP076^4.ax


%------------------------------------------------------------------------------
% File     : ITP076^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ternaryComparisons.ax [Gau19]
%          : HL4076^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  383 ( 144 unt; 202 typ;   0 def)
%            Number of atoms       :  327 ( 231 equ;   5 cnn)
%            Maximal formula atoms :   20 (   0 avg)
%            Number of connectives : 4503 (   5   ~;   5   |;  58   &;4386   @)
%                                         (  27 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   4 avg;4386 nst)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :  555 ( 555   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  197 ( 195 usr;  55 con; 0-5 aty)
%            Number of variables   :  428 (   0   ^ 423   !;   5   ?; 428   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
    u: $tType ).

thf(d,type,
    d: $tType ).

thf(du,type,
    du: $tType ).

thf(mono_2Etyop_2Estring_2Echar,type,
    mono_2Etyop_2Estring_2Echar: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: $tType ).

thf(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

thf(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(tyop_2Estring_2Echar,type,
    tyop_2Estring_2Echar: d ).

thf(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: d ).

thf(s,type,
    s: d > u > du ).

thf(app_2E2,type,
    app_2E2: du > du > u ).

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

thf(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

thf(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

thf(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

thf(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

thf(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

thf(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

thf(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

thf(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

thf(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: du > du > u ).

thf(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

thf(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

thf(c_2EternaryComparisons_2EEQUAL_2E0,type,
    c_2EternaryComparisons_2EEQUAL_2E0: u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2EternaryComparisons_2EGREATER_2E0,type,
    c_2EternaryComparisons_2EGREATER_2E0: u ).

thf(c_2EternaryComparisons_2ELESS_2E0,type,
    c_2EternaryComparisons_2ELESS_2E0: u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

thf(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

thf(c_2Estring_2EORD_2E0,type,
    c_2Estring_2EORD_2E0: u ).

thf(c_2Estring_2EORD_2E1,type,
    c_2Estring_2EORD_2E1: du > u ).

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(c_2EternaryComparisons_2Ebool__compare_2E0,type,
    c_2EternaryComparisons_2Ebool__compare_2E0: u ).

thf(c_2EternaryComparisons_2Ebool__compare_2E2,type,
    c_2EternaryComparisons_2Ebool__compare_2E2: du > du > u ).

thf(c_2EternaryComparisons_2Echar__compare_2E0,type,
    c_2EternaryComparisons_2Echar__compare_2E0: u ).

thf(c_2EternaryComparisons_2Echar__compare_2E2,type,
    c_2EternaryComparisons_2Echar__compare_2E2: du > du > u ).

thf(c_2EternaryComparisons_2Einvert__comparison_2E0,type,
    c_2EternaryComparisons_2Einvert__comparison_2E0: u ).

thf(c_2EternaryComparisons_2Einvert__comparison_2E1,type,
    c_2EternaryComparisons_2Einvert__comparison_2E1: du > u ).

thf(c_2EternaryComparisons_2Elist__compare_2E0,type,
    c_2EternaryComparisons_2Elist__compare_2E0: u ).

thf(c_2EternaryComparisons_2Elist__compare_2E1,type,
    c_2EternaryComparisons_2Elist__compare_2E1: du > u ).

thf(c_2EternaryComparisons_2Elist__compare_2E3,type,
    c_2EternaryComparisons_2Elist__compare_2E3: du > du > du > u ).

thf(c_2EternaryComparisons_2Elist__merge_2E0,type,
    c_2EternaryComparisons_2Elist__merge_2E0: u ).

thf(c_2EternaryComparisons_2Elist__merge_2E3,type,
    c_2EternaryComparisons_2Elist__merge_2E3: du > du > du > u ).

thf(c_2EternaryComparisons_2Enum2ordering_2E0,type,
    c_2EternaryComparisons_2Enum2ordering_2E0: u ).

thf(c_2EternaryComparisons_2Enum2ordering_2E1,type,
    c_2EternaryComparisons_2Enum2ordering_2E1: du > u ).

thf(c_2EternaryComparisons_2Enum__compare_2E0,type,
    c_2EternaryComparisons_2Enum__compare_2E0: u ).

thf(c_2EternaryComparisons_2Enum__compare_2E2,type,
    c_2EternaryComparisons_2Enum__compare_2E2: du > du > u ).

