ITP001 Axioms: ITP080

ITP001 Axioms: ITP080_7.ax

%------------------------------------------------------------------------------
% File     : ITP080_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    : Omega_Automata.ax [Gau19]
%          : HL4080_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  194 (  51 unt;  88 typ;   0 def)
%            Number of atoms       :  936 ( 149 equ)
%            Maximal formula atoms :  128 (   4 avg)
%            Number of connectives : 1008 ( 178   ~; 100   |; 531   &)
%                                         ( 150 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   9 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   83 (  45   >;  38   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   85 (  85 usr;  33 con; 0-4 aty)
%            Number of variables   :  868 ( 631   !; 217   ?; 868   :)
%                                         (  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_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_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_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EMOD_2E0,type,
    c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EMOD_2E2,type,
    c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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_2EPast__Temporal__Logic_2EPALWAYS_2E0,type,
    c_2EPast__Temporal__Logic_2EPALWAYS_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2EPast__Temporal__Logic_2EPALWAYS_2E1,type,
    c_2EPast__Temporal__Logic_2EPALWAYS_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2EPast__Temporal__Logic_2EPBEFORE_2E0,type,
    c_2EPast__Temporal__Logic_2EPBEFORE_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_2EPast__Temporal__Logic_2EPBEFORE_2E2,type,
    c_2EPast__Temporal__Logic_2EPBEFORE_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_2EPast__Temporal__Logic_2EPEVENTUAL_2E0,type,
    c_2EPast__Temporal__Logic_2EPEVENTUAL_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1,type,
    c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2EPast__Temporal__Logic_2EPNEXT_2E0,type,
    c_2EPast__Temporal__Logic_2EPNEXT_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2EPast__Temporal__Logic_2EPNEXT_2E1,type,
    c_2EPast__Temporal__Logic_2EPNEXT_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2EPast__Temporal__Logic_2EPSBEFORE_2E0,type,
    c_2EPast__Temporal__Logic_2EPSBEFORE_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_2EPast__Temporal__Logic_2EPSBEFORE_2E2,type,
    c_2EPast__Temporal__Logic_2EPSBEFORE_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_2EPast__Temporal__Logic_2EPSNEXT_2E0,type,
    c_2EPast__Temporal__Logic_2EPSNEXT_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2EPast__Temporal__Logic_2EPSNEXT_2E1,type,
    c_2EPast__Temporal__Logic_2EPSNEXT_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2EPast__Temporal__Logic_2EPSUNTIL_2E0,type,
    c_2EPast__Temporal__Logic_2EPSUNTIL_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_2EPast__Temporal__Logic_2EPSUNTIL_2E2,type,
    c_2EPast__Temporal__Logic_2EPSUNTIL_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_2EPast__Temporal__Logic_2EPSWHEN_2E0,type,
    c_2EPast__Temporal__Logic_2EPSWHEN_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_2EPast__Temporal__Logic_2EPSWHEN_2E2,type,
    c_2EPast__Temporal__Logic_2EPSWHEN_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_2EPast__Temporal__Logic_2EPUNTIL_2E0,type,
    c_2EPast__Temporal__Logic_2EPUNTIL_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_2EPast__Temporal__Logic_2EPUNTIL_2E2,type,
    c_2EPast__Temporal__Logic_2EPUNTIL_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_2EPast__Temporal__Logic_2EPWHEN_2E0,type,
    c_2EPast__Temporal__Logic_2EPWHEN_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_2EPast__Temporal__Logic_2EPWHEN_2E2,type,
    c_2EPast__Temporal__Logic_2EPWHEN_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_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_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_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b1,axiom,
    ! [A_27a: $tType,A_27b1: $tType,X0_2E0: A_27a,X1_2E0: A_27b1] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b1,X0_2E0,X1_2E0) = app_2E2(A_27b1,tyop_2Epair_2Eprod(A_27a,A_27b1),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b1,tyop_2Epair_2Eprod(A_27a,A_27b1)),c_2Epair_2E_2C_2E0(A_27a,A_27b1),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b2,axiom,
    ! [A_27a: $tType,A_27b2: $tType,X0_2E0: A_27a,X1_2E0: A_27b2] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b2,X0_2E0,X1_2E0) = app_2E2(A_27b2,tyop_2Epair_2Eprod(A_27a,A_27b2),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b2,tyop_2Epair_2Eprod(A_27a,A_27b2)),c_2Epair_2E_2C_2E0(A_27a,A_27b2),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27state_2CA_27state_29,axiom,
    ! [A_27a: $tType,A_27state: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Epair_2Eprod(A_27state,A_27state)] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27state,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27state,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27input_20mono_2EA_27state,axiom,
    ! [A_27input: $tType,A_27state: $tType,X0_2E0: A_27input,X1_2E0: A_27state] : ( c_2Epair_2E_2C_2E2(A_27input,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27input,A_27state),app_2E2(A_27input,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27input,A_27state)),c_2Epair_2E_2C_2E0(A_27input,A_27state),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27state_20mono_2EA_27state,axiom,
    ! [A_27state: $tType,X0_2E0: A_27state,X1_2E0: A_27state] : ( c_2Epair_2E_2C_2E2(A_27state,A_27state,X0_2E0,X1_2E0) = app_2E2(A_27state,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(A_27state,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27state,A_27state)),c_2Epair_2E_2C_2E0(A_27state,A_27state),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b1_29,axiom,
    ! [A_27a: $tType,A_27b1: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b2_29,axiom,
    ! [A_27a: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27input_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27state_29,axiom,
    ! [A_27input: $tType,A_27state: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),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_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_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_2Earithmetic_2EMOD_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_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_2EMOD_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(arityeq1_2Ec_2EPast__Temporal__Logic_2EPALWAYS_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EPast__Temporal__Logic_2EPALWAYS_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2EPast__Temporal__Logic_2EPALWAYS_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPBEFORE_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_2EPast__Temporal__Logic_2EPBEFORE_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_2EPast__Temporal__Logic_2EPBEFORE_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EPast__Temporal__Logic_2EPEVENTUAL_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2EPast__Temporal__Logic_2EPEVENTUAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2EPast__Temporal__Logic_2EPNEXT_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EPast__Temporal__Logic_2EPNEXT_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2EPast__Temporal__Logic_2EPNEXT_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPSBEFORE_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_2EPast__Temporal__Logic_2EPSBEFORE_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_2EPast__Temporal__Logic_2EPSBEFORE_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EPast__Temporal__Logic_2EPSNEXT_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2EPast__Temporal__Logic_2EPSNEXT_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2EPast__Temporal__Logic_2EPSNEXT_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPSUNTIL_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_2EPast__Temporal__Logic_2EPSUNTIL_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_2EPast__Temporal__Logic_2EPSUNTIL_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPSWHEN_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_2EPast__Temporal__Logic_2EPSWHEN_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_2EPast__Temporal__Logic_2EPSWHEN_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPUNTIL_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_2EPast__Temporal__Logic_2EPUNTIL_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_2EPast__Temporal__Logic_2EPUNTIL_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EPast__Temporal__Logic_2EPWHEN_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_2EPast__Temporal__Logic_2EPWHEN_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_2EPast__Temporal__Logic_2EPWHEN_2E0,X0_2E0),X1_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(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_2EOmega__Automata_2EDET__OMEGA__EXISTS__FORALL__THEOREM,axiom,
    ! [A_27input: $tType,A_27state: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)))] :
      ( ! [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V0t0_2E0: tyop_2Enum_2Enum,V10t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F1_2E0,V8q_2E0),V0t0_2E0),V10t_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t_2E0,V0t0_2E0)) )
     => ( ! [V5q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V0t0_2E0: tyop_2Enum_2Enum,V7t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F0_2E0,V5q_2E0),V0t0_2E0),V7t_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0)) )
       => ! [V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V2TransRel_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state),V3InitVal_2E0: A_27state,V4Accept_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool)] :
            ( ? [V5q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
                ( ( app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,V0t0_2E0) = V3InitVal_2E0 )
                & ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = app_2E2(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state,V2TransRel_2E0,c_2Epair_2E_2C_2E2(A_27input,A_27state,app_2E2(tyop_2Enum_2Enum,A_27input,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0)))) )
                & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool,V4Accept_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V1i_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F0_2E0,V5q_2E0),V0t0_2E0)))) )
          <=> ! [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
                ( ( ( app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,V0t0_2E0) = V3InitVal_2E0 )
                  & ! [V9t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = app_2E2(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state,V2TransRel_2E0,c_2Epair_2E_2C_2E2(A_27input,A_27state,app_2E2(tyop_2Enum_2Enum,A_27input,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))) ) )
               => p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool,V4Accept_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V1i_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F1_2E0,V8q_2E0),V0t0_2E0)))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ENEG__DET__AUTOMATA,axiom,
    ! [A_27input: $tType,A_27state: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)))] :
      ( ! [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V0t0_2E0: tyop_2Enum_2Enum,V10t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F1_2E0,V8q_2E0),V0t0_2E0),V10t_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t_2E0,V0t0_2E0)) )
     => ( ! [V5q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V0t0_2E0: tyop_2Enum_2Enum,V7t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F0_2E0,V5q_2E0),V0t0_2E0),V7t_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0)) )
       => ! [V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),V2TransRel_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state),V3InitVal_2E0: A_27state,V4Accept_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool)] :
            ( ~ ? [V5q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
                  ( ( app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,V0t0_2E0) = V3InitVal_2E0 )
                  & ! [V6t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = app_2E2(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state,V2TransRel_2E0,c_2Epair_2E_2C_2E2(A_27input,A_27state,app_2E2(tyop_2Enum_2Enum,A_27input,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27state,V5q_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0)))) )
                  & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool,V4Accept_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V1i_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F0_2E0,V5q_2E0),V0t0_2E0)))) )
          <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
                ( ( app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,V0t0_2E0) = V3InitVal_2E0 )
                & ! [V9t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = app_2E2(tyop_2Epair_2Eprod(A_27input,A_27state),A_27state,V2TransRel_2E0,c_2Epair_2E_2C_2E2(A_27input,A_27state,app_2E2(tyop_2Enum_2Enum,A_27input,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27state,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))) )
                & ~ p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),tyop_2Emin_2Ebool,V4Accept_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27input),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),V1i_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)),F1_2E0,V8q_2E0),V0t0_2E0)))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EOMEGA__CONJ__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2Psi2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool),V3Psi1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool),V4Phi__R2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V5Phi__R1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V6Phi__I2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V7Phi__I1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] :
      ( ( ? [V8q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)] :
            ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,V0t0_2E0)))
            & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V1i_2E0,V8q1_2E0))) )
        & ? [V10q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
            ( p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V10q2_2E0,V0t0_2E0)))
            & ! [V11t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V10q2_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),V1i_2E0,V10q2_2E0))) ) )
    <=> ? [V12q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V13q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
          ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V12q1_2E0,V0t0_2E0)))
          & p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V13q2_2E0,V0t0_2E0)))
          & ! [V14t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V12q1_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V13q2_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0))))) )
          & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V1i_2E0,V12q1_2E0)))
          & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),V1i_2E0,V13q2_2E0))) ) ) ).

