ITP001 Axioms: ITP044

ITP001 Axioms: ITP044_7.ax

%------------------------------------------------------------------------------
% File     : ITP044_7 : 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    : Temporal_Logic.ax [Gau19]
%          : HL4044_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  281 (  57 unt;  75 typ;   0 def)
%            Number of atoms       :  833 ( 189 equ)
%            Maximal formula atoms :   24 (   2 avg)
%            Number of connectives :  770 ( 143   ~;  49   |; 179   &)
%                                         ( 212 <=>; 187  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   77 (  40   >;  37   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   72 (  72 usr;  25 con; 0-4 aty)
%            Number of variables   : 1032 ( 968   !;  44   ?;1032   :)
%                                         (  20  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : 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))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2ETemporal__Logic_2EALWAYS_2E0,type,
    c_2ETemporal__Logic_2EALWAYS_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2ETemporal__Logic_2EALWAYS_2E1,type,
    c_2ETemporal__Logic_2EALWAYS_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EALWAYS_2E2,type,
    c_2ETemporal__Logic_2EALWAYS_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2EBEFORE_2E0,type,
    c_2ETemporal__Logic_2EBEFORE_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2EBEFORE_2E2,type,
    c_2ETemporal__Logic_2EBEFORE_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EBEFORE_2E3,type,
    c_2ETemporal__Logic_2EBEFORE_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2ETemporal__Logic_2EEVENTUAL_2E0,type,
    c_2ETemporal__Logic_2EEVENTUAL_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2ETemporal__Logic_2EEVENTUAL_2E1,type,
    c_2ETemporal__Logic_2EEVENTUAL_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EEVENTUAL_2E2,type,
    c_2ETemporal__Logic_2EEVENTUAL_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2ENEXT_2E0,type,
    c_2ETemporal__Logic_2ENEXT_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2ETemporal__Logic_2ENEXT_2E1,type,
    c_2ETemporal__Logic_2ENEXT_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2ENEXT_2E2,type,
    c_2ETemporal__Logic_2ENEXT_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2ETemporal__Logic_2ESBEFORE_2E0,type,
    c_2ETemporal__Logic_2ESBEFORE_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2ESBEFORE_2E2,type,
    c_2ETemporal__Logic_2ESBEFORE_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2ESBEFORE_2E3,type,
    c_2ETemporal__Logic_2ESBEFORE_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2ETemporal__Logic_2ESUNTIL_2E0,type,
    c_2ETemporal__Logic_2ESUNTIL_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2ESUNTIL_2E2,type,
    c_2ETemporal__Logic_2ESUNTIL_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2ESUNTIL_2E3,type,
    c_2ETemporal__Logic_2ESUNTIL_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2ESWHEN_2E0,type,
    c_2ETemporal__Logic_2ESWHEN_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2ESWHEN_2E2,type,
    c_2ETemporal__Logic_2ESWHEN_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2ESWHEN_2E3,type,
    c_2ETemporal__Logic_2ESWHEN_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2EUNTIL_2E0,type,
    c_2ETemporal__Logic_2EUNTIL_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2EUNTIL_2E2,type,
    c_2ETemporal__Logic_2EUNTIL_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EUNTIL_2E3,type,
    c_2ETemporal__Logic_2EUNTIL_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2EUPTO_2E0,type,
    c_2ETemporal__Logic_2EUPTO_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EUPTO_2E1,type,
    c_2ETemporal__Logic_2EUPTO_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) > tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2EWATCH_2E0,type,
    c_2ETemporal__Logic_2EWATCH_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2EWATCH_2E2,type,
    c_2ETemporal__Logic_2EWATCH_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EWATCH_2E3,type,
    c_2ETemporal__Logic_2EWATCH_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2ETemporal__Logic_2EWHEN_2E0,type,
    c_2ETemporal__Logic_2EWHEN_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2ETemporal__Logic_2EWHEN_2E2,type,
    c_2ETemporal__Logic_2EWHEN_2E2: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2ETemporal__Logic_2EWHEN_2E3,type,
    c_2ETemporal__Logic_2EWHEN_2E3: ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(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(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2ETemporal__Logic_2EALWAYS_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EALWAYS_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2EALWAYS_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EALWAYS_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EALWAYS_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2EALWAYS_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EBEFORE_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EBEFORE_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2EBEFORE_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EBEFORE_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EBEFORE_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2ETemporal__Logic_2EEVENTUAL_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EEVENTUAL_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2EEVENTUAL_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EEVENTUAL_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EEVENTUAL_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2EEVENTUAL_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2ETemporal__Logic_2ENEXT_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2ENEXT_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2ENEXT_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ENEXT_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2ETemporal__Logic_2ENEXT_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2ESBEFORE_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESBEFORE_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2ESBEFORE_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESBEFORE_