ITP001 Axioms: ITP044^7.ax


%------------------------------------------------------------------------------
% File     : ITP044^7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : Temporal_Logic.ax [Gau19]
%          : HL4044^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  195 (  85 unt;  34 typ;   0 def)
%            Number of atoms       :  863 ( 151 equ;  56 cnn)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives : 2321 (  56   ~;  28   |; 142   &;1964   @)
%                                         (  77 <=>;  54  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg;1964 nst)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  405 ( 405   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   34 (  32 usr;   5 con; 0-4 aty)
%            Number of variables   :  677 ( 191   ^ 438   !;  42   ?; 677   :)
%                                         (   6  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

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

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: $tType > $tType > $tType ).

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

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: $tType > $tType > $tType ).

thf(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Earithmetic_2E_2B,type,
    c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Epair_2E_2C,type,
    c_2Epair_2E_2C: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).

thf(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(c_2Enum_2E0,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2E_3C,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2E_3C_3D,type,
    c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: 
      !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).

thf(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(c_2Ebool_2E_3F,type,
    c_2Ebool_2E_3F: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2ETemporal__Logic_2EALWAYS,type,
    c_2ETemporal__Logic_2EALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2ETemporal__Logic_2EBEFORE,type,
    c_2ETemporal__Logic_2EBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EBIT1,type,
    c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebool_2ECOND,type,
    c_2Ebool_2ECOND: 
      !>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).

thf(c_2ETemporal__Logic_2EEVENTUAL,type,
    c_2ETemporal__Logic_2EEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Ebool_2EF,type,
    c_2Ebool_2EF: $o ).

thf(c_2ETemporal__Logic_2ENEXT,type,
    c_2ETemporal__Logic_2ENEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2ENUMERAL,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2ETemporal__Logic_2ESBEFORE,type,
    c_2ETemporal__Logic_2ESBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Enum_2ESUC,type,
    c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2ETemporal__Logic_2ESUNTIL,type,
    c_2ETemporal__Logic_2ESUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2ETemporal__Logic_2ESWHEN,type,
    c_2ETemporal__Logic_2ESWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Ebool_2ET,type,
    c_2Ebool_2ET: $o ).

thf(c_2ETemporal__Logic_2EUNTIL,type,
    c_2ETemporal__Logic_2EUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2ETemporal__Logic_2EUPTO,type,
    c_2ETemporal__Logic_2EUPTO: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) ) > $o ).

thf(c_2ETemporal__Logic_2EWATCH,type,
    c_2ETemporal__Logic_2EWATCH: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2ETemporal__Logic_2EWHEN,type,
    c_2ETemporal__Logic_2EWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EZERO,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

thf(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(logicdef_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(logicdef_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(logicdef_2E_7E,axiom,
    ! [V0: $o] :
      ( ( c_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(logicdef_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
      ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
    <=> ( V0 = V1 ) ) ).

thf(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
    <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
    <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(thm_2ETemporal__Logic_2ENEXT,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ V0P )
      = ( ^ [V1t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Enum_2ESUC @ V1t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0P @ V1t0 )
    <=> ! [V2t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V2t @ V1t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0P @ V1t0 )
    <=> ? [V2t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V2t @ V1t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EWATCH,axiom,
    ! [V0q: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EWATCH @ V0q @ V1b @ V2t0 )
    <=> ! [V3t: tyop_2Enum_2Enum] :
          ( ( ( V0q @ V2t0 )
            = c_2Ebool_2EF )
          & ( ( V0q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) ) )
          <=> ( ( V0q @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) )
              | ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUPTO,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1t1: tyop_2Enum_2Enum,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUPTO @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V1t1 @ V2a ) ) )
    <=> ! [V3t2: tyop_2Enum_2Enum] :
          ( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t2 )
            & ( c_2Eprim__rec_2E_3C @ V3t2 @ V1t1 ) )
         => ( V2a @ V3t2 ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              | ( ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
               => ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              | ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              | ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ( ? [V4t: tyop_2Enum_2Enum] :
                ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
                & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
                & ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
            | ! [V5t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V2t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ? [V4t: tyop_2Enum_2Enum] :
              ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
              & ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              & ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              | ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
              | ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
          & ? [V5t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V0a @ V1b @ V2t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
          & ? [V4t: tyop_2Enum_2Enum] :
              ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
              & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
              & ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWATCH__EXISTS,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
    ? [V2q: tyop_2Enum_2Enum > $o] : ( c_2ETemporal__Logic_2EWATCH @ V2q @ V0b @ V1t0 ) ).