tff(thm_2EOmega__Automata_2EOMEGA__DISJ__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2Psi2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool),V3Psi1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool),V4Phi__R2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V5Phi__R1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V6Phi__I2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V7Phi__I1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] :
      ( ( ? [V8q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)] :
            ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,V0t0_2E0)))
            & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V1i_2E0,V8q1_2E0))) )
        | ? [V10q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
            ( p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V10q2_2E0,V0t0_2E0)))
            & ! [V11t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V10q2_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),V1i_2E0,V10q2_2E0))) ) )
    <=> ? [V12p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V14q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
          ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0))
              & p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V13q1_2E0,V0t0_2E0))) )
            | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0))
              & p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V14q2_2E0,V0t0_2E0))) ) )
          & ! [V15t_2E0: tyop_2Enum_2Enum] :
              ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V13q1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V14q2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
          & ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0))
              & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V1i_2E0,V13q1_2E0))) )
            | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0))
              & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2),V1i_2E0,V14q2_2E0))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__G,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)] :
      ( ( ~ ! [V3t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_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))) )
      & ( ( ! [V5t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0)))
          & ! [V6t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) )
      <=> ! [V7t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0)))
            & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) ) )
      & ( ( ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0)))
          | ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0))) )
      <=> ? [V10p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V11q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,V0t0_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,V0t0_2E0))
            & ! [V12t_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0)))
                    | ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0))) ) )
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0)))
                    | ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0))) ) ) )
            & ! [V13t_2E0: tyop_2Enum_2Enum] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))
                | ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__F,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)] :
      ( ( ~ ? [V3t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_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))) )
      & ( ( ? [V5t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0)))
          | ? [V6t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) )
      <=> ? [V7t_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0)))
            | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0))) ) )
      & ( ( ? [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0)))
          & ? [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0))) )
      <=> ? [V10p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V11q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,V0t0_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,V0t0_2E0))
            & ! [V12t_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0)))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0))) ) )
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0)))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,V0t0_2E0))) ) ) )
            & ? [V13t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__FG,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V2a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V18t_2E0: tyop_2Enum_2Enum,V0t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V2a_2E0),V18t_2E0),V0t0_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_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)] :
          ( ( ~ ? [V3t1_2E0: tyop_2Enum_2Enum] :
                ! [V4t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V3t1_2E0,c_2Earithmetic_2E_2B_2E2(V4t2_2E0,V0t0_2E0))))
          <=> ! [V5t1_2E0: tyop_2Enum_2Enum] :
              ? [V6t2_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) )
          & ( ( ? [V7t1_2E0: tyop_2Enum_2Enum] :
                ! [V8t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V7t1_2E0,c_2Earithmetic_2E_2B_2E2(V8t2_2E0,V0t0_2E0))))
              & ? [V9t1_2E0: tyop_2Enum_2Enum] :
                ! [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,c_2Earithmetic_2E_2B_2E2(V10t2_2E0,V0t0_2E0)))) )
          <=> ? [V11t1_2E0: tyop_2Enum_2Enum] :
              ! [V12t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0))))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0)))) ) )
          & ( ( ? [V13t1_2E0: tyop_2Enum_2Enum] :
                ! [V14t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V13t1_2E0,c_2Earithmetic_2E_2B_2E2(V14t2_2E0,V0t0_2E0))))
              | ? [V15t1_2E0: tyop_2Enum_2Enum] :
                ! [V16t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0)))) )
          <=> ? [V17q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,V0t0_2E0))
                & ! [V18t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V2a_2E0),V18t_2E0),V0t0_2E0)) )
                & ? [V19t1_2E0: tyop_2Enum_2Enum] :
                  ! [V20t2_2E0: tyop_2Enum_2Enum] :
                    ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0))))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0)))) ) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__GF,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1b_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V18t_2E0: tyop_2Enum_2Enum,V0t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1b_2E0),V18t_2E0),V0t0_2E0))
        <=> ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_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)] :
          ( ( ~ ! [V3t1_2E0: tyop_2Enum_2Enum] :
                ? [V4t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V3t1_2E0,c_2Earithmetic_2E_2B_2E2(V4t2_2E0,V0t0_2E0))))
          <=> ? [V5t1_2E0: tyop_2Enum_2Enum] :
              ! [V6t2_2E0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) )
          & ( ( ! [V7t1_2E0: tyop_2Enum_2Enum] :
                ? [V8t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V7t1_2E0,c_2Earithmetic_2E_2B_2E2(V8t2_2E0,V0t0_2E0))))
              | ! [V9t1_2E0: tyop_2Enum_2Enum] :
                ? [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,c_2Earithmetic_2E_2B_2E2(V10t2_2E0,V0t0_2E0)))) )
          <=> ! [V11t1_2E0: tyop_2Enum_2Enum] :
              ? [V12t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0))))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0)))) ) )
          & ( ( ! [V13t1_2E0: tyop_2Enum_2Enum] :
                ? [V14t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V13t1_2E0,c_2Earithmetic_2E_2B_2E2(V14t2_2E0,V0t0_2E0))))
              & ! [V15t1_2E0: tyop_2Enum_2Enum] :
                ? [V16t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0)))) )
          <=> ? [V17q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,V0t0_2E0))
                & ! [V18t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1b_2E0),V18t_2E0),V0t0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0))) )
                & ! [V19t1_2E0: tyop_2Enum_2Enum] :
                  ? [V20t2_2E0: tyop_2Enum_2Enum] :
                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17q_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0)))) ) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOREL__HIERARCHY__G,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,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,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V0t0_2E0)))
      <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))) )
            & ? [V5t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0))) ) )
      & ( ! [V6t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0)))
      <=> ? [V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,V0t0_2E0))
            & ! [V8t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V0t0_2E0))) ) )
            & ? [V9t1_2E0: tyop_2Enum_2Enum] :
              ! [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,c_2Earithmetic_2E_2B_2E2(V10t2_2E0,V0t0_2E0)))) ) )
      & ( ! [V11t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
      <=> ? [V12q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12q_2E0,V0t0_2E0))
            & ! [V13t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0))) ) )
            & ! [V14t1_2E0: tyop_2Enum_2Enum] :
              ? [V15t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,c_2Earithmetic_2E_2B_2E2(V15t2_2E0,V0t0_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOREL__HIERARCHY__F,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,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,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V2t_2E0,V0t0_2E0)))
      <=> ? [V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,V0t0_2E0))
            & ! [V4t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))))
              <=> ( 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,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0))) ) )
            & ? [V5t1_2E0: tyop_2Enum_2Enum] :
              ! [V6t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) )
      & ( ? [V7t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V7t_2E0,V0t0_2E0)))
      <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V8q_2E0,V0t0_2E0))
            & ! [V9t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V8q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0))) ) )
            & ! [V10t1_2E0: tyop_2Enum_2Enum] :
              ? [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V0t0_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2EBOREL__HIERARCHY__FG,axiom,
    ! [V0t0_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ( ? [V2t1_2E0: tyop_2Enum_2Enum] :