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2ESUNTIL_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESUNTIL_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2ESUNTIL_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESUNTIL_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2ESWHEN_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESWHEN_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2ESWHEN_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESWHEN_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2ESWHEN_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EUNTIL_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EUNTIL_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2EUNTIL_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EUNTIL_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EUNTIL_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2ETemporal__Logic_2EUPTO_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] : ( c_2ETemporal__Logic_2EUPTO_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,c_2ETemporal__Logic_2EUPTO_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EWATCH_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWATCH_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EWATCH_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2EWATCH_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWATCH_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EWATCH_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2ETemporal__Logic_2EWHEN_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EWHEN_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2ETemporal__Logic_2EWHEN_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2ETemporal__Logic_2EWHEN_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2ETemporal__Logic_2ENEXT,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ENEXT_2E2(V0P_2E0,V1x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Enum_2ESUC_2E1(V1x_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V0P_2E0,V1t0_2E0))
    <=> ! [V2t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V1t0_2E0))) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0P_2E0,V1t0_2E0))
    <=> ? [V2t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V1t0_2E0))) ) ).

tff(thm_2ETemporal__Logic_2EWATCH,axiom,
    ! [V0q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EWATCH_2E3(V0q_2E0,V1b_2E0,V2t0_2E0))
    <=> ! [V3t_2E0: tyop_2Enum_2Enum] :
          ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0q_2E0,V2t0_2E0) = c_2Ebool_2EF_2E0 )
          & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V3t_2E0,V2t0_2E0))))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0q_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V2t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V2t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUPTO,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1t1_2E0: tyop_2Enum_2Enum,V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t1_2E0,V2a_2E0))))
    <=> ! [V3t2_2E0: tyop_2Enum_2Enum] :
          ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t2_2E0))
            & p(c_2Eprim__rec_2E_3C_2E2(V3t2_2E0,V1t1_2E0)) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t2_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EWHEN_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ( ? [V4t_2E0: tyop_2Enum_2Enum] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) )
            | ! [V5t_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V2t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ? [V4t_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) )
          & ? [V5t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V2t0_2E0))) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V0a_2E0,V1b_2E0,V2t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V2t0_2E0))
          & ? [V4t_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWATCH__EXISTS,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t0_2E0: tyop_2Enum_2Enum] :
    ? [V2q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2ETemporal__Logic_2EWATCH_2E3(V2q_2E0,V0b_2E0,V1t0_2E0)) ).

tff(thm_2ETemporal__Logic_2EWELL__ORDER,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ? [V1n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0))
    <=> ? [V2m_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2m_2E0))
          & ! [V3n_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,V2m_2E0))
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V3n_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE,axiom,
    ! [V0m2_2E0: tyop_2Enum_2Enum,V1m1_2E0: tyop_2Enum_2Enum,V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V1m1_2E0))
        & ! [V3n_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V3n_2E0,V1m1_2E0))
           => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V3n_2E0)) )
        & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V0m2_2E0))
        & ! [V4n_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V0m2_2E0))
           => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V4n_2E0)) ) )
     => ( V1m1_2E0 = V0m2_2E0 ) ) ).

tff(thm_2ETemporal__Logic_2EDELTA__CASES,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ? [V2d_2E0: tyop_2Enum_2Enum] :
          ( ! [V3t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V3t_2E0,V2d_2E0))
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0))) )
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V2d_2E0,V0t0_2E0))) )
      | ! [V4d_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4d_2E0,V0t0_2E0))) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ( ? [V4t_2E0: tyop_2Enum_2Enum] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
            | ! [V5t_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ? [V4t_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ( ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
            & ? [V5t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__IMP,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V1b_2E0,V0t0_2E0))
         => ? [V4t_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V0t0_2E0))
    <=> ! [V2t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V0t0_2E0))) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V0t0_2E0))
    <=> ? [V2t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V0t0_2E0))) ) ).