thf(c_2EternaryComparisons_2Eoption__compare_2E0,type,
    c_2EternaryComparisons_2Eoption__compare_2E0: u ).

thf(c_2EternaryComparisons_2Eoption__compare_2E3,type,
    c_2EternaryComparisons_2Eoption__compare_2E3: du > du > du > u ).

thf(c_2EternaryComparisons_2Eordering2num_2E0,type,
    c_2EternaryComparisons_2Eordering2num_2E0: u ).

thf(c_2EternaryComparisons_2Eordering2num_2E1,type,
    c_2EternaryComparisons_2Eordering2num_2E1: du > u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
    c_2EternaryComparisons_2Eordering__CASE_2E0: u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
    c_2EternaryComparisons_2Eordering__CASE_2E4: du > du > du > du > u ).

thf(c_2EternaryComparisons_2Eordering__size_2E0,type,
    c_2EternaryComparisons_2Eordering__size_2E0: u ).

thf(c_2EternaryComparisons_2Eordering__size_2E1,type,
    c_2EternaryComparisons_2Eordering__size_2E1: du > u ).

thf(c_2EternaryComparisons_2Epair__compare_2E0,type,
    c_2EternaryComparisons_2Epair__compare_2E0: u ).

thf(c_2EternaryComparisons_2Epair__compare_2E4,type,
    c_2EternaryComparisons_2Epair__compare_2E4: du > du > du > du > u ).

thf(c_2EternaryComparisons_2Estring__compare_2E0,type,
    c_2EternaryComparisons_2Estring__compare_2E0: u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Eprim__rec_2E_3C,type,
    mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Earithmetic_2EBIT1,type,
    mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2EBIT2,type,
    mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).

thf(mono_2Ec_2EternaryComparisons_2EEQUAL,type,
    mono_2Ec_2EternaryComparisons_2EEQUAL: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2EternaryComparisons_2EGREATER,type,
    mono_2Ec_2EternaryComparisons_2EGREATER: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2ELESS,type,
    mono_2Ec_2EternaryComparisons_2ELESS: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
    mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Estring_2EORD,type,
    mono_2Ec_2Estring_2EORD: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ).

thf(mono_2Ec_2Earithmetic_2EZERO,type,
    mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2EternaryComparisons_2Ebool__compare,type,
    mono_2Ec_2EternaryComparisons_2Ebool__compare: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Echar__compare,type,
    mono_2Ec_2EternaryComparisons_2Echar__compare: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Einvert__comparison,type,
    mono_2Ec_2EternaryComparisons_2Einvert__comparison: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,type,
    mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Enum2ordering,type,
    mono_2Ec_2EternaryComparisons_2Enum2ordering: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Enum__compare,type,
    mono_2Ec_2EternaryComparisons_2Enum__compare: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Eordering2num,type,
    mono_2Ec_2EternaryComparisons_2Eordering2num: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2Eordering__size,type,
    mono_2Ec_2EternaryComparisons_2Eordering__size: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EternaryComparisons_2Estring__compare,type,
    mono_2Ec_2EternaryComparisons_2Estring__compare: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2E_7E,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(i_mono_2Etyop_2Estring_2Echar,type,
    i_mono_2Etyop_2Estring_2Echar: mono_2Etyop_2Estring_2Echar > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: ( $o > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).

thf(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(i_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    i_mono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > u ).

thf(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(j_mono_2Etyop_2Estring_2Echar,type,
    j_mono_2Etyop_2Estring_2Echar: du > mono_2Etyop_2Estring_2Echar ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29: du > $o > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    j_mono_2Etyop_2EternaryComparisons_2Eordering: du > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).

thf(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(reserved_2Elogic_2E_7E,axiom,
    ! [V0: $o] :
      ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
    <=> ( ( s @ A_27a @ V0_2E0 )
        = ( s @ A_27a @ V1_2E0 ) ) ) ).

thf(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ ( j_mono_2Etyop_2Estring_2Echar @ ( s @ tyop_2Estring_2Echar @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Estring_2Echar @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ).