          ! [V3t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V2t1_2E0,c_2Earithmetic_2E_2B_2E2(V3t2_2E0,V0t0_2E0))))
      <=> ? [V4q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q_2E0,V0t0_2E0))
            & ! [V5t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0)))
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0)))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V5t_2E0,V0t0_2E0)))) ) )
            & ? [V6t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,V0t0_2E0))) ) )
      & ( ? [V7t1_2E0: tyop_2Enum_2Enum] :
          ! [V8t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V7t1_2E0,c_2Earithmetic_2E_2B_2E2(V8t2_2E0,V0t0_2E0))))
      <=> ? [V9p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V10q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,V0t0_2E0))
            & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,V0t0_2E0))
            & ! [V11t_2E0: tyop_2Enum_2Enum] :
                ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
                 => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))) )
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0))))
                 => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
                    | ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0))) ) )
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0))))
                <=> ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
                      & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
                      & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0))) )
                    | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0)))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,c_2Earithmetic_2E_2B_2E2(V11t_2E0,V0t0_2E0))) ) ) ) )
            & ! [V12t1_2E0: tyop_2Enum_2Enum] :
              ? [V13t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V9p_2E0,c_2Earithmetic_2E_2B_2E2(V12t1_2E0,c_2Earithmetic_2E_2B_2E2(V13t2_2E0,V0t0_2E0))))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V10q_2E0,c_2Earithmetic_2E_2B_2E2(V12t1_2E0,c_2Earithmetic_2E_2B_2E2(V13t2_2E0,V0t0_2E0)))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ETEMP__OPS__DEFS__TO__OMEGA,axiom,
    ! [V0l_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)] :
      ( ( ( V0l_2E0 = c_2ETemporal__Logic_2ENEXT_2E1(V2a_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V3t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V3t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Enum_2ESUC_2E1(V3t_2E0)) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2EALWAYS_2E1(V2a_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V4t_2E0))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V4t_2E0))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V4t_2E0))) ) )
          & ! [V5t1_2E0: tyop_2Enum_2Enum] :
            ? [V6t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,V6t2_2E0)))
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,V6t2_2E0))) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2EEVENTUAL_2E1(V2a_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V7t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V7t_2E0))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V7t_2E0))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V7t_2E0))) ) )
          & ! [V8t1_2E0: tyop_2Enum_2Enum] :
            ? [V9t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V8t1_2E0,V9t2_2E0)))
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V8t1_2E0,V9t2_2E0))) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2ESUNTIL_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V10t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V10t_2E0))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V10t_2E0))
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V10t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V10t_2E0))) ) ) )
          & ! [V11t1_2E0: tyop_2Enum_2Enum] :
            ? [V12t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,V12t2_2E0)))
             => ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,V12t2_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,V12t2_2E0))) ) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2ESWHEN_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V13t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V13t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V13t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V13t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V13t_2E0))) )
          & ! [V14t1_2E0: tyop_2Enum_2Enum] :
            ? [V15t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,V15t2_2E0)))
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,V15t2_2E0))) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2ESBEFORE_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V16t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V16t_2E0))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V16t_2E0))
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V16t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V16t_2E0))) ) ) )
          & ! [V17t1_2E0: tyop_2Enum_2Enum] :
            ? [V18t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0)))
             => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0))) ) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2EUNTIL_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V19t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V19t_2E0))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V19t_2E0))
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V19t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V19t_2E0))) ) ) )
          & ! [V20t1_2E0: tyop_2Enum_2Enum] :
            ? [V21t2_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V20t1_2E0,V21t2_2E0)))
             => ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V20t1_2E0,V21t2_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V20t1_2E0,V21t2_2E0))) ) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2EWHEN_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V22t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V22t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V22t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V22t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V22t_2E0))) )
          & ! [V23t1_2E0: tyop_2Enum_2Enum] :
            ? [V24t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V23t1_2E0,V24t2_2E0)))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V23t1_2E0,V24t2_2E0))) ) ) )
      & ( ( V0l_2E0 = c_2ETemporal__Logic_2EBEFORE_2E2(V2a_2E0,V1b_2E0) )
      <=> ( p(c_2Ebool_2ET_2E0)
          & ! [V25t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V25t_2E0))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V25t_2E0))
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V25t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V25t_2E0))) ) ) )
          & ! [V26t1_2E0: tyop_2Enum_2Enum] :
            ? [V27t2_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Earithmetic_2E_2B_2E2(V26t1_2E0,V27t2_2E0)))
             => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V26t1_2E0,V27t2_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V26t1_2E0,V27t2_2E0))) ) ) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPNEXT_2E1(V2a_2E0) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
          & ! [V28t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V28t_2E0)) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V28t_2E0) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPSNEXT_2E1(V2a_2E0) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
          & ! [V29t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V29t_2E0)) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V29t_2E0) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPALWAYS_2E1(V2a_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
          & ! [V30t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V30t_2E0)))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V30t_2E0))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V30t_2E0)) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1(V2a_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
          & ! [V31t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V31t_2E0)))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V31t_2E0))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V31t_2E0)) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSUNTIL_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
          & ! [V32t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V32t_2E0)))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V32t_2E0))
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V32t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V32t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSWHEN_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
          & ! [V33t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V33t_2E0)))
            <=> ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V33t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V33t_2E0)) )
                | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V33t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V33t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSBEFORE_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
          & ! [V34t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V34t_2E0)))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V34t_2E0))
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V34t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V34t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPUNTIL_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
          & ! [V35t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V35t_2E0)))
            <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V35t_2E0))
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V35t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V35t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPWHEN_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
          & ! [V36t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V36t_2E0)))
            <=> ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V36t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V36t_2E0)) )
                | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V36t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V36t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) )
      & ( ( V0l_2E0 = c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPBEFORE_2E2(V2a_2E0,V1b_2E0)) )
      <=> ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
          & ! [V37t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,c_2Enum_2ESUC_2E1(V37t_2E0)))
            <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V37t_2E0))
                & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V37t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0l_2E0,V37t_2E0)) ) ) )
          & p(c_2Ebool_2ET_2E0) ) ) ) ).