thf(thm_2ETemporal__Logic_2EWELL__ORDER,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o] :
      ( ? [V1n: tyop_2Enum_2Enum] : ( V0P @ V1n )
    <=> ? [V2m: tyop_2Enum_2Enum] :
          ( ( V0P @ V2m )
          & ! [V3n: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V3n @ V2m )
             => ( (~) @ ( V0P @ V3n ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE,axiom,
    ! [V0m2: tyop_2Enum_2Enum,V1m1: tyop_2Enum_2Enum,V2P: tyop_2Enum_2Enum > $o] :
      ( ( ( V2P @ V1m1 )
        & ! [V3n: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ V3n @ V1m1 )
           => ( (~) @ ( V2P @ V3n ) ) )
        & ( V2P @ V0m2 )
        & ! [V4n: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ V4n @ V0m2 )
           => ( (~) @ ( V2P @ V4n ) ) ) )
     => ( V1m1 = V0m2 ) ) ).

thf(thm_2ETemporal__Logic_2EDELTA__CASES,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
      ( ? [V2d: tyop_2Enum_2Enum] :
          ( ! [V3t: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V3t @ V2d )
             => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) ) )
          & ( V1b @ ( c_2Earithmetic_2E_2B @ V2d @ V0t0 ) ) )
      | ! [V4d: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4d @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
              | ( ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
               => ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
              | ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
              | ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ( ? [V4t: tyop_2Enum_2Enum] :
                ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                & ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
            | ! [V5t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ? [V4t: tyop_2Enum_2Enum] :
              ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
              & ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
              & ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ( ! [V4t: tyop_2Enum_2Enum] :
                ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                | ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                | ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
            & ? [V5t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__IMP,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
    <=> ! [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
         => ? [V4t: tyop_2Enum_2Enum] :
              ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
              & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
              & ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
    <=> ! [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 )
    <=> ? [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EWATCH__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1q: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b @ V0t0 )
    <=> ( ( ! [V3t: tyop_2Enum_2Enum] : ( (~) @ ( V2b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
         => ! [V4t: tyop_2Enum_2Enum] : ( (~) @ ( V1q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
        & ! [V5d: tyop_2Enum_2Enum] :
            ( ( ( V2b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
              & ! [V6t: tyop_2Enum_2Enum] :
                  ( ( c_2Eprim__rec_2E_3C @ V6t @ V5d )
                 => ( (~) @ ( V2b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) )
           => ( ! [V7t: tyop_2Enum_2Enum] :
                  ( ( c_2Earithmetic_2E_3C_3D @ V7t @ V5d )
                 => ( (~) @ ( V1q @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
              & ! [V8t: tyop_2Enum_2Enum] : ( V1q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
    <=> ! [V3delta: tyop_2Enum_2Enum] :
          ( ( ! [V4t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
               => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
            & ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) )
         => ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
    <=> ( ( ! [V3t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
         => ! [V4t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
        & ! [V5d: tyop_2Enum_2Enum] :
            ( ( ! [V6t: tyop_2Enum_2Enum] :
                  ( ( c_2Eprim__rec_2E_3C @ V6t @ V5d )
                 => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) )
              & ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
           => ! [V7t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ V7t @ V5d )
               => ( V2a @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ! [V3delta: tyop_2Enum_2Enum] :
          ( ( ! [V4t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
               => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
            & ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) )
         => ? [V5t: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V5t @ V3delta )
              & ( V2a @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ! [V4t: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
             => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
          & ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) )
          & ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ! [V4t: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
             => ( ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) )
          & ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__SIGNAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
    <=> ? [V3delta: tyop_2Enum_2Enum] :
          ( ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( c_2Earithmetic_2E_3C_3D @ V4t @ V3delta )
             => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ENEXT__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ V1a @ V0t0 )
    <=> ? [V2t1: tyop_2Enum_2Enum] :
          ( ( c_2Eprim__rec_2E_3C @ V0t0 @ V2t1 )
          & ! [V3t3: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ V0t0 @ V3t3 )
             => ( c_2Earithmetic_2E_3C_3D @ V2t1 @ V3t3 ) )
          & ( V1a @ V2t1 ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
    <=> ! [V2t1: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V2t1 )
         => ( V1a @ V2t1 ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 )
    <=> ? [V2t1: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V2t1 )
          & ( V1a @ V2t1 ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
    <=> ? [V3t1: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
          & ( V1b @ V3t1 )
          & ( c_2ETemporal__Logic_2EUPTO @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1 @ V2a ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
    <=> ! [V3t1: tyop_2Enum_2Enum] :
          ( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
            & ( (~) @ ( V1b @ V3t1 ) )
            & ( c_2ETemporal__Logic_2EUPTO
              @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