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Estring_2Echar,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar] :
      ( ( j_mono_2Etyop_2Estring_2Echar @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) )
      = V0 ) ).

thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( ( s @ A_27a @ X0_2E0 )
        = ( s @ A_27a @ X1_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2EternaryComparisons_2Elist__merge_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2EternaryComparisons_2Elist__merge_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2EternaryComparisons_2Eoption__compare_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Eoption__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Epair__compare_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Epair__compare_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ X3_2E0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Estring_2Echar @ ( i_mono_2Etyop_2Estring_2Echar @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering,V2: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering @ V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E0_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2EternaryComparisons_2Elist__compare_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Elist__compare_2E1_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar @ V0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2EternaryComparisons_2Elist__compare_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ ( tyop_2Emin_2Efun @ tyop_2Estring_2Echar @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E0_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29_29 @ mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ tyop_2EternaryComparisons_2Eordering ) ) ) ) @ c_2EternaryComparisons_2Eordering__CASE_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering,V2: mono_2Etyop_2EternaryComparisons_2Eordering,V3: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering @ V0 @ V1 @ V2 @ V3 ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V2 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V3 ) ) ) ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: $o > $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: $o > mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2Emin_2Efun_28tyop_2Estring_2Echar_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29 > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Estring_2Echar > mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: ( mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ) > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2EternaryComparisons_2Eordering__TY__DEF,axiom,
    ! [F0: mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V1n: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V1n )
          = ( mono_2Ec_2Eprim__rec_2E_3C @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
     => ? [V0rep: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2EternaryComparisons_2Eordering @ F0 @ V0rep ) ) ).

thf(thm_2EternaryComparisons_2Eordering__BIJ,axiom,
    ( ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering] :
        ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0a ) )
        = V0a )
    & ! [V1r: mono_2Etyop_2Enum_2Enum] :
        ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1r @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
      <=> ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ V1r ) )
          = V1r ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__size__def,axiom,
    ! [V0x: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( mono_2Ec_2EternaryComparisons_2Eordering__size @ V0x )
      = mono_2Ec_2Enum_2E0 ) ).

thf(thm_2EternaryComparisons_2Eordering__CASE,axiom,
    ! [A_27a: d,F0: mono_2Etyop_2EternaryComparisons_2Eordering > $o] :
      ( ! [V0x: mono_2Etyop_2EternaryComparisons_2Eordering] :
          ( ( F0 @ V0x )
        <=> ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0x )
            = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
     => ! [V0x: mono_2Etyop_2EternaryComparisons_2Eordering,V1v0_2E0: u,V2v1_2E0: u,V3v2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0x ) ) @ ( s @ A_27a @ V1v0_2E0 ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ A_27a @ V3v2_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0x ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ V1v0_2E0 ) @ ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0x ) ) ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ A_27a @ V3v2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Epair__compare__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0c1_2E0: u,V1c2_2E0: u,V2a_2E0: u,V3b_2E0: u,V4x_2E0: u,V5y_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Epair__compare_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V1c2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2a_2E0 ) @ ( s @ A_27c @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V4x_2E0 ) @ ( s @ A_27d @ V5y_2E0 ) ) ) ) ) )
      = ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0c1_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ A_27b @ V4x_2E0 ) ) ) ) @ mono_2Ec_2EternaryComparisons_2ELESS @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2EternaryComparisons_2Eordering ) ) @ V1c2_2E0 ) @ ( s @ A_27c @ V3b_2E0 ) ) ) @ ( s @ A_27d @ V5y_2E0 ) ) ) ) @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).

thf(thm_2EternaryComparisons_2Enum__compare__def,axiom,
    ! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
      ( ! [V0n1: mono_2Etyop_2Enum_2Enum,V1n2: mono_2Etyop_2Enum_2Enum] :
          ( ( F0 @ V0n1 @ V1n2 )
        <=> ( V0n1 = V1n2 ) )
     => ! [V0n1: mono_2Etyop_2Enum_2Enum,V1n2: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2EternaryComparisons_2Enum__compare @ V0n1 @ V1n2 )
          = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( F0 @ V0n1 @ V1n2 ) @ mono_2Ec_2EternaryComparisons_2EEQUAL @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n1 @ V1n2 ) @ mono_2Ec_2EternaryComparisons_2ELESS @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ) ) ).