tff(thm_2ETemporal__Logic_2EWATCH__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EWATCH_2E3(V1q_2E0,V2b_2E0,V0t0_2E0))
    <=> ( ( ! [V3t_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2b_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0)))
         => ! [V4t_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
        & ! [V5d_2E0: tyop_2Enum_2Enum] :
            ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0)))
              & ! [V6t_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Eprim__rec_2E_3C_2E2(V6t_2E0,V5d_2E0))
                 => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2b_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) ) )
           => ( ! [V7t_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Earithmetic_2E_3C_3D_2E2(V7t_2E0,V5d_2E0))
                 => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1q_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) )
              & ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V8t_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3delta_2E0: tyop_2Enum_2Enum] :
          ( ( ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V4t_2E0,V3delta_2E0))
               => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0))) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0))) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ( ! [V3t_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0)))
         => ! [V4t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
        & ! [V5d_2E0: tyop_2Enum_2Enum] :
            ( ( ! [V6t_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Eprim__rec_2E_3C_2E2(V6t_2E0,V5d_2E0))
                 => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) )
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) )
           => ! [V7t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V7t_2E0,V5d_2E0))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ! [V3delta_2E0: tyop_2Enum_2Enum] :
          ( ( ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V4t_2E0,V3delta_2E0))
               => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0))) )
         => ? [V5t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V5t_2E0,V3delta_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3delta_2E0: tyop_2Enum_2Enum] :
          ( ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V4t_2E0,V3delta_2E0))
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0)))
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0))) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3delta_2E0: tyop_2Enum_2Enum] :
          ( ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V4t_2E0,V3delta_2E0))
             => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) )
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0))) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__SIGNAL,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3delta_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V3delta_2E0,V0t0_2E0)))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Earithmetic_2E_3C_3D_2E2(V4t_2E0,V3delta_2E0))
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ENEXT__LINORD,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ENEXT_2E2(V1a_2E0,V0t0_2E0))
    <=> ? [V2t1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V0t0_2E0,V2t1_2E0))
          & ! [V3t3_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(V0t0_2E0,V3t3_2E0))
             => p(c_2Earithmetic_2E_3C_3D_2E2(V2t1_2E0,V3t3_2E0)) )
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t1_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__LINORD,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V0t0_2E0))
    <=> ! [V2t1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V2t1_2E0))
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t1_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__LINORD,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V0t0_2E0))
    <=> ? [V2t1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V2t1_2E0))
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t1_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__LINORD,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3t1_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0))
          & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,V2a_2E0)))) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__LINORD,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V4t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ! [V3t1_2E0: tyop_2Enum_2Enum] :
              ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0))
                & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0))))) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t1_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__LINORD,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V4t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ? [V3t1_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t1_2E0))
              & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0))
              & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0))))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__LINORD,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V4t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ! [V3t1_2E0: tyop_2Enum_2Enum] :
              ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
                & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0))))) )
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__LINORD,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V4t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ? [V3t1_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t1_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0))
              & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0))))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__LINORD,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V4t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ! [V3t1_2E0: tyop_2Enum_2Enum] :
              ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0t0_2E0,V3t1_2E0))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3t1_2E0))
                & p(c_2ETemporal__Logic_2EUPTO_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0t0_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0))))) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t1_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2EF_2E0 )
     => ( ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V2t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,V2t_2E0)) )
       => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EALWAYS_2E1(V0a_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(F0_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2EF_2E0 )
     => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0a_2E0,V1x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EWHEN_2E3(F0_2E0,V0a_2E0,V1x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__WHEN,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
    <=> ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__NOT__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2EWHEN_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
            & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__AS__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V4t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V4t_2E0))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( p(c_2ETemporal__Logic_2EWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
              & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN__UNTIL,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) )
     => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V1a_2E0,V2x_2E0))
              & p(c_2ETemporal__Logic_2EWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V1a_2E0,V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__HW,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWATCH_2E3(V3q_2E0,V2a_2E0,V0t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
              | ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__UNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2EF_2E0 )
     => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EALWAYS_2E1(V0a_2E0) = c_2ETemporal__Logic_2EUNTIL_2E2(V0a_2E0,F0_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__UNTIL,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
     => ( ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),V2t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,V2t_2E0)) )
       => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0a_2E0,V1x_2E0))
          <=> ~ p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0a_2E0),F1_2E0,V1x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__UNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__UNTIL,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( ~ p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0))
              | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__UNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V4t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V4t_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
              & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__AS__UNTIL,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
    <=> ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__AS__UNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2EF_2E0 )
     => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V2t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EALWAYS_2E1(V0b_2E0) = c_2ETemporal__Logic_2EBEFORE_2E2(F0_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2EF_2E0 )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V1x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(F0_2E0,V0b_2E0,V1x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__BEFORE,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
              | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__AS__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0))
            | p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__AS__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__AS__BEFORE,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
    <=> ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__SWHEN__LEMMA,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0b_2E0))
        <=> ! [V2t1_2E0: tyop_2Enum_2Enum] :
            ? [V3t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,c_2Earithmetic_2E_2B_2E2(V3t2_2E0,V2t1_2E0))) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0,V1a_2E0),V0b_2E0))
          <=> ? [V5t1_2E0: tyop_2Enum_2Enum] :
              ! [V6t2_2E0: tyop_2Enum_2Enum] :
                ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V5t1_2E0)))
                & ~ p(c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V5t1_2E0))) ) )
       => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1a_2E0),V0b_2E0))
            <=> ! [V4t0_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V4t0_2E0) = c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,V4t0_2E0) ) )
         => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1a_2E0),V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F2_2E0,V1a_2E0),V0b_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V3t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,V3t_2E0)) )
       => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V0a_2E0,V1x_2E0))
          <=> ~ p(c_2ETemporal__Logic_2ESWHEN_2E3(F0_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V1x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2ET_2E0 )
     => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EEVENTUAL_2E1(V0a_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(F0_2E0,V0a_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
            | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__NOT__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> ~ p(c_2ETemporal__Logic_2ESWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
            | p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V4t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V4t_2E0))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) ) )
       => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V5t_2E0))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V5t_2E0))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V5t_2E0)) ) )
         => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
              ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
            <=> ( p(c_2ETemporal__Logic_2ESWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
                | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V2x_2E0)) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__NOT__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
            | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2ESWHEN_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__AS__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V3t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0a_2E0,V3t_2E0)) )
       => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V0a_2E0,V1x_2E0))
          <=> ~ p(c_2ETemporal__Logic_2ESUNTIL_2E3(F0_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0a_2E0),V1x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2ET_2E0 )
     => ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EEVENTUAL_2E1(V0a_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E2(F0_2E0,V0a_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__SUNTIL,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V5t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V5t_2E0)) )
     => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
       => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V4t_2E0))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V4t_2E0))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) ) )
         => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
              ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
            <=> ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
                | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V2x_2E0)) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__AS__SUNTIL,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
    <=> ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        | p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2ESUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__AS__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( ~ p(c_2ETemporal__Logic_2ESUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0))
            & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__AS__SBEFORE,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
     => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2t_2E0))
          <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V0b_2E0,V1x_2E0))
          <=> ~ p(c_2ETemporal__Logic_2ESBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),F1_2E0,V1x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__AS__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1t_2E0) = c_2Ebool_2EF_2E0 )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EEVENTUAL_2E1(V0b_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E2(V0b_2E0,F0_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__AS__SBEFORE,axiom,
    ! [F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V4t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
          <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
       => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
            ( p(c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
          <=> ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2x_2E0))
              | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V2x_2E0)) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__AS__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2ESBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__AS__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E2(V0b_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__AS__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( ~ p(c_2ETemporal__Logic_2ESBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0b_2E0,V2x_2E0))