                @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
                  @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) )
         => ( V2a @ V3t1 ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
    <=> ? [V3t1: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
          & ( V2a @ V3t1 )
          & ( (~) @ ( V1b @ V3t1 ) )
          & ( c_2ETemporal__Logic_2EUPTO
            @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
              @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ! [V3t1: tyop_2Enum_2Enum] :
          ( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
            & ( c_2ETemporal__Logic_2EUPTO
              @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
                @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
                  @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) ) ) ) ) )
         => ( (~) @ ( V1b @ V3t1 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
    <=> ? [V3t1: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
          & ( V2a @ V3t1 )
          & ( V1b @ V3t1 )
          & ( c_2ETemporal__Logic_2EUPTO
            @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
              @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
                @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__LINORD,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
    <=> ! [V3t1: tyop_2Enum_2Enum] :
          ( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
            & ( V1b @ V3t1 )
            & ( c_2ETemporal__Logic_2EUPTO
              @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
                @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
                  @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) )
         => ( V2a @ V3t1 ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__WHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
      = ( c_2ETemporal__Logic_2EWHEN
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__WHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
      = ( ^ [V1t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EWHEN
              @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V0a
              @ V1t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__AS__WHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EWHEN @ V0b
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V2t ) @ ( V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EWHEN
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__WHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__NOT__WHEN,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
    <=> ( (~)
        @ ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
          @ V1b
          @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__AS__WHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2ETemporal__Logic_2EWHEN @ V0b
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
              @ V2t )
            @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__AS__WHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2ETemporal__Logic_2EWHEN
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
              @ V2t0 )
            @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ V1a
              @ V2t )
            @ ( c_2ETemporal__Logic_2EWHEN
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
              @ V1a
              @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__HW,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ? [V3q: tyop_2Enum_2Enum > $o] :
          ( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V2a @ V0t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
              | ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__UNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
      = ( c_2ETemporal__Logic_2EUNTIL @ V0a
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__UNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
      = ( ^ [V1t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V2t ) )
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V1t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EUNTIL
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EUNTIL
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ V0b
                @ V2t0 ) )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
              @ V2t )
            @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__AS__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__AS__UNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EUNTIL
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
              @ V0b
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0b )
      = ( c_2ETemporal__Logic_2EBEFORE
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0b )
      = ( ^ [V1t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EBEFORE
              @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V0b
              @ V1t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE @ V0b
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
                @ V2t0 ) )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2EBEFORE
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ V0b
                @ V2t0 ) )
            @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EBEFORE @ V0b
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2EBEFORE
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
              @ V0b
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__AS__BEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__SWHEN__LEMMA,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( c_2Ebool_2ECOND @ $o
      @ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
        @ ^ [V2t1: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
            @ ^ [V3t2: tyop_2Enum_2Enum] : ( V0b @ ( c_2Earithmetic_2E_2B @ V3t2 @ V2t1 ) ) ) )
      @ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
        @ ^ [V4t0: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ V4t0 ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ V4t0 ) ) )
      @ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
        @ ^ [V5t1: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
            @ ^ [V6t2: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ ( c_2Earithmetic_2E_2B @ V6t2 @ V5t1 ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ ( c_2Earithmetic_2E_2B @ V6t2 @ V5t1 ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__SWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
      = ( ^ [V1t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESWHEN
              @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V3t ) )
              @ V1t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SWHEN,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
      = ( c_2ETemporal__Logic_2ESWHEN
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2ET
        @ V0a ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ V2t )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__NOT__SWHEN,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