thf(thm_2EternaryComparisons_2Echar__compare__def,axiom,
    ! [V0c1: mono_2Etyop_2Estring_2Echar,V1c2: mono_2Etyop_2Estring_2Echar] :
      ( ( mono_2Ec_2EternaryComparisons_2Echar__compare @ V0c1 @ V1c2 )
      = ( mono_2Ec_2EternaryComparisons_2Enum__compare @ ( mono_2Ec_2Estring_2EORD @ V0c1 ) @ ( mono_2Ec_2Estring_2EORD @ V1c2 ) ) ) ).

thf(thm_2EternaryComparisons_2Estring__compare__def,axiom,
    ( mono_2Ec_2EternaryComparisons_2Estring__compare
    = ( mono_2Ec_2EternaryComparisons_2Elist__compare_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Estring_2Echar @ mono_2Ec_2EternaryComparisons_2Echar__compare ) ) ).

thf(thm_2EternaryComparisons_2Einvert__comparison__def,axiom,
    ( ( ( mono_2Ec_2EternaryComparisons_2Einvert__comparison @ mono_2Ec_2EternaryComparisons_2EGREATER )
      = mono_2Ec_2EternaryComparisons_2ELESS )
    & ( ( mono_2Ec_2EternaryComparisons_2Einvert__comparison @ mono_2Ec_2EternaryComparisons_2ELESS )
      = mono_2Ec_2EternaryComparisons_2EGREATER )
    & ( ( mono_2Ec_2EternaryComparisons_2Einvert__comparison @ mono_2Ec_2EternaryComparisons_2EEQUAL )
      = mono_2Ec_2EternaryComparisons_2EEQUAL ) ) ).

thf(thm_2EternaryComparisons_2Enum2ordering__ordering2num,axiom,
    ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0a ) )
      = V0a ) ).

thf(thm_2EternaryComparisons_2Eordering2num__num2ordering,axiom,
    ! [V0r: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0r @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
    <=> ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ V0r ) )
        = V0r ) ) ).

thf(thm_2EternaryComparisons_2Enum2ordering__11,axiom,
    ! [V0r: mono_2Etyop_2Enum_2Enum,V1r_27: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0r @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
     => ( ( mono_2Ec_2Eprim__rec_2E_3C @ V1r_27 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
       => ( ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ V0r )
            = ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ V1r_27 ) )
        <=> ( V0r = V1r_27 ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering2num__11,axiom,
    ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering,V1a_27: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0a )
        = ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V1a_27 ) )
    <=> ( V0a = V1a_27 ) ) ).

thf(thm_2EternaryComparisons_2Enum2ordering__ONTO,axiom,
    ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering] :
    ? [V1r: mono_2Etyop_2Enum_2Enum] :
      ( ( V0a
        = ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ V1r ) )
      & ( mono_2Ec_2Eprim__rec_2E_3C @ V1r @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering2num__ONTO,axiom,
    ! [V0r: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0r @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
    <=> ? [V1a: mono_2Etyop_2EternaryComparisons_2Eordering] :
          ( V0r
          = ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V1a ) ) ) ).

thf(thm_2EternaryComparisons_2Enum2ordering__thm,axiom,
    ( ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ mono_2Ec_2Enum_2E0 )
      = mono_2Ec_2EternaryComparisons_2ELESS )
    & ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      = mono_2Ec_2EternaryComparisons_2EEQUAL )
    & ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      = mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).

thf(thm_2EternaryComparisons_2Eordering2num__thm,axiom,
    ( ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2ELESS )
      = mono_2Ec_2Enum_2E0 )
    & ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2EEQUAL )
      = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
    & ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2EGREATER )
      = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__EQ__ordering,axiom,
    ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering,V1a_27: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0a = V1a_27 )
    <=> ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V0a )
        = ( mono_2Ec_2EternaryComparisons_2Eordering2num @ V1a_27 ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__case__def,axiom,
    ! [A_27a: d] :
      ( ! [V0v0_2E0: u,V1v1_2E0: u,V2v2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2ELESS ) ) @ ( s @ A_27a @ V0v0_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) @ ( s @ A_27a @ V2v2_2E0 ) ) )
          = ( s @ A_27a @ V0v0_2E0 ) )
      & ! [V3v0_2E0: u,V4v1_2E0: u,V5v2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EEQUAL ) ) @ ( s @ A_27a @ V3v0_2E0 ) @ ( s @ A_27a @ V4v1_2E0 ) @ ( s @ A_27a @ V5v2_2E0 ) ) )
          = ( s @ A_27a @ V4v1_2E0 ) )
      & ! [V6v0_2E0: u,V7v1_2E0: u,V8v2_2E0: u] :
          ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) @ ( s @ A_27a @ V6v0_2E0 ) @ ( s @ A_27a @ V7v1_2E0 ) @ ( s @ A_27a @ V8v2_2E0 ) ) )
          = ( s @ A_27a @ V8v2_2E0 ) ) ) ).

