ITP001 Axioms: ITP111^4.ax
%------------------------------------------------------------------------------
% File : ITP111^4 : TPTP v8.2.0. 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 : intto.ax [Gau19]
% : HL4111^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 226 ( 89 unt; 129 typ; 0 def)
% Number of atoms : 118 ( 92 equ; 3 cnn)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 1187 ( 3 ~; 1 |; 1 &;1172 @)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg;1172 nst)
% Number of types : 8 ( 7 usr)
% Number of type conns : 284 ( 284 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 122 usr; 41 con; 0-4 aty)
% Number of variables : 149 ( 0 ^ 148 !; 1 ?; 149 :)
% 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_2Einteger_2Eint,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: $tType ).
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: 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_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: d ).
thf(tyop_2Etoto_2Etoto,type,
tyop_2Etoto_2Etoto: d > 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_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_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_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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Etoto_2ETO_2E0,type,
c_2Etoto_2ETO_2E0: u ).
thf(c_2Etoto_2ETO_2E1,type,
c_2Etoto_2ETO_2E1: du > u ).
thf(c_2Etoto_2ETO__of__LinearOrder_2E0,type,
c_2Etoto_2ETO__of__LinearOrder_2E0: u ).
thf(c_2Etoto_2ETO__of__LinearOrder_2E1,type,
c_2Etoto_2ETO__of__LinearOrder_2E1: 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_2Etoto_2Eapto_2E0,type,
c_2Etoto_2Eapto_2E0: u ).
thf(c_2Etoto_2Eapto_2E1,type,
c_2Etoto_2Eapto_2E1: du > u ).
thf(c_2Eintto_2EintOrd_2E0,type,
c_2Eintto_2EintOrd_2E0: u ).
thf(c_2Eintto_2EintOrd_2E2,type,
c_2Eintto_2EintOrd_2E2: du > du > u ).
thf(c_2Einteger_2Eint__lt_2E0,type,
c_2Einteger_2Eint__lt_2E0: u ).
thf(c_2Einteger_2Eint__neg_2E0,type,
c_2Einteger_2Eint__neg_2E0: u ).
thf(c_2Einteger_2Eint__neg_2E1,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
thf(c_2Einteger_2Eint__of__num_2E0,type,
c_2Einteger_2Eint__of__num_2E0: u ).
thf(c_2Einteger_2Eint__of__num_2E1,type,
c_2Einteger_2Eint__of__num_2E1: du > u ).
thf(c_2Eintto_2Eintto_2E0,type,
c_2Eintto_2Eintto_2E0: u ).
thf(c_2Etoto_2EnumOrd_2E0,type,
c_2Etoto_2EnumOrd_2E0: u ).
thf(c_2Etoto_2EnumOrd_2E2,type,
c_2Etoto_2EnumOrd_2E2: du > du > 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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2EternaryComparisons_2Eordering,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2EternaryComparisons_2Eordering: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
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_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > 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_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_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_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Etoto_2ETO_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Etoto_2ETO_2Emono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ).
thf(mono_2Ec_2Etoto_2ETO__of__LinearOrder_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Etoto_2ETO__of__LinearOrder_2Emono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
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_2Etoto_2Eapto_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Eintto_2EintOrd,type,
mono_2Ec_2Eintto_2EintOrd: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(mono_2Ec_2Einteger_2Eint__lt,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__neg,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__of__num,type,
mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Eintto_2Eintto,type,
mono_2Ec_2Eintto_2Eintto: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ).
thf(mono_2Ec_2Etoto_2EnumOrd,type,
mono_2Ec_2Etoto_2EnumOrd: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > 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_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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > 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_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > 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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: ( mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > u ).
thf(i_mono_2Etyop_2Einteger_2Eint,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > 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(i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29: du > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
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_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29: du > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ).
thf(j_mono_2Etyop_2Einteger_2Eint,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
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(j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: du > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 ).
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_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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ 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_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ 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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
= ( s @ tyop_2Einteger_2Eint @ 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(ij_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ 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_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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_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_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ 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(ji_2Emono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ 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_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(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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( V0 @ V1 ) ) )
= ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ 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_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2ETO_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_2Ctyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_29 @ mono_2Ec_2Etoto_2ETO_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) ) @ c_2Etoto_2ETO_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2ETO_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ ( mono_2Ec_2Etoto_2ETO_2Emono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( c_2Etoto_2ETO_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2ETO__of__LinearOrder_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2Etoto_2ETO__of__LinearOrder_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2ETO__of__LinearOrder_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2ETO__of__LinearOrder_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( mono_2Ec_2Etoto_2ETO__of__LinearOrder_2Emono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2ETO__of__LinearOrder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2Eapto_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_29 @ mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2Eapto_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Etoto_2Eapto_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29 @ ( mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2EternaryComparisons_2Eordering ) ) @ ( c_2Etoto_2Eapto_2E1 @ ( s @ ( tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 @ V0 ) ) ) ) ) ).
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_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29_20mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering ) > mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2EternaryComparisons_2Eordering,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Einteger_2Eint] :
( ( 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_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,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_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2EternaryComparisons_2Eordering_29_29,axiom,
! [V0: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2EternaryComparisons_2Eordering,V1: mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Eintto_2EintOrd,axiom,
( mono_2Ec_2Eintto_2EintOrd
= ( mono_2Ec_2Etoto_2ETO__of__LinearOrder_2Emono_2Etyop_2Einteger_2Eint @ mono_2Ec_2Einteger_2Eint__lt ) ) ).
thf(thm_2Eintto_2Eintto,axiom,
( mono_2Ec_2Eintto_2Eintto
= ( mono_2Ec_2Etoto_2ETO_2Emono_2Etyop_2Einteger_2Eint @ mono_2Ec_2Eintto_2EintOrd ) ) ).
thf(thm_2Eintto_2Eapintto__thm,axiom,
( ( mono_2Ec_2Etoto_2Eapto_2Emono_2Etyop_2Einteger_2Eint @ mono_2Ec_2Eintto_2Eintto )
= mono_2Ec_2Eintto_2EintOrd ) ).
thf(thm_2Eintto_2Epos__pos__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Etoto_2EnumOrd @ V0m @ V1n ) ) ).
thf(thm_2Eintto_2Eneg__neg__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) )
= ( mono_2Ec_2Etoto_2EnumOrd @ V1n @ V0m ) ) ).
thf(thm_2Eintto_2EBIT1__nz,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Eintto_2EBIT2__nz,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n )
= mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Eintto_2Eneg__lt__BIT1__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__lt__BIT2__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__BIT1__lt__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__BIT2__lt__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= mono_2Ec_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__ZERO__eq__ZERO__thm,axiom,
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Earithmetic_2EZERO ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) ).
thf(thm_2Eintto_2EBIT1__gt__neg__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2EBIT2__gt__neg__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2Egt__neg__BIT1__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2Egt__neg__BIT2__thm,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= mono_2Ec_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2EZERO__eq__neg__ZERO__thm,axiom,
( ( mono_2Ec_2Eintto_2EintOrd @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Earithmetic_2EZERO ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Earithmetic_2EZERO ) ) )
= mono_2Ec_2EternaryComparisons_2EEQUAL ) ).
%------------------------------------------------------------------------------