    <=> ( (~)
        @ ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
          @ V1b
          @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__AS__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2ETemporal__Logic_2ESWHEN @ V0b
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
              @ V2t )
            @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2ETemporal__Logic_2ESWHEN
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
              @ V2t0 )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V5t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__NOT__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESWHEN @ V0b
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__AS__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESWHEN @ V0b
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V2t ) @ ( V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__AS__SWHEN,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESWHEN
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__SUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
      = ( ^ [V1t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2ET
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V3t ) )
              @ V1t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SUNTIL,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
      = ( c_2ETemporal__Logic_2ESUNTIL
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2ET
        @ V0a ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__SUNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
              @ V2t )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) )
              @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__AS__SUNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b @ V2t ) @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__SUNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESUNTIL
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
              @ V0b
              @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__SUNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESUNTIL
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__AS__SUNTIL,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESUNTIL
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ V0b
                @ V2t0 ) )
            @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0b )
      = ( ^ [V1t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESBEFORE
              @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
              @ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
              @ V1t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0b )
      = ( c_2ETemporal__Logic_2ESBEFORE @ V0b
        @ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F
            @ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V3t ) ) @ ( V0b @ V3t ) )
              @ V2t0 )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_7E
            @ ( c_2ETemporal__Logic_2ESBEFORE
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
              @ V0b
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESBEFORE @ V0b
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) @ ( V0b @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_2F_5C
            @ ( c_2Ebool_2E_7E
              @ ( c_2ETemporal__Logic_2ESBEFORE
                @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
                @ V0b
                @ V2t0 ) )
            @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__AS__SBEFORE,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( ^ [V2t0: tyop_2Enum_2Enum] :
            ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b @ V2t0 )
            @ ( c_2ETemporal__Logic_2EALWAYS
              @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
              @ V2t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a
          @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a
          @ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) )
      & ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V1a )
        = ( ^ [V10t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( V0b @ V3t ) ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
          @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
          @ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V1a )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
          @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
          @ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V1a )
        = ( c_2ETemporal__Logic_2EALWAYS
          @ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
          @ ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
          @ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V8t: tyop_2Enum_2Enum] : ( V1a @ V8t ) ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V1a )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( V0b @ V3t ) ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
          @ ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
          @ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V1a )
        = ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__SIMP,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
          @ V0b )
        = ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
          @ V0b )
        = ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
          @ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
        = ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
          @ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
        = ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V1a )
        = ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EWHEN
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EUNTIL
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EBEFORE
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESWHEN
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESUNTIL
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESBEFORE
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
        @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2EIMMEDIATE__EVENT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
      ( ( V1b @ V0t0 )
     => ( ! [V2a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
            = ( V2a @ V0t0 ) )
        & ! [V3a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EUNTIL @ V3a @ V1b @ V0t0 )
            = c_2Ebool_2ET )
        & ! [V4a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EBEFORE @ V4a @ V1b @ V0t0 )
            = c_2Ebool_2EF )
        & ! [V5a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESWHEN @ V5a @ V1b @ V0t0 )
            = ( V5a @ V0t0 ) )
        & ! [V6a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESUNTIL @ V6a @ V1b @ V0t0 )
            = c_2Ebool_2ET )
        & ! [V7a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESBEFORE @ V7a @ V1b @ V0t0 )
            = c_2Ebool_2EF ) ) ) ).