tff(thm_2EOmega__Automata_2EAUTOMATON__TEMP__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0phi_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),V3Phi__R2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V4Phi__R1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),V5Phi__I2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Ebool),V6Phi__I1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),V7Phi__F_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),tyop_2Emin_2Ebool),V8Phi_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( ? [V9q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
            ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,V6Phi__I1_2E0,V9q1_2E0))
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,V4Phi__R1_2E0,V9q1_2E0))
            & ? [V10q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
                ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Ebool,V5Phi__I2_2E0,V10q2_2E0))
                & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V3Phi__R2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10q2_2E0,V9q1_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),tyop_2Emin_2Ebool,V7Phi__F_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V9q1_2E0,V10q2_2E0))) ) )
      <=> ? [V11q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V12q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
            ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,V6Phi__I1_2E0,V11q1_2E0))
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Ebool,V5Phi__I2_2E0,V12q2_2E0))
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,V4Phi__R1_2E0,V11q1_2E0))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V3Phi__R2_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V12q2_2E0,V11q1_2E0)))
            & p(app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),tyop_2Emin_2Ebool,V7Phi__F_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V11q1_2E0,V12q2_2E0))) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2ETemporal__Logic_2ENEXT_2E1(V0phi_2E0)))
      <=> ? [V13q0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V14q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V15t_2E0: tyop_2Enum_2Enum] :
                ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13q0_2E0,V15t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0phi_2E0,V15t_2E0) )
                & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V14q1_2E0,V15t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13q0_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V14q1_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPNEXT_2E1(V0phi_2E0)))
      <=> ? [V16q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V16q_2E0,c_2Enum_2E0_2E0))
            & ! [V17t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V16q_2E0,c_2Earithmetic_2E_2B_2E2(V17t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0phi_2E0,V17t_2E0) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V16q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPSNEXT_2E1(V0phi_2E0)))
      <=> ? [V18q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V18q_2E0,c_2Enum_2E0_2E0))
            & ! [V19t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V18q_2E0,c_2Earithmetic_2E_2B_2E2(V19t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0phi_2E0,V19t_2E0) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V18q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPALWAYS_2E1(V2a_2E0))))
      <=> ? [V20q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V20q_2E0,c_2Enum_2E0_2E0))
            & ! [V21t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V20q_2E0,c_2Earithmetic_2E_2B_2E2(V21t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V21t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V20q_2E0,V21t_2E0)) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V20q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1(V2a_2E0))))
      <=> ? [V22q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V22q_2E0,c_2Enum_2E0_2E0))
            & ! [V23t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V22q_2E0,c_2Earithmetic_2E_2B_2E2(V23t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V23t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V22q_2E0,V23t_2E0)) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V22q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSUNTIL_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V24q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V24q_2E0,c_2Enum_2E0_2E0))
            & ! [V25t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V24q_2E0,c_2Earithmetic_2E_2B_2E2(V25t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V25t_2E0))
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V25t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V24q_2E0,V25t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V24q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSWHEN_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V26q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V26q_2E0,c_2Enum_2E0_2E0))
            & ! [V27t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V26q_2E0,c_2Earithmetic_2E_2B_2E2(V27t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V27t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V27t_2E0)) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V27t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V26q_2E0,V27t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V26q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPSNEXT_2E1(c_2EPast__Temporal__Logic_2EPSBEFORE_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V28q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V28q_2E0,c_2Enum_2E0_2E0))
            & ! [V29t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V28q_2E0,c_2Earithmetic_2E_2B_2E2(V29t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V29t_2E0))
                  & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V29t_2E0))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V28q_2E0,V29t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V28q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPUNTIL_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V30q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V30q_2E0,c_2Enum_2E0_2E0))
            & ! [V31t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V30q_2E0,c_2Earithmetic_2E_2B_2E2(V31t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V31t_2E0))
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V31t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V30q_2E0,V31t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V30q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPWHEN_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V32q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V32q_2E0,c_2Enum_2E0_2E0))
            & ! [V33t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V32q_2E0,c_2Earithmetic_2E_2B_2E2(V33t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V33t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V33t_2E0)) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V33t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V32q_2E0,V33t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V32q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,c_2EPast__Temporal__Logic_2EPNEXT_2E1(c_2EPast__Temporal__Logic_2EPBEFORE_2E2(V2a_2E0,V1b_2E0))))
      <=> ? [V34q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V34q_2E0,c_2Enum_2E0_2E0))
            & ! [V35t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V34q_2E0,c_2Earithmetic_2E_2B_2E2(V35t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
              <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V35t_2E0))
                  & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V35t_2E0))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V34q_2E0,V35t_2E0)) ) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V8Phi_2E0,V34q_2E0)) ) ) ) ).