thf(thm_2EternaryComparisons_2Edatatype__ordering,axiom,
    ! [V0ordering: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2EternaryComparisons_2Eordering > $o] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( V0ordering @ mono_2Ec_2EternaryComparisons_2ELESS @ mono_2Ec_2EternaryComparisons_2EEQUAL @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).

thf(thm_2EternaryComparisons_2Eordering__distinct,axiom,
    ( ( (~) @ ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EEQUAL ) )
    & ( (~) @ ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EGREATER ) )
    & ( (~) @ ( mono_2Ec_2EternaryComparisons_2EEQUAL = mono_2Ec_2EternaryComparisons_2EGREATER ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__nchotomy,axiom,
    ! [V0a: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0a = mono_2Ec_2EternaryComparisons_2ELESS )
      | ( V0a = mono_2Ec_2EternaryComparisons_2EEQUAL )
      | ( V0a = mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).

thf(thm_2EternaryComparisons_2Eordering__Axiom,axiom,
    ! [A_27a: d,V0x0_2E0: u,V1x1_2E0: u,V2x2_2E0: u] :
    ? [V3f_2E0: u] :
      ( ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ A_27a ) @ V3f_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2ELESS ) ) ) )
        = ( s @ A_27a @ V0x0_2E0 ) )
      & ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ A_27a ) @ V3f_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EEQUAL ) ) ) )
        = ( s @ A_27a @ V1x1_2E0 ) )
      & ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ A_27a ) @ V3f_2E0 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ) )
        = ( s @ A_27a @ V2x2_2E0 ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__induction,axiom,
    ! [V0P: mono_2Etyop_2EternaryComparisons_2Eordering > $o] :
      ( ( ( V0P @ mono_2Ec_2EternaryComparisons_2EEQUAL )
        & ( V0P @ mono_2Ec_2EternaryComparisons_2EGREATER )
        & ( V0P @ mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ! [V1a: mono_2Etyop_2EternaryComparisons_2Eordering] : ( V0P @ V1a ) ) ).