            & p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V0b_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__AS__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V0b_2E0,V2x_2E0))
            | p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__SIMP,axiom,
    ! [F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V9t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F4_2E0,V9t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V5t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V5t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V7t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V7t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2EF_2E0 )
           => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V3t_2E0))
                <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
             => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                  ( ( c_2ETemporal__Logic_2EWHEN_2E2(F0_2E0,V0b_2E0) = c_2ETemporal__Logic_2EALWAYS_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0)) )
                  & ! [V4x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(F2_2E0,V0b_2E0,V4x_2E0) = c_2Ebool_2ET_2E0 )
                  & ! [V6x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,F3_2E0,V6x_2E0) = c_2Ebool_2ET_2E0 )
                  & ! [V8x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,F4_2E0,V8x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V8x_2E0) )
                  & ! [V10x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EWHEN_2E3(V1a_2E0,V1a_2E0,V10x_2E0) = c_2Ebool_2ET_2E0 ) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__SIMP,axiom,
    ! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V8t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V8t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V5t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V5t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
           => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EUNTIL_2E3(F0_2E0,V0b_2E0,V2x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2x_2E0) )
                & ! [V4x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EUNTIL_2E3(F1_2E0,V0b_2E0,V4x_2E0) = c_2Ebool_2ET_2E0 )
                & ( c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,F2_2E0) = c_2ETemporal__Logic_2EALWAYS_2E1(V1a_2E0) )
                & ! [V7x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,F3_2E0,V7x_2E0) = c_2Ebool_2ET_2E0 )
                & ! [V9x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V1a_2E0,V9x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V9x_2E0) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__SIMP,axiom,
    ! [F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V9t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F4_2E0,V9t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V5t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V5t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V7t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V7t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V2t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2t_2E0) = c_2Ebool_2EF_2E0 )
           => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V10t_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F5_2E0,V1a_2E0),V10t_2E0))
                <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V10t_2E0)) )
             => ( ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0),V3t_2E0))
                  <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) )
               => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                    ( ( c_2ETemporal__Logic_2EBEFORE_2E2(F0_2E0,V0b_2E0) = c_2ETemporal__Logic_2EALWAYS_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0b_2E0)) )
                    & ! [V4x_2E0: tyop_2Enum_2Enum] :
                        ( p(c_2ETemporal__Logic_2EBEFORE_2E3(F2_2E0,V0b_2E0,V4x_2E0))
                      <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4x_2E0)) )
                    & ! [V6x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,F3_2E0,V6x_2E0) = c_2Ebool_2ET_2E0 )
                    & ! [V8x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2EBEFORE_2E3(V1a_2E0,F4_2E0,V8x_2E0) = c_2Ebool_2EF_2E0 )
                    & ( c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V1a_2E0) = c_2ETemporal__Logic_2EALWAYS_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F5_2E0,V1a_2E0)) ) ) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__SIMP,axiom,
    ! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V8t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V8t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V4t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V4t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
           => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESWHEN_2E3(F0_2E0,V0b_2E0,V2x_2E0) = c_2Ebool_2EF_2E0 )
                & ( c_2ETemporal__Logic_2ESWHEN_2E2(F1_2E0,V0b_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E1(V0b_2E0) )
                & ! [V5x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,F2_2E0,V5x_2E0) = c_2Ebool_2EF_2E0 )
                & ! [V7x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESWHEN_2E3(V1a_2E0,F3_2E0,V7x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V7x_2E0) )
                & ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V1a_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E1(V1a_2E0) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__SIMP,axiom,
    ! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V8t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V8t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V4t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V4t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
           => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(F0_2E0,V0b_2E0,V2x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2x_2E0) )
                & ( c_2ETemporal__Logic_2ESUNTIL_2E2(F1_2E0,V0b_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E1(V0b_2E0) )
                & ! [V5x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,F2_2E0,V5x_2E0) = c_2Ebool_2EF_2E0 )
                & ! [V7x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,F3_2E0,V7x_2E0) = c_2Ebool_2ET_2E0 )
                & ! [V9x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(V1a_2E0,V1a_2E0,V9x_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V9x_2E0) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__SIMP,axiom,
    ! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V8t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V8t_2E0) = c_2Ebool_2ET_2E0 )
     => ( ! [V5t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V5t_2E0) = c_2Ebool_2ET_2E0 )
       => ( ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6t_2E0) = c_2Ebool_2EF_2E0 )
         => ( ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V3t_2E0) = c_2Ebool_2EF_2E0 )
           => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(F0_2E0,V0b_2E0,V2x_2E0) = c_2Ebool_2EF_2E0 )
                & ! [V4x_2E0: tyop_2Enum_2Enum] :
                    ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(F1_2E0,V0b_2E0,V4x_2E0))
                  <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4x_2E0)) )
                & ( c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,F2_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E1(V1a_2E0) )
                & ! [V7x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,F3_2E0,V7x_2E0) = c_2Ebool_2EF_2E0 )
                & ! [V9x_2E0: tyop_2Enum_2Enum] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(V1a_2E0,V1a_2E0,V9x_2E0) = c_2Ebool_2EF_2E0 ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EBEFORE_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
     => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ).