tff(thm_2EOmega__Automata_2EBUECHI__TRANSLATION,axiom,
    ! [V0phi_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),V3Phi_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2ENEXT_2E1(V0phi_2E0)))
      <=> ? [V4q0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V5q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V6t_2E0: tyop_2Enum_2Enum] :
                ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q0_2E0,V6t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0phi_2E0,V6t_2E0) )
                & ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V5q1_2E0,V6t_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V4q0_2E0,c_2Earithmetic_2E_2B_2E2(V6t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V5q1_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2EALWAYS_2E1(V2a_2E0)))
      <=> ? [V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V8t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,V8t_2E0))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V8t_2E0))
                  & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
            & ! [V9t1_2E0: tyop_2Enum_2Enum] :
              ? [V10t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,V10t2_2E0)))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,V10t2_2E0))) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V7q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2EEVENTUAL_2E1(V2a_2E0)))
      <=> ? [V11q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V12t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,V12t_2E0))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V12t_2E0))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V12t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) )
            & ! [V13t1_2E0: tyop_2Enum_2Enum] :
              ? [V14t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11q_2E0,c_2Earithmetic_2E_2B_2E2(V13t1_2E0,V14t2_2E0)))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V13t1_2E0,V14t2_2E0))) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V11q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2ESUNTIL_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V15q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V16t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V15q_2E0,V16t_2E0))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V16t_2E0))
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V16t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V15q_2E0,c_2Earithmetic_2E_2B_2E2(V16t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
            & ! [V17t1_2E0: tyop_2Enum_2Enum] :
              ? [V18t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V15q_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0)))
               => ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0)))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V17t1_2E0,V18t2_2E0))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V15q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2EUNTIL_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V19q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V20t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V19q_2E0,V20t_2E0))
              <=> ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V20t_2E0))
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V20t_2E0))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V19q_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
            & ! [V21t1_2E0: tyop_2Enum_2Enum] :
              ? [V22t2_2E0: tyop_2Enum_2Enum] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V19q_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,V22t2_2E0)))
               => ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,V22t2_2E0)))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,V22t2_2E0))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V19q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2ESWHEN_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V23q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V24t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V23q_2E0,V24t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V24t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V24t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V23q_2E0,c_2Earithmetic_2E_2B_2E2(V24t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
            & ! [V25t1_2E0: tyop_2Enum_2Enum] :
              ? [V26t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V23q_2E0,c_2Earithmetic_2E_2B_2E2(V25t1_2E0,V26t2_2E0)))
               => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V25t1_2E0,V26t2_2E0))) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V23q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2EWHEN_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V27q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V28t_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V27q_2E0,V28t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V28t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V28t_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V27q_2E0,c_2Earithmetic_2E_2B_2E2(V28t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
            & ! [V29t1_2E0: tyop_2Enum_2Enum] :
              ? [V30t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V27q_2E0,c_2Earithmetic_2E_2B_2E2(V29t1_2E0,V30t2_2E0)))
                | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V29t1_2E0,V30t2_2E0))) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V27q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2ESBEFORE_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V31q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V32t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V31q_2E0,V32t_2E0))
              <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V32t_2E0))
                  & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V32t_2E0))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V31q_2E0,c_2Earithmetic_2E_2B_2E2(V32t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
            & ! [V33t1_2E0: tyop_2Enum_2Enum] :
              ? [V34t2_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V31q_2E0,c_2Earithmetic_2E_2B_2E2(V33t1_2E0,V34t2_2E0)))
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V33t1_2E0,V34t2_2E0)))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V33t1_2E0,V34t2_2E0))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V31q_2E0)) ) )
      & ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,c_2ETemporal__Logic_2EBEFORE_2E2(V2a_2E0,V1b_2E0)))
      <=> ? [V35q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2ET_2E0)
            & ! [V36t_2E0: tyop_2Enum_2Enum] :
                ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V35q_2E0,V36t_2E0))
              <=> ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,V36t_2E0))
                  & ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,V36t_2E0))
                    | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V35q_2E0,c_2Earithmetic_2E_2B_2E2(V36t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
            & ! [V37t1_2E0: tyop_2Enum_2Enum] :
              ? [V38t2_2E0: tyop_2Enum_2Enum] :
                ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V35q_2E0,c_2Earithmetic_2E_2B_2E2(V37t1_2E0,V38t2_2E0)))
               => ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2a_2E0,c_2Earithmetic_2E_2B_2E2(V37t1_2E0,V38t2_2E0)))
                  | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1b_2E0,c_2Earithmetic_2E_2B_2E2(V37t1_2E0,V38t2_2E0))) ) )
            & p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V3Phi_2E0,V35q_2E0)) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__CONJ__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2Psi2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V3Psi1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V4Phi__R2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V5Phi__R1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V6Phi__I2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V7Phi__I1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] :
      ( ( ? [V8q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)] :
            ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,V0t0_2E0)))
            & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V0t0_2E0)))))
            & ? [V10t1_2E0: tyop_2Enum_2Enum] :
              ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b1,V8q1_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V0t0_2E0)))))) )
        & ? [V12q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
            ( p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V12q2_2E0,V0t0_2E0)))
            & ! [V13t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V12q2_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))))
            & ? [V14t1_2E0: tyop_2Enum_2Enum] :
              ! [V15t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,c_2Earithmetic_2E_2B_2E2(V15t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b2,V12q2_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,c_2Earithmetic_2E_2B_2E2(V15t2_2E0,V0t0_2E0)))))) ) )
    <=> ? [V16q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V17q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
          ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V7Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V16q1_2E0,V0t0_2E0)))
          & p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V6Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V17q2_2E0,V0t0_2E0)))
          & ! [V18t_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V5Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V16q1_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)))))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V4Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V17q2_2E0,c_2Earithmetic_2E_2B_2E2(V18t_2E0,V0t0_2E0))))) )
          & ? [V19t1_2E0: tyop_2Enum_2Enum] :
            ! [V20t2_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V3Psi1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b1,V16q1_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0))))))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V2Psi2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b2,V17q2_2E0,c_2Earithmetic_2E_2B_2E2(V19t1_2E0,c_2Earithmetic_2E_2B_2E2(V20t2_2E0,V0t0_2E0)))))) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__DISJ__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3Psi2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V4Psi1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V5Phi__R2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool),V6Phi__R1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool),V7Phi__I2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V8Phi__I1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] :
      ( ( ? [V9q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1)] :
            ( p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V8Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V9q1_2E0,V0t0_2E0)))
            & ! [V10t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V6Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V9q1_2E0,c_2Earithmetic_2E_2B_2E2(V10t_2E0,V0t0_2E0)))))
            & ? [V11t1_2E0: tyop_2Enum_2Enum] :
              ! [V12t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V4Psi1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b1,V9q1_2E0,c_2Earithmetic_2E_2B_2E2(V11t1_2E0,c_2Earithmetic_2E_2B_2E2(V12t2_2E0,V0t0_2E0)))))) )
        | ? [V13q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
            ( p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V7Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V13q2_2E0,V0t0_2E0)))
            & ! [V14t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V5Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V13q2_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))))
            & ? [V15t1_2E0: tyop_2Enum_2Enum] :
              ! [V16t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V3Psi2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b2,V13q2_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0)))))) ) )
    <=> ? [V17p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V18q1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b1),V19q2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b2)] :
          ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,V0t0_2E0))
              & p(app_2E2(A_27b1,tyop_2Emin_2Ebool,V8Phi__I1_2E0,app_2E2(tyop_2Enum_2Enum,A_27b1,V18q1_2E0,V0t0_2E0))) )
            | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,V0t0_2E0))
              & p(app_2E2(A_27b2,tyop_2Emin_2Ebool,V7Phi__I2_2E0,app_2E2(tyop_2Enum_2Enum,A_27b2,V19q2_2E0,V0t0_2E0))) ) )
          & ! [V20t_2E0: tyop_2Enum_2Enum] :
              ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V6Phi__R1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b1,V18q1_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)))))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V5Phi__R2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b2,V19q2_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,V0t0_2E0)))))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V20t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
          & ? [V21t1_2E0: tyop_2Enum_2Enum] :
            ! [V22t2_2E0: tyop_2Enum_2Enum] :
              ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V1t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b1),tyop_2Emin_2Ebool,V4Psi1_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b1,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,c_2Earithmetic_2E_2B_2E2(V22t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b1,V18q1_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,c_2Earithmetic_2E_2B_2E2(V22t2_2E0,V0t0_2E0)))))) )