thf(thm_2ETemporal__Logic_2ENO__EVENT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V2t ) )
        @ V0t0 )
     => ( ! [V3a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EWHEN @ V3a @ V1b @ V0t0 )
            = c_2Ebool_2ET )
        & ! [V4a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EUNTIL @ V4a @ V1b @ V0t0 )
            = ( c_2ETemporal__Logic_2EALWAYS @ V4a @ V0t0 ) )
        & ! [V5a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EBEFORE @ V5a @ V1b @ V0t0 )
            = c_2Ebool_2ET )
        & ! [V6a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESWHEN @ V6a @ V1b @ V0t0 )
            = c_2Ebool_2EF )
        & ! [V7a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESUNTIL @ V7a @ V1b @ V0t0 )
            = c_2Ebool_2EF )
        & ! [V8a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2ESBEFORE @ V8a @ V1b @ V0t0 )
            = ( c_2ETemporal__Logic_2EEVENTUAL @ V8a @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESOME__EVENT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
      <=> ! [V2a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
            = ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
      <=> ! [V3a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EUNTIL @ V3a @ V1b @ V0t0 )
            = ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1b @ V0t0 ) ) )
      & ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
      <=> ! [V4a: tyop_2Enum_2Enum > $o] :
            ( ( c_2ETemporal__Logic_2EBEFORE @ V4a @ V1b @ V0t0 )
            = ( c_2ETemporal__Logic_2ESBEFORE @ V4a @ V1b @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EMORE__EVENT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2EWHEN
          @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
          @ V0b ) )
      & ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2EUNTIL
          @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) )
          @ V0b ) )
      & ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2EBEFORE
          @ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V4t ) ) )
          @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2ESWHEN
          @ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V5t ) @ ( V0b @ V5t ) )
          @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2ESUNTIL
          @ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V6t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V6t ) ) )
          @ V0b ) )
      & ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
        = ( c_2ETemporal__Logic_2ESBEFORE
          @ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V7t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V7t ) ) )
          @ V0b ) ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__NEXT,axiom,
    ! [V0P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT
        @ ^ [V1t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0P @ V1t ) ) )
      = ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0P @ V2t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EAND__NEXT,axiom,
    ! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
      = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EOR__NEXT,axiom,
    ! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
      = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EIMP__NEXT,axiom,
    ! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
      = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEQUIV__NEXT,axiom,
    ! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
      = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V0a ) )
      = ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
      = ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__NEXT,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V0a @ V1b ) )
      = ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V1P @ V0t0 )
    <=> ( ( V1P @ V0t0 )
        & ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1P ) @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1P: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1P @ V0t0 )
    <=> ( ( V1P @ V0t0 )
        | ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1P ) @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EWATCH__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1q: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b @ V0t0 )
    <=> ( ( (~) @ ( V1q @ V0t0 ) )
        & ( c_2Ebool_2ECOND @ $o @ ( V2b @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1q ) @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b ) @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
      = ( c_2Ebool_2ECOND @ $o @ ( V1b @ V0t0 ) @ ( V2a @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
    <=> ( ( (~) @ ( V1b @ V0t0 ) )
       => ( ( V2a @ V0t0 )
          & ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ( ( (~) @ ( V1b @ V0t0 ) )
        & ( ( V2a @ V0t0 )
          | ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
      = ( c_2Ebool_2ECOND @ $o @ ( V1b @ V0t0 ) @ ( V2a @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) @ V0t0 ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
    <=> ( ( (~) @ ( V1b @ V0t0 ) )
       => ( ( V2a @ V0t0 )
          & ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__REC,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
    <=> ( ( (~) @ ( V1b @ V0t0 ) )
        & ( ( V2a @ V0t0 )
          | ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) @ V0t0 ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__FIX,axiom,
    ! [V0y: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( V0y
        = ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V2t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    <=> ( ( V0y
          = ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
        | ( V0y
          = ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__FIX,axiom,
    ! [V0y: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( V0y
        = ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V2t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V2t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    <=> ( ( V0y
          = ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
        | ( V0y
          = ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__FIX,axiom,
    ! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( V0y
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V1b @ V3t ) @ ( V2a @ V3t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
    <=> ( ( V0y
          = ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
        | ( V0y
          = ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__FIX,axiom,
    ! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( V0y
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V1b @ V3t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    <=> ( ( V0y
          = ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
        | ( V0y
          = ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__FIX,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o,V2y: tyop_2Enum_2Enum > $o] :
      ( ( V2y
        = ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V2y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
    <=> ( ( V2y
          = ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
        | ( V2y
          = ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
    <=> ? [V3J: tyop_2Enum_2Enum > $o] :
          ( ( V3J @ V0t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                & ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
             => ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
          & ! [V5d: tyop_2Enum_2Enum] :
              ( ( ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
                & ( V3J @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