tff(thm_2ETemporal__Logic_2EIMMEDIATE__EVENT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0))
     => ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0) )
        & ! [V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E3(V3a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ET_2E0 )
        & ! [V4a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E3(V4a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2EF_2E0 )
        & ! [V5a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E3(V5a_2E0,V1b_2E0,V0t0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5a_2E0,V0t0_2E0) )
        & ! [V6a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(V6a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ET_2E0 )
        & ! [V7a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(V7a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2EF_2E0 ) ) ) ).

tff(thm_2ETemporal__Logic_2ENO__EVENT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V2t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1b_2E0),V0t0_2E0))
         => ( ! [V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E3(V3a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ET_2E0 )
            & ! [V4a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E3(V4a_2E0,V1b_2E0,V0t0_2E0) = c_2ETemporal__Logic_2EALWAYS_2E2(V4a_2E0,V0t0_2E0) )
            & ! [V5a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E3(V5a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ET_2E0 )
            & ! [V6a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E3(V6a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2EF_2E0 )
            & ! [V7a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E3(V7a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2EF_2E0 )
            & ! [V8a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E3(V8a_2E0,V1b_2E0,V0t0_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E2(V8a_2E0,V0t0_2E0) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESOME__EVENT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1b_2E0,V0t0_2E0))
      <=> ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0) = c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0) ) )
      & ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1b_2E0,V0t0_2E0))
      <=> ! [V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E3(V3a_2E0,V1b_2E0,V0t0_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E3(V3a_2E0,V1b_2E0,V0t0_2E0) ) )
      & ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1b_2E0,V0t0_2E0))
      <=> ! [V4a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E3(V4a_2E0,V1b_2E0,V0t0_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E3(V4a_2E0,V1b_2E0,V0t0_2E0) ) ) ) ).

tff(thm_2ETemporal__Logic_2EMORE__EVENT,axiom,
    ! [F5_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V7t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F5_2E0,V1a_2E0),V0b_2E0),V7t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V7t_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V7t_2E0)) ) )
     => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V6t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F4_2E0,V1a_2E0),V0b_2E0),V6t_2E0))
          <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V6t_2E0))
              & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V6t_2E0)) ) )
       => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V4t_2E0))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V4t_2E0))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V4t_2E0)) ) )
         => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V3t_2E0))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3t_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3t_2E0)) ) )
           => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5t_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F3_2E0,V1a_2E0),V0b_2E0),V5t_2E0))
                <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V5t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V5t_2E0)) ) )
             => ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V2t_2E0))
                  <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V2t_2E0)) ) )
               => ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                    ( ( c_2ETemporal__Logic_2EWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1a_2E0),V0b_2E0),V0b_2E0) )
                    & ( c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0,V1a_2E0),V0b_2E0),V0b_2E0) )
                    & ( c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EBEFORE_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F2_2E0,V1a_2E0),V0b_2E0),V0b_2E0) )
                    & ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F3_2E0,V1a_2E0),V0b_2E0),V0b_2E0) )
                    & ( c_2ETemporal__Logic_2ESUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F4_2E0,V1a_2E0),V0b_2E0),V0b_2E0) )
                    & ( c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F5_2E0,V1a_2E0),V0b_2E0),V0b_2E0) ) ) ) ) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__NEXT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2t_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0P_2E0),V1x_2E0))
        <=> ~ p(c_2ETemporal__Logic_2ENEXT_2E2(V0P_2E0,V1x_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EAND__NEXT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V3t_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0Q_2E0,V3t_2E0)) ) )
     => ! [V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ENEXT_2E2(V1P_2E0,V2x_2E0))
            & p(c_2ETemporal__Logic_2ENEXT_2E2(V0Q_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EOR__NEXT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V3t_2E0))
            | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0Q_2E0,V3t_2E0)) ) )
     => ! [V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ENEXT_2E2(V1P_2E0,V2x_2E0))
            | p(c_2ETemporal__Logic_2ENEXT_2E2(V0Q_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EIMP__NEXT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V3t_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V3t_2E0))
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0Q_2E0,V3t_2E0)) ) )
     => ! [V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V2x_2E0))
        <=> ( p(c_2ETemporal__Logic_2ENEXT_2E2(V1P_2E0,V2x_2E0))
           => p(c_2ETemporal__Logic_2ENEXT_2E2(V0Q_2E0,V2x_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEQUIV__NEXT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V3t_2E0))
        <=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V3t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0Q_2E0,V3t_2E0) ) )
     => ! [V0Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V0Q_2E0),V2x_2E0))