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V17p_2E0,c_2Earithmetic_2E_2B_2E2(V1t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b2),tyop_2Emin_2Ebool,V3Psi2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b2,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,c_2Earithmetic_2E_2B_2E2(V22t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b2,V19q2_2E0,c_2Earithmetic_2E_2B_2E2(V21t1_2E0,c_2Earithmetic_2E_2B_2E2(V22t2_2E0,V0t0_2E0)))))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__NEXT__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V5Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V5Phi__I_2E0),V4Phi__R_2E0),V1i_2E0),V3Psi_2E0),V6t0_2E0))
        <=> ? [V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V5Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V7q_2E0,V6t0_2E0)))
              & ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V6t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,V6t0_2E0)))))
              & ? [V9t1_2E0: tyop_2Enum_2Enum] :
                ! [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V3Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,c_2Earithmetic_2E_2B_2E2(V10t2_2E0,V6t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,c_2Earithmetic_2E_2B_2E2(V10t2_2E0,V6t0_2E0)))))) ) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2c_2E0: A_27b,V3Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V4Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ENEXT_2E2(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V5Phi__I_2E0),V4Phi__R_2E0),V1i_2E0),V3Psi_2E0),V0t0_2E0))
        <=> ? [V11p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V12q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11p_2E0,V0t0_2E0) = c_2Ebool_2EF_2E0 )
              & ( app_2E2(tyop_2Enum_2Enum,A_27b,V12q_2E0,V0t0_2E0) = V2c_2E0 )
              & ! [V13t_2E0: tyop_2Enum_2Enum] :
                  ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)) = V2c_2E0 )
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V5Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V11p_2E0,c_2Earithmetic_2E_2B_2E2(V13t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
              & ? [V14t1_2E0: tyop_2Enum_2Enum] :
                ! [V15t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V3Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V1i_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,c_2Earithmetic_2E_2B_2E2(V15t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V12q_2E0,c_2Earithmetic_2E_2B_2E2(V14t1_2E0,c_2Earithmetic_2E_2B_2E2(V15t2_2E0,V0t0_2E0)))))) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__SUNTIL__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V13q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V0t0_2E0: tyop_2Enum_2Enum,V3c_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V13q_2E0),V0t0_2E0),V3c_2E0))
        <=> ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,V0t0_2E0) = V3c_2E0 ) )
     => ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
          <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
                ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
                & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
                & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                  ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
       => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2ETemporal__Logic_2ESUNTIL_2E3(V1phi_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V0t0_2E0))
          <=> ? [V12p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
                ( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,V0t0_2E0)),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V13q_2E0),V0t0_2E0),V3c_2E0)))
                & ! [V14t_2E0: tyop_2Enum_2Enum] :
                    ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)) = V3c_2E0 )
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                    | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)) = V3c_2E0 )
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                      & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                    | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
                & ? [V15t1_2E0: tyop_2Enum_2Enum] :
                  ! [V16t2_2E0: tyop_2Enum_2Enum] :
                    ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0)))))) ) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__UNTIL__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V13q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V0t0_2E0: tyop_2Enum_2Enum,V3c_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V13q_2E0),V0t0_2E0),V3c_2E0))
        <=> ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,V0t0_2E0) = V3c_2E0 ) )
     => ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
            ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
          <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
                ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
                & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
                & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                  ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
       => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2ETemporal__Logic_2EUNTIL_2E3(V1phi_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V0t0_2E0))
          <=> ? [V12p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
                ( p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,V0t0_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,V0t0_2E0)),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V13q_2E0),V0t0_2E0),V3c_2E0)))
                & ! [V14t_2E0: tyop_2Enum_2Enum] :
                    ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)) = V3c_2E0 )
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                    | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & ( app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)) = V3c_2E0 )
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                      & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                    | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))
                      & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,V0t0_2E0)))))
                      & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V14t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
                & ? [V15t1_2E0: tyop_2Enum_2Enum] :
                  ! [V16t2_2E0: tyop_2Enum_2Enum] :
                    ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0))))
                    | p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V13q_2E0,c_2Earithmetic_2E_2B_2E2(V15t1_2E0,c_2Earithmetic_2E_2B_2E2(V16t2_2E0,V0t0_2E0)))))) ) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__SBEFORE__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
        <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
              & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
              & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ESBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V1phi_2E0,V0t0_2E0))
        <=> ? [V12p1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13p2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V14q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0) = V3c_2E0 ) )
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0))) ) )
              & ! [V15t_2E0: tyop_2Enum_2Enum] :
                  ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
              & ? [V16t1_2E0: tyop_2Enum_2Enum] :
                ! [V17t2_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))))
                  & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0)))))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__BEFORE__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
        <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
              & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
              & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EBEFORE_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V1phi_2E0,V0t0_2E0))
        <=> ? [V12p1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13p2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V14q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0) = V3c_2E0 ) )
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0))) ) )
              & ! [V15t_2E0: tyop_2Enum_2Enum] :
                  ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
              & ? [V16t1_2E0: tyop_2Enum_2Enum] :
                ! [V17t2_2E0: tyop_2Enum_2Enum] :
                  ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))))
                  | p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0)))))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__SWHEN__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
        <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
              & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
              & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2ESWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V1phi_2E0,V0t0_2E0))
        <=> ? [V12p1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13p2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V14q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0) = V3c_2E0 ) )
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0))) ) )
              & ! [V15t_2E0: tyop_2Enum_2Enum] :
                  ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
              & ? [V16t1_2E0: tyop_2Enum_2Enum] :
                ! [V17t2_2E0: tyop_2Enum_2Enum] :
                  ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))))
                  & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0)))))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ECO__BUECHI__WHEN__CLOSURE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))))] :
      ( ! [V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7t0_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V7t0_2E0))
        <=> ? [V8q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,V7t0_2E0)))
              & ! [V9t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V9t_2E0,V7t0_2E0)))))
              & ? [V10t1_2E0: tyop_2Enum_2Enum] :
                ! [V11t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V8q_2E0,c_2Earithmetic_2E_2B_2E2(V10t1_2E0,c_2Earithmetic_2E_2B_2E2(V11t2_2E0,V7t0_2E0)))))) ) )
     => ! [V0t0_2E0: tyop_2Enum_2Enum,V1phi_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3c_2E0: A_27b,V4Psi_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5Phi__R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V6Phi__I_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2ETemporal__Logic_2EWHEN_2E3(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),F0_2E0,V6Phi__I_2E0),V5Phi__R_2E0),V2i_2E0),V4Psi_2E0),V1phi_2E0,V0t0_2E0))
        <=> ? [V12p1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V13p2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V14q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
              ( ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0) = V3c_2E0 ) )
                | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,V0t0_2E0))
                  & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,V0t0_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,V0t0_2E0))) ) )
              & ! [V15t_2E0: tyop_2Enum_2Enum] :
                  ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = V3c_2E0 ) )
                  | ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ( app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)) = V3c_2E0 )
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1phi_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(A_27b,tyop_2Emin_2Ebool,V6Phi__I_2E0,app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0))))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) )
                  | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))
                    & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V5Phi__R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,V0t0_2E0)))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))
                    & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V13p2_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V0t0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) )
              & ? [V16t1_2E0: tyop_2Enum_2Enum] :
                ! [V17t2_2E0: tyop_2Enum_2Enum] :
                  ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V12p1_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))))
                  | p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V4Psi_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V2i_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0))),app_2E2(tyop_2Enum_2Enum,A_27b,V14q_2E0,c_2Earithmetic_2E_2B_2E2(V16t1_2E0,c_2Earithmetic_2E_2B_2E2(V17t2_2E0,V0t0_2E0)))))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2ENEXT__AS__CO__BUECHI,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))
    <=> ? [V2p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V3q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2p_2E0,V0t0_2E0))
          & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,V0t0_2E0))
          & ! [V4t_2E0: tyop_2Enum_2Enum] :
              ( ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & ~ 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,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0))))
                & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & ~ 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,V1a_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0))))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,V0t0_2E0)))
                & 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,V2p_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0))))
                & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ).