             => ( V2a @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__INVARIANT,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b @ V2t0 )
    <=> ? [V3J: tyop_2Enum_2Enum > $o] :
          ( ( V3J @ V2t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
                & ( (~) @ ( V0b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) )
             => ( ( V1a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
                & ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
    <=> ? [V3J: tyop_2Enum_2Enum > $o] :
          ( ( V3J @ V0t0 )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                & ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
             => ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
          & ! [V5d: tyop_2Enum_2Enum] :
              ( ( V3J @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
             => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
    <=> ? [V2J: tyop_2Enum_2Enum > $o] :
          ( ( V2J @ V0t0 )
          & ! [V3t: tyop_2Enum_2Enum] :
              ( ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) )
             => ( ( V1a @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) )
                & ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
    <=> ? [V2J: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
          ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V2J @ V0t0 ) )
          & ! [V3t: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) ) @ ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
              | ( ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
                = c_2Enum_2E0 ) )
          & ! [V4t: tyop_2Enum_2Enum] :
              ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V2J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                & ( ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                  = c_2Enum_2E0 ) )
             => ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
    <=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
            ( ( V3J1 @ V0t0 )
            & ! [V4t: tyop_2Enum_2Enum] :
                ( ( ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
                  & ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
               => ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
            & ! [V5d: tyop_2Enum_2Enum] :
                ( ( ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
                  & ( V3J1 @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
               => ( V2a @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) )
        & ? [V6J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ V0t0 ) )
            & ! [V7t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                | ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                  = c_2Enum_2E0 ) )
            & ! [V8t: tyop_2Enum_2Enum] :
                ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
                  & ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
                    = c_2Enum_2E0 ) )
               => ( V1b @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
    <=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
            ( ( V3J1 @ V0t0 )
            & ! [V4t: tyop_2Enum_2Enum] :
                ( ( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                  & ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
               => ( ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                  & ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) )
        & ? [V5J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V5J2 @ V0t0 ) )
            & ! [V6t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) @ ( V5J2 @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
                | ( ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
                  = c_2Enum_2E0 ) )
            & ! [V7t: tyop_2Enum_2Enum] :
                ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V5J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                  & ( ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                    = c_2Enum_2E0 ) )
               => ( V1b @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__INVARIANT,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
    <=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
            ( ( V3J1 @ V0t0 )
            & ! [V4t: tyop_2Enum_2Enum] :
                ( ( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
                  & ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
               => ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
            & ! [V5d: tyop_2Enum_2Enum] :
                ( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
               => ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) )
        & ? [V6J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ V0t0 ) )
            & ! [V7t: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                | ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
                  = c_2Enum_2E0 ) )
            & ! [V8t: tyop_2Enum_2Enum] :
                ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
                  & ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
                    = c_2Enum_2E0 ) )
               => ( V2a @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) ) ) ) ).

thf(thm_2ETemporal__Logic_2EALWAYS__IDEM,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
      = ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2EALWAYS @ V0a ) ) ) ).

thf(thm_2ETemporal__Logic_2EEVENTUAL__IDEM,axiom,
    ! [V0a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
      = ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) ) ).

thf(thm_2ETemporal__Logic_2EWHEN__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2EUNTIL__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2EBEFORE__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESWHEN__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESUNTIL__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ESBEFORE__IDEM,axiom,
    ! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
      ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
      = ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) @ V0b ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__ALWAYS,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2EEVENTUAL
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) )
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__EVENTUAL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2EALWAYS
        @ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) )
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__WHEN,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2ESWHEN
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__UNTIL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2ESBEFORE
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__BEFORE,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2ESUNTIL
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__SWHEN,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2EWHEN
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__SUNTIL,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2EBEFORE
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

thf(thm_2ETemporal__Logic_2ENOT__SBEFORE,axiom,
    ! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
      ( ( (~) @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 ) )
    <=> ( c_2ETemporal__Logic_2EUNTIL
        @ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
        @ V1b
        @ V0t0 ) ) ).

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