thf(thm_2EternaryComparisons_2Eordering__case__cong,axiom,
    ! [A_27a: d,V0v2_27_2E0: u,V1v1_27_2E0: u,V2v0_27_2E0: u,V3M: mono_2Etyop_2EternaryComparisons_2Eordering,V4M_27: mono_2Etyop_2EternaryComparisons_2Eordering,V5v0_2E0: u,V6v1_2E0: u,V7v2_2E0: u] :
      ( ( ( V3M = V4M_27 )
        & ( ( V4M_27 = mono_2Ec_2EternaryComparisons_2ELESS )
         => ( ( s @ A_27a @ V5v0_2E0 )
            = ( s @ A_27a @ V2v0_27_2E0 ) ) )
        & ( ( V4M_27 = mono_2Ec_2EternaryComparisons_2EEQUAL )
         => ( ( s @ A_27a @ V6v1_2E0 )
            = ( s @ A_27a @ V1v1_27_2E0 ) ) )
        & ( ( V4M_27 = mono_2Ec_2EternaryComparisons_2EGREATER )
         => ( ( s @ A_27a @ V7v2_2E0 )
            = ( s @ A_27a @ V0v2_27_2E0 ) ) ) )
     => ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V3M ) ) @ ( s @ A_27a @ V5v0_2E0 ) @ ( s @ A_27a @ V6v1_2E0 ) @ ( s @ A_27a @ V7v2_2E0 ) ) )
        = ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V4M_27 ) ) @ ( s @ A_27a @ V2v0_27_2E0 ) @ ( s @ A_27a @ V1v1_27_2E0 ) @ ( s @ A_27a @ V0v2_27_2E0 ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__case__eq,axiom,
    ! [A_27a: d,V0x: mono_2Etyop_2EternaryComparisons_2Eordering,V1v2_2E0: u,V2v1_2E0: u,V3v0_2E0: u,V4v_2E0: u] :
      ( ( ( s @ A_27a @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0x ) ) @ ( s @ A_27a @ V3v0_2E0 ) @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ A_27a @ V1v2_2E0 ) ) )
        = ( s @ A_27a @ V4v_2E0 ) )
    <=> ( ( ( V0x = mono_2Ec_2EternaryComparisons_2ELESS )
          & ( ( s @ A_27a @ V3v0_2E0 )
            = ( s @ A_27a @ V4v_2E0 ) ) )
        | ( ( V0x = mono_2Ec_2EternaryComparisons_2EEQUAL )
          & ( ( s @ A_27a @ V2v1_2E0 )
            = ( s @ A_27a @ V4v_2E0 ) ) )
        | ( ( V0x = mono_2Ec_2EternaryComparisons_2EGREATER )
          & ( ( s @ A_27a @ V1v2_2E0 )
            = ( s @ A_27a @ V4v_2E0 ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eordering__eq__dec,axiom,
    ( ! [V0x: mono_2Etyop_2EternaryComparisons_2Eordering] :
        ( ( V0x = V0x )
      <=> mono_2Ec_2Ebool_2ET )
    & ( ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EEQUAL )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2ELESS = mono_2Ec_2EternaryComparisons_2EGREATER )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2EEQUAL = mono_2Ec_2EternaryComparisons_2EGREATER )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2EEQUAL = mono_2Ec_2EternaryComparisons_2ELESS )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2EGREATER = mono_2Ec_2EternaryComparisons_2ELESS )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2EGREATER = mono_2Ec_2EternaryComparisons_2EEQUAL )
    <=> mono_2Ec_2Ebool_2EF )
    & ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2ELESS )
      = mono_2Ec_2Enum_2E0 )
    & ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2EEQUAL )
      = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
    & ( ( mono_2Ec_2EternaryComparisons_2Eordering2num @ mono_2Ec_2EternaryComparisons_2EGREATER )
      = ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
    & ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ mono_2Ec_2Enum_2E0 )
      = mono_2Ec_2EternaryComparisons_2ELESS )
    & ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      = mono_2Ec_2EternaryComparisons_2EEQUAL )
    & ( ( mono_2Ec_2EternaryComparisons_2Enum2ordering @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
      = mono_2Ec_2EternaryComparisons_2EGREATER ) ) ).

thf(thm_2EternaryComparisons_2Ebool__compare__ind,axiom,
    ! [V0P: $o > $o > $o] :
      ( ( ( V0P @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2ET )
        & ( V0P @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2EF )
        & ( V0P @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2EF )
        & ( V0P @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2ET ) )
     => ! [V1v: $o,V2v1: $o] : ( V0P @ V1v @ V2v1 ) ) ).

thf(thm_2EternaryComparisons_2Ebool__compare__def,axiom,
    ( ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2ET )
      = mono_2Ec_2EternaryComparisons_2EEQUAL )
    & ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2EF )
      = mono_2Ec_2EternaryComparisons_2EEQUAL )
    & ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2ET @ mono_2Ec_2Ebool_2EF )
      = mono_2Ec_2EternaryComparisons_2EGREATER )
    & ( ( mono_2Ec_2EternaryComparisons_2Ebool__compare @ mono_2Ec_2Ebool_2EF @ mono_2Ec_2Ebool_2ET )
      = mono_2Ec_2EternaryComparisons_2ELESS ) ) ).