tff(thm_2EOmega__Automata_2ESUNTIL__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ).

tff(thm_2EOmega__Automata_2EUNTIL__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0))))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2ESBEFORE__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ).

tff(thm_2EOmega__Automata_2EBEFORE__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0))))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2ESWHEN__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ).

tff(thm_2EOmega__Automata_2EWHEN__AS__CO__BUECHI,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(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( ~ 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,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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) )
              | ( 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,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V4t_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0t0_2E0)))) ) )
          & ? [V5t1_2E0: tyop_2Enum_2Enum] :
            ! [V6t2_2E0: tyop_2Enum_2Enum] :
              ( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0))))
              | p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3q_2E0,c_2Earithmetic_2E_2B_2E2(V5t1_2E0,c_2Earithmetic_2E_2B_2E2(V6t2_2E0,V0t0_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2EBUECHI__PERIODIC__MODEL,axiom,
    ! [A_27a: $tType,A_27state: $tType,V0TransRel_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool),V1InitState_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool),V2Accept_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool)] :
      ( ! [V3s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
        ? [V4x0_2E0: tyop_2Enum_2Enum,V5l_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V5l_2E0))
          & ( app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,V4x0_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,c_2Earithmetic_2E_2B_2E2(V4x0_2E0,V5l_2E0)) ) )
     => ( ? [V6i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Enum_2E0_2E0)))
            & ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V6i_2E0,V8t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,V8t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))
            & ! [V9t1_2E0: tyop_2Enum_2Enum] :
              ? [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,V10t2_2E0)))) )
      <=> ? [V11x0_2E0: tyop_2Enum_2Enum,V12l_2E0: tyop_2Enum_2Enum,V13j_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V14p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V12l_2E0))
            & ! [V15t2_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V15t2_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,c_2Earithmetic_2EMOD_2E2(V15t2_2E0,V12l_2E0))) )
            & ! [V16t2_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V16t2_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,c_2Earithmetic_2EMOD_2E2(V16t2_2E0,V12l_2E0))) )
            & p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Enum_2E0_2E0)))
            & ! [V17t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,V17t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,V17t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V17t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))
            & ! [V18t1_2E0: tyop_2Enum_2Enum] :
              ? [V19t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V18t1_2E0,V19t2_2E0)))) ) ) ) ).