        <=> ( c_2ETemporal__Logic_2ENEXT_2E2(V1P_2E0,V2x_2E0) = c_2ETemporal__Logic_2ENEXT_2E2(V0Q_2E0,V2x_2E0) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2EALWAYS_2E1(V0a_2E0)) = c_2ETemporal__Logic_2EALWAYS_2E1(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2EEVENTUAL_2E1(V0a_2E0)) = c_2ETemporal__Logic_2EEVENTUAL_2E1(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2EWHEN_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2EWHEN_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2EUNTIL_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2EUNTIL_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2EBEFORE_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2EBEFORE_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2ESWHEN_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2ESWHEN_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2ESUNTIL_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2ESUNTIL_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__NEXT,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ENEXT_2E1(c_2ETemporal__Logic_2ESBEFORE_2E2(V0a_2E0,V1b_2E0)) = c_2ETemporal__Logic_2ESBEFORE_2E2(c_2ETemporal__Logic_2ENEXT_2E1(V0a_2E0),c_2ETemporal__Logic_2ENEXT_2E1(V1b_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V1P_2E0,V0t0_2E0))
    <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V0t0_2E0))
        & p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EALWAYS_2E1(V1P_2E0),V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1P_2E0,V0t0_2E0))
    <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1P_2E0,V0t0_2E0))
        | p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EEVENTUAL_2E1(V1P_2E0),V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2EWATCH__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EWATCH_2E3(V1q_2E0,V2b_2E0,V0t0_2E0))
    <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1q_2E0,V0t0_2E0))
        & p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2b_2E0,V0t0_2E0),c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EALWAYS_2E1(V1q_2E0),V0t0_2E0),c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EWATCH_2E2(V1q_2E0,V2b_2E0),V0t0_2E0))) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0),c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EWHEN_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0))
       => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0))
          & p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EUNTIL_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0))
        & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0))
          | p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2EBEFORE_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0),c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2ESWHEN_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0))
       => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0))
          & p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2ESUNTIL_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__REC,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V0t0_2E0))
        & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V0t0_2E0))
          | p(c_2ETemporal__Logic_2ENEXT_2E2(c_2ETemporal__Logic_2ESBEFORE_2E2(V2a_2E0,V1b_2E0),V0t0_2E0)) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__FIX,axiom,
    ! [V0y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V2x_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2x_2E0))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,c_2Earithmetic_2E_2B_2E2(V2x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
    <=> ( ( V0y_2E0 = c_2ETemporal__Logic_2EALWAYS_2E1(V1a_2E0) )
        | ! [V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V3x_2E0) = c_2Ebool_2EF_2E0 ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__FIX,axiom,
    ! [V0y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V2x_2E0))
        <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2x_2E0))
            | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,c_2Earithmetic_2E_2B_2E2(V2x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
    <=> ( ( V0y_2E0 = c_2ETemporal__Logic_2EEVENTUAL_2E1(V1a_2E0) )
        | ! [V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V3x_2E0) = c_2Ebool_2ET_2E0 ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__FIX,axiom,
    ! [V0y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3x_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3x_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,c_2Earithmetic_2E_2B_2E2(V3x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
    <=> ( ( V0y_2E0 = c_2ETemporal__Logic_2EWHEN_2E2(V2a_2E0,V1b_2E0) )
        | ( V0y_2E0 = c_2ETemporal__Logic_2ESWHEN_2E2(V2a_2E0,V1b_2E0) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__FIX,axiom,
    ! [V0y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,V3x_2E0))
        <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V3x_2E0))
           => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3x_2E0))
              & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0y_2E0,c_2Earithmetic_2E_2B_2E2(V3x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
    <=> ( ( V0y_2E0 = c_2ETemporal__Logic_2EUNTIL_2E2(V2a_2E0,V1b_2E0) )
        | ( V0y_2E0 = c_2ETemporal__Logic_2ESUNTIL_2E2(V2a_2E0,V1b_2E0) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__FIX,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2y_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V3x_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2y_2E0,V3x_2E0))
        <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,V3x_2E0))
            & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V3x_2E0))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2y_2E0,c_2Earithmetic_2E_2B_2E2(V3x_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
    <=> ( ( V2y_2E0 = c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0) )
        | ( V2y_2E0 = c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0) ) ) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,V0t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) )
          & ! [V5d_2E0: tyop_2Enum_2Enum] :
              ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__INVARIANT,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t0_2E0: tyop_2Enum_2Enum] :
      ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1a_2E0,V0b_2E0,V2t0_2E0))
    <=> ? [V3J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,V2t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0))) )
             => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V2t0_2E0)))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ? [V3J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,V0t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) )