thf(thm_2EternaryComparisons_2Eoption__compare__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1c_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        & ! [V2c_2E0: u,V3v0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V2c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v0_2E0 ) ) ) ) ) )
        & ! [V4c_2E0: u,V5v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5v3_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        & ! [V6c_2E0: u,V7v1_2E0: u,V8v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V6c_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7v1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V8v2_2E0 ) ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10v1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Eoption__compare__def,axiom,
    ! [A_27a: d,A_27b: d,V0v3_2E0: u,V1v2_2E0: u,V2v1_2E0: u,V3v0_2E0: u,V4c_2E0: u] :
      ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2EternaryComparisons_2EEQUAL )
      & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v0_2E0 ) ) ) ) ) )
        = mono_2Ec_2EternaryComparisons_2ELESS )
      & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v3_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
        = mono_2Ec_2EternaryComparisons_2EGREATER )
      & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Eoption__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2v1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1v2_2E0 ) ) ) ) ) )
        = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V4c_2E0 ) @ ( s @ A_27a @ V2v1_2E0 ) ) ) @ ( s @ A_27b @ V1v2_2E0 ) ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Elist__compare__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3v8_2E0: u,V4v9_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ V3v8_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V4v9_2E0 ) ) ) ) ) )
        & ! [V5cmp_2E0: u,V6v4_2E0: u,V7v5_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7v5_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V8cmp_2E0: u,V9x_2E0: u,V10l1_2E0: u,V11y_2E0: u,V12l2_2E0: u] :
            ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V8cmp_2E0 ) @ ( s @ A_27a @ V9x_2E0 ) ) ) @ ( s @ A_27b @ V11y_2E0 ) ) ) )
                = mono_2Ec_2EternaryComparisons_2EEQUAL )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V12l2_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V8cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ V11y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V12l2_2E0 ) ) ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V15v2_2E0 ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Elist__compare__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2EternaryComparisons_2EEQUAL )
      & ! [V1v9_2E0: u,V2v8_2E0: u,V3cmp_2E0: u] :
          ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ V2v8_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V1v9_2E0 ) ) ) ) ) )
          = mono_2Ec_2EternaryComparisons_2ELESS )
      & ! [V4v5_2E0: u,V5v4_2E0: u,V6cmp_2E0: u] :
          ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4v5_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2EternaryComparisons_2EGREATER )
      & ! [V7y_2E0: u,V8x_2E0: u,V9l2_2E0: u,V10l1_2E0: u,V11cmp_2E0: u] :
          ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27b @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V9l2_2E0 ) ) ) ) ) )
          = ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) @ ( s @ A_27b @ V7y_2E0 ) ) ) ) @ mono_2Ec_2EternaryComparisons_2ELESS @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2EternaryComparisons_2Eordering ) ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V9l2_2E0 ) ) ) ) @ mono_2Ec_2EternaryComparisons_2EGREATER ) ) ) ).

thf(thm_2EternaryComparisons_2Ecompare__equal,axiom,
    ! [A_27a: d,V0cmp_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u] :
          ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2EEQUAL )
        <=> ( ( s @ A_27a @ V1x_2E0 )
            = ( s @ A_27a @ V2y_2E0 ) ) )
     => ! [V3l1_2E0: u,V4l2_2E0: u] :
          ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2EternaryComparisons_2Elist__compare_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l2_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2EEQUAL )
        <=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l1_2E0 )
            = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4l2_2E0 ) ) ) ) ).

thf(thm_2EternaryComparisons_2Elist__merge__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1a__lt_2E0: u,V2l1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1a__lt_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V3a__lt_2E0: u,V4v4_2E0: u,V5v5_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V3a__lt_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5v5_2E0 ) ) ) ) ) )
        & ! [V6a__lt_2E0: u,V7x_2E0: u,V8l1_2E0: u,V9y_2E0: u,V10l2_2E0: u] :
            ( ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V6a__lt_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27a @ V9y_2E0 ) ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V6a__lt_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l2_2E0 ) ) ) ) )
              & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V6a__lt_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27a @ V9y_2E0 ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V6a__lt_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l2_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V6a__lt_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V9y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10l2_2E0 ) ) ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V11v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V12v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V13v2_2E0 ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Elist__merge__def,axiom,
    ! [A_27a: d] :
      ( ! [V0l1_2E0: u,V1a__lt_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1a__lt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) )
      & ! [V2v5_2E0: u,V3v4_2E0: u,V4a__lt_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4a__lt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2v5_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2v5_2E0 ) ) ) )
      & ! [V5y_2E0: u,V6x_2E0: u,V7l2_2E0: u,V8l1_2E0: u,V9a__lt_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V9a__lt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V9a__lt_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V9a__lt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EternaryComparisons_2Elist__merge_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V9a__lt_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V7l2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2EternaryComparisons_2Einvert__eq__EQUAL,axiom,
    ! [V0x: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( ( mono_2Ec_2EternaryComparisons_2Einvert__comparison @ V0x )
        = mono_2Ec_2EternaryComparisons_2EEQUAL )
    <=> ( V0x = mono_2Ec_2EternaryComparisons_2EEQUAL ) ) ).

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