tff(thm_2EOmega__Automata_2EBUECHI__PERIODIC__REDUCTION__THM,axiom,
    ! [A_27a: $tType,A_27state: $tType,V0TransRel_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool),V1InitState_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool),V2Accept_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool)] :
      ( ! [V3s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
        ? [V4x0_2E0: tyop_2Enum_2Enum,V5l_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V5l_2E0))
          & ( app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,V4x0_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,c_2Earithmetic_2E_2B_2E2(V4x0_2E0,V5l_2E0)) ) )
     => ( ? [V6i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Enum_2E0_2E0)))
            & ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V6i_2E0,V8t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,V8t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))
            & ! [V9t1_2E0: tyop_2Enum_2Enum] :
              ? [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,V10t2_2E0)))) )
      <=> ? [V11x0_2E0: tyop_2Enum_2Enum,V12l_2E0: tyop_2Enum_2Enum,V13j_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V14p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V12l_2E0))
            & ! [V15t2_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V15t2_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,c_2Earithmetic_2EMOD_2E2(V15t2_2E0,V12l_2E0))) )
            & ! [V16t2_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V16t2_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,c_2Earithmetic_2EMOD_2E2(V16t2_2E0,V12l_2E0))) )
            & p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Enum_2E0_2E0)))
            & ! [V17t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V17t_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V12l_2E0)))
               => p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,V17t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,V17t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V17t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
            & ? [V18t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V18t_2E0,V12l_2E0))
                & p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V18t_2E0)))) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EBUECHI__PROP__REDUCTION,axiom,
    ! [A_27a: $tType,A_27state: $tType,V0TransRel_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool),V1InitState_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool),V2Accept_2E0: tyop_2Emin_2Efun(A_27state,tyop_2Emin_2Ebool)] :
      ( ! [V3s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
        ? [V4x0_2E0: tyop_2Enum_2Enum,V5l_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V5l_2E0))
          & ( app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,V4x0_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V3s_2E0,c_2Earithmetic_2E_2B_2E2(V4x0_2E0,V5l_2E0)) ) )
     => ( ? [V6i_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V7q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Enum_2E0_2E0)))
            & ! [V8t_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V6i_2E0,V8t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,V8t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V8t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))
            & ! [V9t1_2E0: tyop_2Enum_2Enum] :
              ? [V10t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V7q_2E0,c_2Earithmetic_2E_2B_2E2(V9t1_2E0,V10t2_2E0)))) )
      <=> ? [V11x0_2E0: tyop_2Enum_2Enum,V12l_2E0: tyop_2Enum_2Enum,V13j_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V14p_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27state)] :
            ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V12l_2E0))
            & p(app_2E2(A_27state,tyop_2Emin_2Ebool,V1InitState_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Enum_2E0_2E0)))
            & ! [V15t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V15t_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V12l_2E0)))
               => p(app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state)),tyop_2Emin_2Ebool,V0TransRel_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(A_27state,A_27state),app_2E2(tyop_2Enum_2Enum,A_27a,V13j_2E0,V15t_2E0),c_2Epair_2E_2C_2E2(A_27state,A_27state,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,V15t_2E0),app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V15t_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))) )
            & ? [V16t_2E0: tyop_2Enum_2Enum] :
                ( p(c_2Eprim__rec_2E_3C_2E2(V16t_2E0,V12l_2E0))
                & p(app_2E2(A_27state,tyop_2Emin_2Ebool,V2Accept_2E0,app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V16t_2E0)))) )
            & ( app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,V11x0_2E0) = app_2E2(tyop_2Enum_2Enum,A_27state,V14p_2E0,c_2Earithmetic_2E_2B_2E2(V11x0_2E0,V12l_2E0)) ) ) ) ) ).

tff(thm_2EOmega__Automata_2EEQUALITY__THM,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
      ( ( V0x_2E0 = V1y_2E0 )
    <=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V0x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1y_2E0) ) ) ).

tff(thm_2EOmega__Automata_2ELESS__THM,axiom,
    ! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0x_2E0,V1y_2E0))
    <=> ? [V2P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V0x_2E0))
          & ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V1y_2E0))
          & ! [V3z_2E0: tyop_2Enum_2Enum] :
              ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,c_2Enum_2ESUC_2E1(V3z_2E0)))
             => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2P_2E0,V3z_2E0)) ) ) ) ).

tff(thm_2EOmega__Automata_2EFORALL__EXISTS__THM,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1t1_2E0: tyop_2Enum_2Enum] :
        ? [V2t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2E_2B_2E2(V1t1_2E0,V2t2_2E0)))
    <=> ! [V3t1_2E0: tyop_2Enum_2Enum] :
        ? [V4t2_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3t1_2E0,V4t2_2E0))
          & p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V4t2_2E0)) ) ) ).

tff(thm_2EOmega__Automata_2EEXISTS__FORALL__THM,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ? [V1t1_2E0: tyop_2Enum_2Enum] :
        ! [V2t2_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2E_2B_2E2(V1t1_2E0,V2t2_2E0)))
    <=> ? [V3t1_2E0: tyop_2Enum_2Enum] :
        ! [V4t2_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V3t1_2E0,V4t2_2E0))
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V4t2_2E0)) ) ) ).

tff(thm_2EOmega__Automata_2EELGOT__LEMMA,axiom,
    ! [A_27a: $tType,V0PHI_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ? [V1x_2E0: A_27a] :
        ! [V2p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V2p_2E0),V1x_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ! [V4x_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V4x_2E0))
             => ! [V5p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V5p_2E0),V4x_2E0)) )
          & ? [V6z_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V6z_2E0)) ) ) ).

tff(thm_2EOmega__Automata_2EELGOT1__THM,axiom,
    ! [A_27a: $tType,V0PHI_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ? [V1x_2E0: A_27a] :
        ! [V2p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V2p_2E0),V1x_2E0))
    <=> ? [V3q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
        ! [V4p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5x_2E0: A_27a] :
        ? [V6z_2E0: A_27a] :
          ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V5x_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V4p_2E0),V5x_2E0)) )
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V6z_2E0)) ) ) ).

tff(thm_2EOmega__Automata_2EELGOT2__THM,axiom,
    ! [A_27a: $tType,V0PHI_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V1x_2E0: A_27a] :
        ? [V2p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V2p_2E0),V1x_2E0))
    <=> ! [V3q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
        ? [V4p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5x_2E0: A_27a] :
        ! [V6z_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V6z_2E0))
         => ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0PHI_2E0,V4p_2E0),V5x_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3q_2E0,V5x_2E0)) ) ) ) ).

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