          & ! [V5d_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0)))
             => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V0t0_2E0))
    <=> ? [V2J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2J_2E0,V0t0_2E0))
          & ! [V3t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2J_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0)))
             => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2J_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1b_2E0,V0t0_2E0))
    <=> ? [V2J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
          ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,V0t0_2E0)))
          & ! [V3t_2E0: tyop_2Enum_2Enum] :
              ( p(c_2Eprim__rec_2E_3C_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0))))
              | ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V3t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))))
                & ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2J_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ? [V3J1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,V0t0_2E0))
            & ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) )
            & ! [V5d_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) ) )
        & ? [V6J2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,V0t0_2E0)))
            & ! [V7t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))))
                | ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
            & ! [V8t_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))))
                  & ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ? [V3J1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,V0t0_2E0))
            & ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) ) ) )
        & ? [V5J2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,V0t0_2E0)))
            & ! [V6t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))))
                | ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
            & ! [V7t_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))))
                  & ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V5J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__INVARIANT,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
    <=> ( ? [V3J1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,V0t0_2E0))
            & ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) )
            & ! [V5d_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3J1_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0)))
               => ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V5d_2E0,V0t0_2E0))) ) )
        & ? [V6J2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,V0t0_2E0)))
            & ! [V7t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))))
                | ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
            & ! [V8t_2E0: tyop_2Enum_2Enum] :
                ( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))))
                  & ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6J2_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))) = c_2Enum_2E0_2E0 ) )
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2ETemporal__Logic_2EALWAYS__IDEM,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EALWAYS_2E1(V0a_2E0) = c_2ETemporal__Logic_2EALWAYS_2E1(c_2ETemporal__Logic_2EALWAYS_2E1(V0a_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EEVENTUAL__IDEM,axiom,
    ! [V0a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EEVENTUAL_2E1(V0a_2E0) = c_2ETemporal__Logic_2EEVENTUAL_2E1(c_2ETemporal__Logic_2EEVENTUAL_2E1(V0a_2E0)) ) ).

tff(thm_2ETemporal__Logic_2EWHEN__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EWHEN_2E2(c_2ETemporal__Logic_2EWHEN_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2EUNTIL__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EUNTIL_2E2(c_2ETemporal__Logic_2EUNTIL_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2EBEFORE__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2EBEFORE_2E2(c_2ETemporal__Logic_2EBEFORE_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2ESWHEN__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESWHEN_2E2(c_2ETemporal__Logic_2ESWHEN_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2ESUNTIL__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESUNTIL_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESUNTIL_2E2(c_2ETemporal__Logic_2ESUNTIL_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2ESBEFORE__IDEM,axiom,
    ! [V0b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0) = c_2ETemporal__Logic_2ESBEFORE_2E2(c_2ETemporal__Logic_2ESBEFORE_2E2(V1a_2E0,V0b_2E0),V0b_2E0) ) ).

tff(thm_2ETemporal__Logic_2ENOT__ALWAYS,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2EALWAYS_2E2(V1a_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2EEVENTUAL_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__EVENTUAL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V2t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,V2t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2EEVENTUAL_2E2(V1a_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2EALWAYS_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1a_2E0),V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__WHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2EWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2ESWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__UNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2EUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2ESBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__BEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2EBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2ESUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__SWHEN,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2ESWHEN_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2EWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__SUNTIL,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2ESUNTIL_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2EBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

tff(thm_2ETemporal__Logic_2ENOT__SBEFORE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V3t_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V3t_2E0)) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2ETemporal__Logic_2ESBEFORE_2E3(V2a_2E0,V1b_2E0,V0t0_2E0))
        <=> p(c_2ETemporal__Logic_2EUNTIL_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V2a_2E0),V1b_2E0,V0t0_2E0)) ) ) ).

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